Symposium DS03—Combining Machine Learning with Simulations for Materials Modeling

Nature produces a variety of materials with many functions, often out of simple and abundant materials, and at low energy. Such systems - examples of which include silk, tendon, bone, nacre or diatoms - provide broad inspiration for engineering. Here we explore the translation of biological composites to engineering applications, using a variety of tools including molecular modeling, AI and machine learning, and experimental synthesis and characterization. We review a series of studies focused on the mechanical behavior of materials, especially deformation and fracture, and how these phenomena can be modeled using a combination of molecular dynamics and machine learning, to generate a novel simulated evolutionary process that offers directed adaptation of biomaterial properties. We also present case studies of protein material optimization using genetic algorithms, applied to 3D printed composites, molecular design, and a translation of protein folding to music and back. We also review a close integration of music and materials, and review our recent research on a new bio-inspired compositional technique called materiomusic.

Inorganic crystalline materials with a magnetic ground state are of interest in various applications such as spintronics, memristors, and data-storage. Even when magnetism is not the key property of interest, studying magnetic materials with Density Functional Theory requires spin-polarized calculations to find the ground state structure and energy. However, computational exploration of magnetic materials is challenging due to the complexity of their electronic and magnetic states. In particular, calculating the ground state of a magnetic material requires careful initialization because spin-polarized DFT calculations are prone to getting trapped in local minima. Previous efforts to resolve this challenge have included high-throughput workflows wherein many possible magnetic orderings are enumerated and calculated. However, this workflow is computationally intensive and requires many spin-polarized DFT optimizations to correctly identify the magnetic ground state of a single material. In this work we present a graph convolutional neural network for predicting per-atom magnetic moment magnitudes given crystal structure. This model is trained on ~ 30,000 magnetic transition metal oxides retrieved from the Materials Project and in-house calculations, and is able to estimate per-atom magnetic moment within an MAE of 0.33 bohr magnetons. We see significant speed-ups for spin-polarized DFT calculations initialized with per-atom magnetic moments predicted by our model. Finally, we extend our model to predict collinear magnetic orderings by attaching a +/- classification to each atom. After training this extended model on the transition metal oxides that have been analyzed through a magnetic ordering workflow, we are able to predict the magnitude and sign of the magnetic moment on each atom with high accuracy and thus significantly decrease the number of calculations required to find the ordered magnetic ground state. We anticipate the use of our model to screen materials for interesting magnetic behavior and for the inverse design of novel materials with desired magnetic properties. We also propose the generalization of the presented model to predict other per-site properties—such as band structures and Bader charges—thus enabling fine-tuned exploration and design in varied materials problems.

The development of accurate and efficient molecular dynamics force fields are a crucial step in an overall materials discovery workflow that complements experiments with theoretical simulations. In order to facilitate the ongoing development of automated machine-learned force fields using tools like FLARE++ and Nequip, we have generated a benchmarking dataset of molten single-element bulk structures with a vacancy defect in order to study the interplay between many body behavior and model performance. This dataset contains ab initio molecular dynamics simulations capturing high-temperature crystalline and melted phases. We attempt to explain the difference in model performance across implementation, levels of descriptor fidelity, and individual systems based on differences in elemental properties, and using interpretable machine learning models, reveal the interplay between elemental properties and many-body character revealed by these differences in performance.

As machine learning (ML) workflows become more prevalent and computationally demanding in materials science, there is an emerging need to integrate deep domain expertise with efficient high-performance computing and appropriate ML methods. In cases where design goals require explorations of vast areas of chemical/material space, or target properties are prohibitively expensive to compute, efficient use of resources and careful choice of method enable previously inaccessible capabilities for material design. Here, we explore interactive supercomputing for applying ML to challenges in materials and chemistry. We discuss the scaling of ML methods for materials and molecular design, with respect to supercomputing resources and dataset size. We present two workflows for high-throughput virtual screening (HTVS) and ML to engineer quantum states in layered materials. An approach based on deep transfer learning, machine learning, and first-principles calculations is shown to rapidly predict key properties of point defects in 2D materials. Properties including band gap and bulk formation energy are predicted for over 4,000 2D materials using deep transfer learning. 10,000 dopant, vacancy, divacancy, and antisite defect structures are generated in 150 wide band-gap materials and more than 1,000 defect band structures are computed via first-principles methods. We identify over 100 promising, unexplored dopant defect structures in layered metal chalcogenides, hexagonal nitrides, and metal halides including GeS, h-AlN, and MgI₂. The hybrid HTVS/ML approach is also used to discover 18 transition metal oxide materials with coexisting magnetic and topological quantum orders.

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This material is based upon work supported by the Under Secretary of Defense for Research and Engineering under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Under Secretary of Defense for Research and Engineering.

The enhanced properties of composite materials are exploited in many fields, from aerospace to electronics industries, from automotive to biomedical applications. Furthermore, smart properties (i.e. material responses influenced by external stimuli) of composites are highly desirable to design next-generation devices in a broad variety of industries. Composites are typically made of polymeric matrices reinforced with macroscopic fillers, e.g. carbon or glass fibers. Recently, nanostructured fillers have been also employed to further improve the effective and smart properties of composites. Carbon nanostructures such as graphene or carbon nanotubes are particularly suitable for that, since they show superior thermal, mechanical and electrical properties. Nevertheless, the properties of nanocomposites are determined by phenomena spanning from the nano to the macro scale and, thus, should be simulated by tailored multi-scale modelling techniques.

In this presentation, hybrid multi-scale and data-driven models to predict the properties of polymer nanocomposites reinforced with carbon nanofillers are presented and experimentally validated. Firstly, the coarse-grained interaction potentials describing some thermoset and thermoplastic polymer matrices obtained from atomistic simulations are compared between each other, to define the mesoscopic configuration more suitable to mimic the thermal-physical properties measured experimentally. Secondly, carbon nanofillers with high thermal, mechanical, and electrical properties are coarse-grained as well, and then introduced in a representative volume element of the nanocomposite to be simulated. Thirdly, sensitivity analyses are carried out by means of the coarser mesoscopic model, to identify the geometrical and physical-chemical features influencing more the thermomechanical response of the considered nanocomposites. Results are compared against both experiment and continuum simulations, to validate the proposed approach and highlight its advantages with respect to consolidated modelling strategies. Finally, data-driven algorithms based on machine learning are employed to improve the prediction capability of the multi-scale model, in order to account for the nonlinear effects in the heat transfer processes. In perspective, such hybrid data- and physics-driven methods should allow to investigate also other properties of nanocomposites, for instance electromagnetic ones.

This work has received funding from the European Union’s Horizon 2020 research and innovation program SMARTFAN under grant agreement N. 760779.

Machine learning (ML) has begun to accelerate materials discovery by providing advances in efficiency needed to overcome the combinatorial challenge of computational materials design. In ML-assisted materials discovery, an automated quantum chemistry (QC) calculation workflow is used to generate datasets to train surrogate models, which serve as alternatives to rapidly explore a large space to identify candidate materials. However, current workflows with density functional theory (DFT) as workhorse leads to many attempted calculations that are doomed to fail and brings biases/inaccuracy to the training data that may be out of the domain of applicability of DFT. This includes many compelling functional materials and catalytic processes that are difficult because of their complex electronic structure, such as systems involving strained chemical bonds, open-shell radicals and diradicals, or metal-organic bonds to open-shell transition-metal centers. We address these challenges of computation efficiency and accuracy by integrating ML approaches into conventional DFT-based QC workflows.

More than half of the computational resource and time is wasted on unfruitful geometry optimizations during the transitional metal complex (TMC) design. To address this issue, we built two types of classifiers to predict the likelihood of calculation success: 1. static model prior to calculations and 2. dynamic model on-the-fly monitoring calculations. The static classifier is a near zero-cost model that rapidly filters out candidate calculations most likely to fail, while the dynamic model monitors and terminates an already running calculation if it is predicted to fail with high confidence. The prediction of the dynamic classifier is interpretable and helps reveal the failure modes in geometry optimizations. Together, these classifiers save half of the computation resources. We have also demonstrated the usefulness of these classifiers on the active learning discovery of candidate catalysts for small alkane activation.

Many interesting functional materials may have complex electronic structures difficult for DFT. We developed multiple types of classifiers to predict the presence of strong correlation, which is usually a sign of a system being out of the domain of applicability of DFT. Our models only require calculations at DFT cost and can classify which systems in a dataset will require more expensive but accurate wavefunction theory calculations, leading to overall high fidelity of the entire dataset. These models far outperform the existing unsupervised learning (i.e., clustering) methods and conventional cutoff-based approach widely used in the chemistry community in distinguishing systems that contain strong MR character. In addition, since electronic structure information is encoded as the inputs, our models are readily transferable to larger systems and systems with unseen elements. All these classifier models represent the first efforts toward autonomous workflows that move past the need for expert determination of the robustness of DFT-based materials discoveries.

Metal-organic frameworks (MOF) hold great promise in applications on gas adsorption, catalysis, and supercapacitors because of their porous structure and modularity. Despite having a symmetrical and apparently well-organized structure formed by metal clusters connected via organic linkers, these materials have low thermal, mechanical, and chemical stability, yielding a high defect density and disorder. To overcome the stability problem, a zirconium-based MOF called UiO-66 was presented as a solution due to its high connectivity with 12 connected clusters in the face-centered-cubic topology. However, a better understanding of the nature of defects and disorder in UiO-66 MOFs is still required.

Inelastic Neutron Scattering (INS) has been proven to be a good ally in the investigation of structural and dynamic disorder but it requires detailed modeling of the system in order to characterize peak positions and intensities, and subsequently materials properties. The high computational cost of the electronic modeling has limited investigations with INS to crystalline materials, dampening the study of disordered large systems such as MOFs.

To address the trade-off between simulation cost and accuracy, we developed an automated workflow that connects various atomic simulation tools in order to investigate the relationship between material properties, lattice dynamics, and INS spectra. This workflow allows an accurate and efficient method of calculating phonon modes and the INS spectrum with the use of a broad range of quantum mechanical approximations, including density functional theory (DFT) and density functional tight-binding (DFTB). We have also implemented a machine-learned force field based on Chebyshev polynomials (Chebyshev Interaction Model for Efficient Simulation - ChIMES) to improve the accuracy of the DFTB simulations with ~100x reduction in computational expense while retaining most of the accuracy of DFT. Besides the benefits of a tool that automates the simulation and consequent analysis of the INS spectrum, our efforts expand the possibilities of investigating more complex structures that would be unfeasible with ab initio methods.

Fire has fascinated humankind since the prehistoric era and, according to different traditions, was selected as one of the four main elements that “make of all things in Nature”. Science and art have both used fire as a tool and inspiration over the years. From a scientific-technological standpoint, fire is one of the fundamental agents to enable chemical reactions, and its controlled dynamics have been widely studied to optimize and control combustion processes. Another field of interest concerns fire detection and monitoring for safety purposes since an efficient control of fire since its activation has a huge impact not only on people and animal protection but also on environmental sustainability.
As for visual and music arts, fire has been used as a tool and inspiration for creating paintings but, more interestingly, has inspired composers to create melodies able to evoke its power and perpetual shape mutation without using the audible dull sounds emitted from the interaction with air.

Rooted in the interactions between sound and flames, here we report a new method to use fire for a variety of purposes, including sonification, art, and the design and manufacturing of nature-inspired materials. At the root of the work is a new method to sonify fire, thereby offering a translation from the silent nature of flames, to represent audible information, and to generate de novo flame images.

We use a simple setup composed of a flame from a candle whose deformation, due to an acoustic source, is recorded through a digital camera. We used the tones from an octave to create a direct mapping between the deformations of the flame and pure sounds. To encode and decode images of the flames exposed to different frequencies, we used a convolutional variational autoencoder trained on a set of 1,300 unlabeled images (100 images for each audible condition), and uses a 2-dimensional latent space vector.

This tool provides a new interactive musical instrument, which from the observation of a flame, or interaction of it with the environment – such as wind or temperature fluctuations, or different environmental gases – will result in flame shape and dynamics changes, which in turn is associated with particular sounds.

Additionally, we are able to generate de novo images by applying the trained deep neural network model to augment images, thus creating a deep inceptionism of fire, and use a deep convolutional variational autoencoder to realize synthetic flame shapes, including temporal sequences that resemble flickering flames.
From the materials science standpoint, we realize new materials inspired by fire by using autoencoder to generate image stacks to yield 3D geometries that are manufactured using 3D printing. This represents the first even generation of nature-inspired materials from fire, and can be a platform to be used for other natural phenomena in the quest for de novo architectures, geometries, and design ideas. These concepts provide a new dimension of nature-inspired design, as it yields novel image data that can be manipulated, or associated with, other forms of expression, and creates new directions in artistic and scientific research through the creative manipulation of data with structural similarities across fields. This work also underscores the fundamental importance of vibrations as a translational means to find semblances of structures across manifestations, from the invisible, to the visible, to material form.

Semiconductors with desirable electronic band structure and optical absorption are sought for solar cells, electronic devices, infrared sensors and quantum computing. Compositional manipulation via alloying at cation or anion sites, or via incorporation of point defects and impurities, can help tune the properties of semiconductors in known chemical spaces. In this work, we develop AI-based frameworks for the on-demand prediction and multi-objective optimization of the phase stability, band gap, optical absorption spectra, photovoltaic efficiency, dielectric constant, defect formation energies, and impurity energy levels in two broad classes of semiconductors, namely (a) halide perovskites with the general formula ABX₃ (where A is a large organic or inorganic monovalent cation, B is a divalent cation and X is a halogen anion), and (b) group IV, III-V and II-VI semiconductors in binary, ternary and quaternary forms. These frameworks are powered by high-throughput density functional theory (DFT) computations, unique encoding of the atom-composition-structure information, and rigorous training of advanced neural network-based predictive and optimization models.

Bayesian optimization-based active learning approaches are applied to systematically improve prediction accuracies and comprehensively traverse the compositional chemical space. Multi-fidelity learning helps to bridge the gap between (high quantities of) low accuracy calculations and (lower quantities of) high-fidelity data, constituted of either accurate, expensive computations or experimental measurements collected from the published literature. High-accuracy predictions based on modest datasets are thus accomplished for (a) band gaps and formation energies at the HSE06 level of theory utilizing PBE-level data, (b) defect and impurity energy levels with experimental accuracy utilizing PBE-level data, (c) large supercell properties utilizing smaller cell calculations, and (d) properties of all alloy compositions utilizing data from end-point and selected mixed compositions. The best predictive models are combined with two different multi-objective optimization techniques, namely, state-of-the-art genetic algorithms and variational autoencoders, to determine optimal semiconductor atom-composition-structure combinations with desired stability, optoelectronic, and defect properties. Finally, AI-based recommendations are synergistically coupled with targeted synthesis and characterization, leading to successful validation and discovery of novel compositions for improved performance in solar cells.

References
1. A. Mannodi-Kanakkithodi, J. S. Park, N. Jeon, D. H. Cao, D. J. Gosztola, A. B. F. Martinson, M. K. Y. Chan, "Comprehensive Computational Study of Partial Lead Substitution in Methylammonium Lead Bromide", Chemistry of Materials 31 (10), 3599–3612 (2019).
2. A. Mannodi-Kanakkithodi, M. Toriyama, F. G. Sen, M. Davis, R. F. Klie, M. K. Y. Chan, "Machine learned impurity level prediction in semiconductors: the example of Cd-based chalcogenides", npj Computational Materials 6, 39 (2020).
3. A. Mannodi-Kanakkithodi, M. K. Y. Chan, "Computational Data-Driven Materials Discovery", Trends in Chemistry 3, 2, 79–82, (2021).
4. X. Xiang, L. Jacoby, A. Mannodi-Kanakkithodi, R. Biegaj, M. K. Y. Chan, "Universal Machine Learning Framework for Impurity Level Prediction in Group IV, III-V and II-VI Semiconductor", in preparation.
5. A. Mannodi-Kanakkithodi, R. E. Kumar, D. Fenning, M. K. Y. Chan, "Data-Driven Design of Novel Halide Perovskite Alloys", in preparation.

The solution of the inverse problem involves reconstructing a model from a set of observations; such a task is crucial to the majority of indirect experimental measurements, which use a variety of fitting procedures. Unfortunately, this approach often requires crude approximations and generates a misalignment between theory and experiments. A typical example is the effective mass of the charge carriers in a complex semiconductor.
To reconcile theory with experiments, we propose an innovative approach based on bi-directional training of an invertible neural network. Supported by specific domain knowledge, deep learning models are trained to correctly predict both the outcome from a set of model parameters and the parameters themselves. We will apply this approach to the electronic transport properties of materials to link the features of the band structure to conductivity, Seebeck coefficient, and carrier concentrations.
During the talk, we introduce m*2T, a code we developed to inspect the direct problem. The software involves the prediction of transport properties from band structure models which we use to efficiently generate meaningful data to train the invertible neural network. Results on the solution of the inverse problem will also be discussed.

Although simulations excel at mapping an input material to its output property, their direct application to inverse design (i.e., mapping an input property to an optimal output material) has traditionally been limited by their high computing cost and lack of differentiability—so that simulations are often replaced by surrogate machine learning models in inverse design problems. Here, taking the example of the inverse design of a porous matrix featuring targeted sorption isotherm, we introduce a computational inverse design framework that addresses these challenges. We reformulate a lattice density functional theory of sorption in terms of a convolutional neural network with fixed hard-coded weights that leverages automated end-to-end differentiation. Thanks to its differentiability, the simulation is used to directly train a deep generative model, which outputs an optimal porous matrix based on an arbitrary input sorption isotherm curve. Importantly, this pipeline leverages for the first time the power of tensor processing units (TPU)—an emerging family of dedicated chips, which, although they are specialized in deep learning, are flexible enough for intensive scientific simulations. This approach holds promise to accelerate inverse materials design.

A GPU-accelerated computational modeling method for simulating X-ray diffraction (XRD) is developed and implemented to track microstructure evolution through three-dimensional (3D) discrete dislocation dynamics (DDD). This is leveraged to generate a large repository of computational XRD images, and machine learned feature vectors for processing experimental XRD images. The physics-based model implements ray-tracing techniques, Bragg-scattering theory, alloy composition, and a virtual sensor to capture micro-Laue and Debye-Scherrer images from simulated synchrotron X-ray emission. The computational speed improvement provided by this GPU-accelerated method allows for in-situ tracking of diffraction patterns over the course of a virtual experiment, and XRD image data generation from large scale 3D DDD simulations. Implementing convolutional neural networks on this data, we demonstrate that dislocation density can be tracked through time as a function of XRD peak broadening. By determining feature importance (feature attribution) within the machine learned model, the known microstructure is attributed to spreading in Laue-spots. Spreading phenomenon observed in experimental XRD patterns is then associated by similarity analysis to a microstructure in the computational repository, providing insight into the experimental sample.

Polymers are an important class of materials that display morphological complexity and diverse inter-atomic interactions. These two and other factors have defied large-scale and long-time quantum-accurate atomic-level simulations of polymer dynamics which are required to access many properties such as the glass transition or melting temperature. Traditional simulation methods utilize parameterized classical potentials or force fields which often lack accuracy, transferability, and versatility. To overcome these issues, here, we develop general machine learning based models for the polymer dynamics of hydrocarbons that learn from reference quantum mechanical data. Once learned, these models can emulate the parent quantum calculations in accuracy, but be about a billion orders of magnitude faster. Using our models, we perform glass transition temperature calculations of a diverse set of polymers that demonstrate a pathway towards high-throughput data generation using molecular dynamics. Challenges that remain are discussed and pathways to overcome such challenges are presented.

Identifying individual atoms in material samples is a challenging task in high-resolution transmission electron microscopy (HR-TEM) since the signal to noise ratio is often low to prevent that the electron beam causes irreversible changes in the sample. This is an area where machine learning can step in to assist the process.

Here we will report advancements on the tailoring of deep learning neural networks for fast detection of nanoparticles and atomic columns. This concept has previously been demonstrated for tracking gold atoms in HR-TEM image sequences [1] with an industry standard U-net architecture [2].

Training a network to distinguish between atomic species in multi-component material samples is possible by feeding the network a focal series of images. For example, providing three images of an MoS₂ sample at three different defocus settings allows a neural network to differentiate between atomic columns consisting of either 1 molybdenum, 2 sulphur, or 1 sulphur atom in HR-TEM images.

We have simulated HR-TEM images of bare MoS₂ and MoS₂ on graphene substrates in the (001) crystal direction. A training set of 10,000 images and a validation set of 500 images has been simulated applying microscopy parameter values randomly sampled from a specified range.

This work presents the superiority of the MSD-net [3], over the U-net architecture, in distinguishing between the described atomic columns in simulated HR-TEM images of MoS₂. Results show that the MSD-net achieves higher F1-scores overall for the validation set of data.

Next to identifying atomic columns, we display the ability of the MSD-net to segment entire nanoparticles and substrates, which is shown to assist in Fourier analyses by separating the nanoparticle from the substrate and providing a clarified image of the Fourier domain. This ultimately assists the process in determining crystal orientation and facet information in experimental images. The MSD-net is trained on a dataset consisting of unsupported Au nanoparticles and Au nanoparticles supported on CeO₂, both in the [110] zone axis, following a similar methodology as described for the MoS₂ datasets, but where the entire nanoparticle is labelled.

To improve the ability of the MSD-net in analyzing experimental images, we present a new method to include thermal vibrations in HR-TEM image simulations. This method consists of extracting a mean standard deviation of atomic positions dependent on their coordination number from a series of molecular dynamics simulations. These values are then used to perturb the atoms correctly by a simple translation of the positions. This is the frozen phonon approximation, but with vibrational amplitudes depending on the local structure obtained from molecular dynamics simulations. As a result, this includes thermal vibrational effects into the simulated images at a low computational cost.

In conclusion, the MSD-net is shown to outperform the U-net in identifying atomic columns in multi-component materials. This along with nanoparticle segmentation and the computationally cheap implementation of thermal vibrations presents promising applications in the future of HR-TEM image analysis and developing deep learning assisted tools for information extraction.

1. Madsen, Jacob, et al. “A Deep Learning Approach to Identify Local Structures in Atomic-Resolution Transmission Electron Microscopy Images.” Adv. Theory Simul., vol. 1, no. 8, Wiley-VCH Verlag, 2018, p. 1800037, doi:10.1002/adts.201800037.
2. Ronneberger, Olaf, et al. “U-Net: Convolutional Networks for Biomedical Image Segmentation.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9351, Springer Verlag, 2015, pp. 234–41, doi:10.1007/978-3-319-24574-4_28.
3. Pelt, Daniël M., and Sethian, James A. “A Mixed-Scale Dense Convolutional Neural Network for Image Analysis.” PNAS of the United States of America, vol. 115, 2018, pp. 254–59.

In polycrystalline alloys, the grain boundary network has a variety of local atomic environments (site-types) that can be energetically more favorable for a solute atom to substitutionally occupy over the bulk (intra-grain) lattice. This can cause the segregation of solute atoms at the grain boundary - a well-documented phenomenon that is known to significantly impact the material properties, including, for example, mechanical, electrochemical, and magnetic properties. However, to date, there is a limited understanding of the spectrum of such atomic environments at the grain boundary, and their different affinities to solute atoms i.e. whether it promotes or prohibits solute segregation, as quantified by the segregation energy for that site-type. In this talk, we show our recently developed machine-learning framework, which can be used to predict the segregation energy of a solute atom at a grain boundary site, based solely on its unalloyed (pure solvent) local atomic environment. We also highlight the utility of the framework by using it to develop an extensive database for grain boundary solute segregation spectra for over 200 alloys.

Spinel compounds represent an important class of technologically-relevant materials, used in diverse applications ranging from dielectrics, sensors and energy materials. While solid solutions combining two “single” spinels have been known for a long time, no ordered “double” spinel chemistries have been reported till date. Our recent computational investigations, based on a unique approach combining theory and experiments, indeed suggest presence of such distinctly-ordered double spinels for a wide range of cation chemistries.^[1-2] This talk will focus on applications of informatics-based tools to understand design rules within this newly-identified double spinel chemical space.^[2]

[1] Pilania, G., Kocevski, V., Valdez, J.A., Kreller, C.R. and Uberuaga, B.P., Prediction of structure and cation ordering in an ordered normal-inverse double spinel. Communications Materials, 1(1) 1-11 (2020).
[2] Kocevski, V., Pilania, G. and Uberuaga, B.P., High-throughput investigation of the formation of double spinels. Journal of Materials Chemistry A, 8(48), 25756-25767 (2020).

Lithium dendrite formation in Li-ion batteries causes fire when the dendrite continues to grow over many charge/discharge cycles and reaches the other electrode. Our recent lattice Monte Carlo (MC) simulation was based on the diffusion-limited aggregation model which accounts for metal dendrite growth in electrolytes and suggested that ionic liquids can substantially inhibit the dendrite growth and make the dendrite surface relatively uniform. However, the height and aspect ratio of the dendrite varies nonmonotonically with the ion concentrations, the model parameters, and applied voltage. Due to this complexity of the simulation results, challenges remain to identify the properties of ionic liquids for efficient dendrite inhibition. To address this issue, we have developed ensemble neural networks (NNs) that capture the MC simulation data. Our ensemble NNs outperform normal, single NNs and can learn the severe nonmonotonicity of the height and aspect ratio of the dendrite, thus enabling significant reduction in the MC simulation time.

Materials fracture is a complex multiscale process in which macroscopic behavior is inexorably linked to atomic-scale interactions. While molecular dynamics (MD) simulations can provide detailed fracture behavior, it remains computationally infeasible to probe the general problems of understanding fracture mechanisms and designing fracture behavior with this method alone. Here we present a machine learning (ML) approach consisting of a convolutional neural network to predict fracture propagation in 2D materials guided by a genetic algorithm to optimize for particular behaviors of interest. By training this ML model with fracture information from MD, we are able to replace traditional MD simulations with ML predictions and treat the fracture of larger systems, in less time, with consistency to MD baselines. Our method is transferrable to multiple 2D materials and both identifies specific novel fracture mechanisms and allows us to design material structures with controlled fracture paths.

2D single sheet materials, owing to their exceptional mechanical, thermal, electrical and optical properties over their bulk counterparts, are being explored at a rapid pace. Molecular simulations remain a popular technique to explore the structure and dynamics of such materials. Accessibility to accurate and fast interatomic force-fields would promote the discovery and property evaluations of such novel materials. In this work, we introduce, design and test a machine learning workflow capable of searching the high dimensional parameter space and subsequent refining of a Tersoff type Bond Order Potential (BOP). We select Phosphorene as a representative system of interest and the parameter search is performed using a multi-reward reinforcement learning (RL) agent that has been programmed with Monte Carlo Tree Search (MCTS). The training data comprising of structure, energetics, equation of state (EOS), elastic constants and phonon dispersions was curated from Density Functional Theory (DFT) calculations for multiple phosphorene polymorphs. We demonstrate that the new class of RL trained bond order models adequately capture all the properties of the different Phospherene polymorphs. We next perform Molecular Dynamics (MD) using parameters obtained from this approach to access the effect of strain and temperature on phase transition between black and blue phosphorene. Overall, the models are computationally cheap yet accurate and can be used to simulate dynamics and structural transformations of Phosphorene polymorphs for a wide variety of energy applications.

Various machine learning models have been used to predict the properties of polycrystalline materials, but none of them directly consider the physical interactions among neighboring grains despite such microscopic interactions critically determining macroscopic material properties. Here, we develop a graph neural network (GNN) model for obtaining an embedding of polycrystalline microstructure which incorporates not only the physical features of individual grains but also their interactions. The embedding is then linked to the target property using a feed-forward neural network. Using the magnetostriction of polycrystalline Tb_0.3Dy_0.7Fe₂ alloys as an example, we show that a single GNN model with fixed network architecture and hyperparameters allows for a low prediction error of ~10% over a group of remarkably different microstructures as well as quantifying the importance of each feature in each grain of a microstructure to its magnetostriction. Such microstructure-graph-based GNN model therefore enables an accurate and interpretable prediction of the properties of polycrystalline materials.

The accurate prediction of phonon modes is important for scientific progress in fields ranging from heat and electron transport in thermoelectrics to correlated disorder in metal-organic frameworks (MOFs). Density Functional Theory (DFT) is a simulation method that is highly accurate at predicting the phonon modes, but it is computationally more expensive and requires more computational hours than simulation methods such as Density Functional Tight Binding (DFTB). Recently, the Chebyshev Interaction Model for Efficient Simulation (ChIMES) was developed as an approach to correct DFTB calculations by training a machine learning model. DFTB with ChIMES was shown to be effective at improving phonon predictions in a number of small-molecule systems. However, this method has never been applied to charge-transfer salt systems, some of the most promising hole conducting materials. In this study, training sets were created for TTF-TCNQ and TCNQ systems and the models were validated by testing each training set on both systems with DFTB. The accuracy of each training set was compared against the Inelastic Neutron Scattering (INS) spectra created using DFT.

To understand the magnetism of solids at high temperature we need to study the interplay between vibrations and the magnetic degrees of freedom. The variation in magnitude of the atomic magnetic moments, the longitudinal spin fluctuations (LSF), is a degree of freedom of particular relevance in metallic magnets. The LSF energy depending on the local magnetic moment size of an atom, called the LSF energy landscape, can be calculated using density functional theory. It has been seen that, at elevated temperature, these LSF energy landscapes depend on the local environment of the atom i.e., they are influenced by both the lattice disorder caused by vibrations and the variations in the transverse orientations of neighboring moments. To simulate a magnetic material in e.g., an ab initio molecular dynamics simulation one needs to know how the atoms and their moments will interact with each other which, in principle, would require calculating the LSF energy landscape of each atom at every step in time. In this work we have developed a machine learning approach to predict the shapes of the energy landscapes to dramatically accelerate this process. The material used when developing this approach is bcc Fe at the Curie temperature and ambient pressure. The machine learning method used is kernel ridge regression. Two machine learning models are trained to predict the two parameters involved in determining the shape of the LSF energy landscape. As a critical test of the generality of the trained machine learning models, they are applied to predict the LSF energy landscapes of bcc Fe at temperature and pressure comparable to the conditions at the Earth's core.
Our machine learning approach is compared to other approximative methods for determining the shape of the landscapes and is shown to significantly reduce the errors. By applying the trained machine learning models in combined atomistic spin dynamics – ab initio molecular dynamics, the effects of LSF:s can be incorporated without having to explicitly calculate each LSF energy landscape in each time step. We perform such dynamical ab initio simulations for bcc Fe at both the Curie temperature and at the conditions of the Earth's core. This reveals the relevance of magnetic fluctuations on the low-density-problem of the current Earth core models.

The chemical and structural properties of nanoclusters are of great interest in numerous applications. A systematic study of structure-property relationship necessitates the knowledge of atomically precise structures of stable clusters over a variety of sizes. However, experimental characterization of the structures of these non-crystalline materials can be challenging. Computationally searching for stable structures using ab initio calculations is a feasible solution, but can be computationally expensive. In this work, we present a procedure that can accelerate prediction of low-energy nanocluster structures by combining genetic algorithms with interatomic potentials actively learned on-the-fly. A pool-based genetic algorithm is implemented to efficiently sample the configuration space, and moment tensor potentials are used to rapidly relax and evaluate the energies of predicted clusters. Moment tensor potentials are regularly retrained on-the-fly on density functional theory (DFT) calculations of structures that are poorly represented by existing training data and of low-energy pool clusters. Only DFT energies of pool clusters are reported at the end to guarantee ab initio level of accuracy. We demonstrate an acceleration rate of ~12 times on average, comparing our procedure with genetic algorithm using purely DFT calculations. Moreover, for aluminum clusters with 21 to 55 atoms, which we used as the benchmarking systems, our genetic algorithm search identified structures with lower energy in 25 sizes than any reported clusters in the literatures, and confirmed equivalent structures for another 8 sizes. This work demonstrates a feasible way to systematically discover stable structures for large nanoclusters and provides insights into the transferability of machine-learned interatomic potentials for nanoclusters. We believe the new procedure can greatly facilitate the discovery and design of novel nanomaterials for a wide range of applications.

Machine learning interatomic potentials (MLIPs) with high efficiency and quantum accuracy are emerging as an enabling capability to simulate complex atomic level processes. To address the challenge of reliability and automated training of MLIPs, we introduced Bayesian active learning (BAL) that relies on quantified prediction uncertainty to drive an autonomous data acquisition strategy [1]. In this workflow, Bayesian MLIPs are constructed from Gaussian process (GP) based on atomic cluster expansion (ACE) descriptors. By developing a highly efficient approximation of the GP uncertainty, whose cost is independent of the training set size, we gain orders of magnitude speedup compared to inference with exact GPs.
As a demonstration, we train a MLIP for silicon carbide (SiC), a wide-gap semiconductor with diverse applications in electronics and physics. For example, point defects in SiC are promising candidates for stable controllable qubits, and an accurate description is desired of their long-time evolution. The resulting MLIP has excellent agreement with the density functional theory and outperforms previous empirical potentials in the prediction of elastic and thermal properties of pristine bulk, as well dynamics of point defects. The highly efficient active learning workflow can be extended to other systems and accelerate the discovery and understanding of materials for quantum technologies.

[1] Yu Xie et al, "Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene". npj computational materials (2021).

Solid polymer electrolytes (SPEs) are seen as promising alternatives to conventional liquid electrolytes in lithium battery systems due to their low density, mechanical compliance, and low flammability but are challenged by lower ionic conductivity. Molecular dynamics (MD) simulations can be used to guide the design of novel SPEs by allowing quantitative determination of separable anion and cation diffusions as well as local solvation environments. Classical potential MD simulations update molecular conformations by the net force on each atom due to bonds, angles and torsions as well as Coulomb and dispersion interactions. However, these classical potentials require the prior knowledge of materials- and local environment-specific parameters such as unique bond stiffnesses, which are often not well defined.
In this work, we explore the effects of anharmonic bonded interactions on polymer segmental motion and resulting ionic solvation and conductivity in polymer electrolyte systems. An in-house, neural network-based workflow, named AuTopology, was used to learn the interatomic potential parameters of distinct atomic environments for two different classical models from DFT forces as training data. The learned harmonic OPLS model and anharmonic PCFF+ model parameters were then used to equilibrate condensed-phase simulations at a variety of experimentally-relevant concentrations. These simulations were allowed to run for hundreds of nanoseconds to determine the individual anion and cation diffusivities and resulting conductivities. Using this framework and an in-house database of molecular conformations, we have been able to reproduce wB97XD3-level DFT forces from trained OPLS force fields to within 5.5 kcal/mol-A as well as compare the condensed phase solvation and conductivities between the OPLS and PCFF+ models for PEO and carbonate systems.

In the current study, we have developed Deep Learning Potentials as implemented in DeepMD code to model physical and thermo-mechanical properties of complex metal-rich carbides. These phases are critical to the creep properties of advanced Ni-based Superalloys. For this purpose, we utilized the results from ab-initio calculations following the Density Functional Theory approximations including the energy, forces, and virial database as generated from the Vienna Ab-initio Software Package. The efficiency and validity of the developed potentials were verified through a series of predictive molecular dynamics simulations of thermomechanical properties that are of interest to the development of advanced superalloys. In addition, we compared the Deep Learning Potentials to the analytical potentials of Reference-Free Modified Embedded Atomic Method (RF-MEAM) that we obtained by using a combined parametrization approach of Conjugate Gradient Minimization (CGM) and Genetic Algorithms as implemented in MEAMfit V2 code. The support from the National Energy Technology Laboratory (Grant No. FE0031554) is gratefully acknowledged. We also would like to thank NERSC for the supercomputer facility.

Deep learning based methods have been widely applied to predict various kinds of molecular properties in the pharmaceutical industry with increasing success. The solvation free energy is an important index in the field of organic synthesis, medicinal chemistry, drug delivery, and biological processes. However, accurate experimental solvation free energy determination is a time-consuming process, and hence, methods to assess this quantity in the absence of physical samples are of interest. Here, we propose two novel models for the problem of free solvation energy predictions, based on the Graph Neural Network (GNN) architectures: Message Passing Neural Network (MPNN) and Graph Attention Network (GAT). GNNs are capable of summarizing the predictive information of a molecule as low-dimensional features directly from its graph structure, without reliance on extensive intra-molecular descriptors. Consequently, accurate predictions of the molecular properties can be made without time consuming experimental measurements. We show that our proposed models also outperform all quantum mechanical and molecular dynamics methods in addition to existing alternative machine learning based approaches in the task of solvation free energy prediction. The novelty of our neural network model is that we take pair-wise interaction of solute and solvent into consideration. We believe our proposed architecture can be used for pair-wise interactions such as solvent-solute, protein-ligand, and etc.

Chalcogenide alloys are key materials for both selector and memory elements found in next generation non-volatile memory cells. Developing robust material stacks for memory devices is crucial for optimal device performance and long-term endurance. However, Joule heating and high electric fields during operation can often lead to atomic interdiffusion at interfaces that can degrade device performance over time. While first principles atomistic simulation can provide insight into the electronic structure and local atomic bonding configurations, due to computational constraints, this approach is limited to small atomic systems (<1000 atoms) and time scales (~10 ps). To evaluate long term device performance, we need an approach that can comfortably address complex atomic configurations at different temperatures and time scales.

While classical molecular dynamics is up for the task, the field has suffered from a lack of robust empirical potentials for materials beyond traditional semiconductors. Machine learning provides one promising approach to use ab-initio insight from density functional theory to inform the systematic development of new empirical potentials. In this work, we developed a robust set of machine learning potentials to examine the interaction between Ge-Se alloys and Ti electrodes. Previous experimental investigations have shown evidence for strong interfacial interaction between Ti and chalcogenide alloys[1-3]. The first principles training set draws from a range of linear combination of atomic orbitals (LCAO) DFT calculations on bulk crystal compounds, multilayer structures, and ab-initio molecular dynamic runs at different temperatures. Using this data set, we trained the empirical potentials using the moment tensor potential framework[4] implemented in QuantumATK[5]. The initial empirical potentials were also further refined by active learning which incorporates new configurations in the training dataset. The amorphous chalcogenide glasses and interface structures were intentionally not part of the training set. The machine learning empirical potentials provide accurate predictions for key material parameters in the training data (lattice constant, bulk modulus, etc). They are also able to generate reasonable atomic models for Ge-Se amorphous materials outside the training set. Long term (> 1 ns) molecular dynamic simulations[6] using these potentials shows clear evidence of interdiffusion at the Ti|Ge-Se interfaces. In this presentation, we will discuss the evolution of the composition profile over time and the impact interdiffusion will have on the electronic properties of these device structures.

[1] S. G. Alberici, R. Zonca, and B. Pahshmakov, Applied Surface Science, 231-232, 821 (2004)
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[4] A. V. Shapeev, Multiscale Modeling and Simulation, 14, 1153 (2016).
[5] S. Smidstrup et al., Journal of Physics: Condensed Matter, 32, 015901 (2020).
[6] J. Schneider et al., Modeling Simul. Mater. Sci. Eng. 25, 085007 (2017).

Background: For complex biological dynamics in silico studies, conventional all-atomic (AA) simulations are far too computationally expensive for large-scale systems which take up to months or even years. In the last decade, a rise in coarse-grained (CG) modeling allows for the extension of time-scales compared to the AA model, by combining atoms in larger macromolecules and leading to significant simulation speedups. Such modeling techniques hold promise, yet the most crucial part in retaining accuracy compared to all-atom models is the parameterization of CG force fields.
Methods: We evaluate two methods for parameterizing CG models for improved accuracy: a conventional iterative Boltzmann inversion (IBI) by comparing target radial distribution functions, and the CG-Net neural network model which intelligently learns the parameters from short all-atomic trajectories. CG-Net is fed inputs as Cartesian coordinates of CG particles and serves as the potential energy function from which particle forces can be computed. Network weights represent parameters of this potential energy function, and the loss function for the discrepancy between atomistic dynamics and NN-predicted CG dynamics is minimized. The molecule studied was the protein chignolin (PDB: 1UAO) at 350K (the folding transition temperature), selected to make the training time for CG-Net manageable and the ground-truth AA simulation easier to compute. After the AA equilibrium was computed using NAMD, the molecule was coarse-grained by extracting the alpha carbon atoms. After the first guess for the CG parameters was computed using VMD’s CG Builder GUI, an IBI analysis was performed to iteratively generate improved parameters. Iterations are repeated until differences in RMSD values are negligible. The full AA-ground truth serves as a basis of comparison for these models.
Results: The original AA chignolin molecule used contains 138 atoms in 10 amino acid residues, with 141 bonds, 249 angles, and 369 dihedrals built using the LAMMPS topology file. After the initial apha-carbon coarse-grained model was defined, with 10 beads each representing approximately 14 atoms, both the nonbonded Lennard-Jones and bonded interaction parameters were computed using IBI. The bonded interaction parameters were tuned until the stiffness constants differed ~10% from those derived from the atomic-scale simulations. The CG model is simple, containing only 9 bonds and 8 angles built using a custom topology file and effectively reducing the degrees of freedom by 94-97%, but the IBI showed that the CG model is stable when used on chignolin due to bond lengths and angles having little alteration through successive iterations. RMSD and RDF values were also computed and compared to the all-atom simulations for validation of this method. This analysis was done both in vacuum and with chignolin solvated in TIP3P water.
Discussion and Future Work: The focus of this work was to conduct performance analysis of two different methods for parameterizing CG force fields, allowing us to accelerate the conventional AA model by 16-30 orders of magnitude. ML methods such as CG-Net show the potential for improving accuracy of CG models making it an effective technique to study large macromolecules. However, one limitation of CG-Net is the precision that is lost from modeling CG bead interactions instead of atomic interactions. Drawbacks of IBI include the inability to work with hybrid CG models and the failure to account for dihedral angles. Future work will be done to implement a combined CG model which utilizes both techniques for improved accuracy. Such techniques can be applied in many ways to study a variety of materials, including human fibrinogen and the SARS-COV-2 spike glycoprotein.
Acknowledgment: The project is supported by the Stony Brook Garcia Center for Materials Research and the Garcia High School Program.

We present Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant deep learning approach for learning interatomic potentials for molecular dynamics simulations. Instead of the commonly deployed invariant convolutions over scalar features, NequIP uses E(3)-equivariant convolutions over geometric tensors, better representing the symmetries of Euclidean space. The proposed model obtains state-of-the-art accuracy on a challenging set of diverse molecules and materials while at the same exhibiting remarkable sample efficiency. Interestingly, NequIP outperforms existing, invariant models with up to three orders of magnitude fewer training data and performs better than kernel methods, even on tiny data sets, thereby challenging the widely held belief that deep neural networks require massive training sets. We show results from molecular dynamics simulations using NequIP on a series of technologically relevant bulk materials as well as the folding of small proteins. The method is implemented in a scalable and highly efficient software implementation, integrated with the molecular dynamics code LAMMPS, and can be used to simulate large time- and length-scales at high accuracy and low computational cost.

Message Passing Graph Neural Networks (MPNNs) based on pairwise interactions have emerged as the leading paradigm for modeling atomistic systems by recursively propagating information along a molecular graph. While MPNNs have consistently been demonstrated to give low generalization errors, they inherently have a low level of interpretability, are not systematically improvable, and are difficult to scale to large numbers of atoms. Here, we introduce the Deep Interatomic Cluster Expansion (DICE), an equivariant neural network that leverages many-body information in a single interaction, without the need for message passing or convolutions. The method can be systematically improved by including higher-order interactions at linear cost, has physically meaningful hyperparameters, and is embarrassingly parallel. DICE builds on a novel, learnable E(3)-equivariant many-body representation that utilizes weighted tensor products of geometric features to describe N-point correlations of atoms. The proposed many-body representation overcomes the exponential scaling of a naive cluster expansion and instead scales linearly with the number of simultaneously correlated particles. We demonstrate that the use of higher-order correlations of atoms systematically improves the accuracy. We further find that DICE gives excellent performance across a wide variety of settings, outperforming both MPNNs as well as kernel-based methods on small data sets.

While neural network (NN) interatomic potentials enable fast prediction of potential energy surfaces with an accuracy matching that of the electronic structure methods, they often show volatile behaviors when extrapolating outside well-learned training domains. Domains with low prediction confidence can be identified using uncertainty quantification methods. However, arriving at such uncertainty regions requires thorough exploration of the NN phase space, often using slow atomistic simulations. Here, we exploit automatic differentiation to drive atomistic systems towards high-likelihood, high-uncertainty configurations without the need for atomistic simulations. Adversarial attacks are employed on an uncertainty metric to sample informative geometries that expand training domains of the NNs. In combination with an active learning loop, this approach provides a efficient way to bootstrap and improve NN potentials, while decreasing number of calls to the ground truth method. We demonstrate this framework on sampling of kinetic barriers, collective variables in molecules, and supramolecular chemistry. This framework can also be extended to any NN potential architecture and materials system.

Quantitative understanding and controlling interfacial reactions between the gas-phase and solid surfaces are crucial for improving numerous catalysis and energy conversion systems. For example, the adsorption of CO on Pt surfaces is important for a variety of industrial processes (e.g., water-gas-shift reaction, PEM fuel cell catalyst poisoning). CO/Pt interaction is poorly understood but known to strongly affect the metal surface structure and dynamics. An accurate and fast reactive model could provide enormous insight into the current, and future, design of such Pt-based catalysts. Density functional theoretical (DFT) methods and existing parametric interatomic potentials have long struggled with accurately describing heterogeneous interactions.
Here, we employ the FLARE framework [1] to actively learn the CO/Pt interaction, using a mapped Gaussian Process (MGP) machine-learning model, with molecular dynamics used to sample configurational space. The model accurately reproduces DFT energies, forces, and stresses as well as rigorous quantitative Bayesian uncertainties. When predictive uncertainty falls outside of the accepted tolerance, additional DFT calculations are performed to augment the training set.
We then use the MGP model to conduct large-scale MD to explore the effect of CO adsorption on various Pt-surface facets and benchmark to expected outcomes as provided by experiment.
[1] J. Vandermause et al, NPJ Computational Materials 6 (2020).

A lot of progress has been made in recent years in the development of machine learning (ML) potentials for atomistic simulations [1]. Neural network potentials (NNPs), which have been introduced more than two decades ago [2], are an important class of ML potentials. While the first generation of NNPs has been restricted to small molecules with only a few degrees of freedom, the second generation extended the applicability of ML potentials to high-dimensional systems containing thousands of atoms by constructing the total energy as a sum of environment-dependent atomic energies [3]. Long-range electrostatic interactions can be included in third-generation NNPs employing environment-dependent charges [4], but only recently limitations of this locality approximation could be overcome by the introduction of fourth-generation NNPs [5], which are able to describe non-local charge transfer using a global charge equilibration step in combination with an accurate short-range term. In this talk an overview about the evolution of high-dimensional neural network potentials will be given along with typical applications in large-scale atomistic simulations.

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[5] T. W. Ko, J. A. Finkler, S. Goedecker, J. Behler, Nature Comm. 12 (2021) 398.

Gaussian process regression (GPR) has gained increasing attention for the construction of interatomic potentials. In particular, GPR has been shown to produce spectroscopically accurate potential energy surfaces (PES) of molecules from fewer samples than neural networks (J Chem Phys 148 (2018) 241702). This, the absence of non-linear parameters other than a small number of hyperparameters, and the capability to compute estimates of uncertainties make GPR a promising method. GPR, however, suffers from rapidly escalating CPU cost with the number of training data. Both the cost of model training and the cost of computing the PES at points post-training increase, making calculations with more than a few tens of thousand training data not routinely feasible. The increasing cost is due to the need to calculate a matrix-vector product with the inverse of a covariance matrix matrix K. We explore a local version of GPR, LGPR, in which for each test point, a local covariance matrix K' is built, equivalent to using blocks of a permuted K. This approach raises the prefactor of the CPU cost but allows working with arbitrarily large training datasets. We test the approach in comparison with the classic GPR on PESs of formaldehyde and UF6 using very large test sets and property calculations and show that the size of K' can be considerably reduced compared to K with a small extra error.

Molecular dynamics (MD) is a widely used tool for studying materials at the atomistic scale. However, the accuracy of MD simulations is limited by the interatomic potential. This is especially true for modeling materials in extreme environments where the interatomic potential is typically utilized far from the equilibrium properties it was fitted to. Recently, machine learning has been used to develop interatomic potentials where the potential is trained on large datasets of quantum accurate data as opposed to fitting the potential to a physics based functional form. These types of machine learning interatomic potentials (MLIAPs) have been shown to have increased accuracy compared to traditional potentials [1]. One such MLIAP method, the spectral neighbor analysis potential (SNAP) [2] has been applied to a variety of materials with increased accuracy [2,3]. In this talk, we will discuss the development of SNAP potentials for molecular dynamics simulations of materials in extreme environments such as radiation or high pressure and temperature environments.

[1] Zuo, et al, J. Phys. Chem. A 124, 731-745 (2020)
[2] Thompson, et al. J. Comp. Phys. 285, 316-330 (2015)
[3] Wood, et al. Phys. Rev. B 99, 184305 (2019)

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525

With the recent improvement of algorithms and rapid growth of computing power, machine learning is fast becoming an emerging tool for predicting and understanding material behavior across multiple length scales. With Peta-scale supercomputing resources, we are now able to generate a large number of data sets with existing deterministic material models to train the machine learning algorithms. In this technical presentation, we will discuss our recent attempts to quantify microstructural effects on material strength and fracture response at both the atomistic and the meso-scale.

The first part of the talk will discuss the utilization of machine learning to elucidate the structure-property relationship at grain boundaries of nanocrystalline metals. We now know that the strength of nanocrystalline metals is ultimately controlled by the absorption, emission, or transmission of single dislocations at the grain boundaries, which closely depend on the local atomistic stress state at the grain boundaries. Here, we develop a machine learning algorithm based on an artificial neural network (ANN) to predict the local atomistic stress (output) along [110] bicrystal symmetrical tilt Cu grain boundaries from the local atomic configuration (input). We demonstrate that successful predictions of the atomistic stress state can be achieved by ensuring that the training set comprises of grain boundaries with both the same type and sequence of structural units. The predictive accuracy can be significantly improved by including the deformed configuration and stress state in the training dataset. This atomistic constitutive law will be used to predict the atomistic stress state from DFT calculations or HRTEM imaging, thus extending the notion of atomistic stress beyond MD domain.

The second part of this talk examines the ability of ANNs to predict the tortuous crack path in a heterogeneous microstructure, comprising of two distinct size-scales of voids which is commonplace in additively manufactured metals – the larger-scale voids represent the ~30 µm defects resulting from gas bubbles or unsintered powder in the additive manufacturing process, while the smaller ~2-10 µm background voids originate from nucleated particles or inclusions responsible for ductile fracture process in metal alloys. A small-scale yielding, modified boundary layer model with monotonic K_I-T displacement loading was used to study crack propagation through a material with local distribution of dual-scale pre-existing voids resembling AM Ti-6Al-4V. The Gurson ductile damage model was implemented to model both the background pores and the larger AM defects, and the initial porosity distribution ahead of the current crack-tip, and resulting crack propagation path was used to train an ANN. The machine learning algorithms provide critical insights into the effects of porosity distributions on the crack propagation path, supporting the notion of achieving fracture by design.

Accurately predicting binding affinities of a given protein-ligand system fast and robustly is of high importance for drug discovery and experimental microbiology simulations. Compared with deterministic models which require heavy computational workloads, deep learning models are faster yet with great generalization capabilities, providing an efficient path for knowledge discovery in molecular scientific studies.
We present MR-Net, a state-of-the-art deep learning model on PDBbind v.2019 and v.2016 datasets for protein-ligand binding affinity prediction. The proposed architecture consists of 2 transformer modules, a fully convolutional encoder and a fully convolutional decoder. To maximize the amount of extracted features from the input, 3 different representations of a given system are used: SMILES string, point cloud and atom sequence.Only the binding pocket of the system is used for the prediction. The point cloud representation is a 4D tensor of shape (length of the feature vector, x, y, z) where each atom is represented on a grid of resolution 0.5 Angstroms where the maximum distance between each atom is 30 Angstroms. The number of features in the feature vector is determined as 32. For SMILES and sequences, transformer modules are used, whereas for the point-cloud a fully convolutional encoder is proposed. The encoder is constructed with 3D depthwise separable convolution modules where skip connections are utilized to maximize the gradient flow. The transformer modules are designed with the “deeper better than larger” principle. The embedding dimension is determined as 64 and learnt from the data with additional positional encoding. The dictionary sizes are 65 and 25 for the SMILES transformer and the sequence transformer respectively. For SMILES strings, inputs longer than 2500 characters are truncated. With average pooling and convolutions with kernel size of 3, the outputs of each module are reshaped into (1, 64, 64) and concatenated along the first dimension. Then, the resulting matrix is fed into a fully convolutional decoder consisting of 2D convolutions connected to a fully connected layer. The proposed network is trained with a custom loss function aiming to minimize the Root Mean Squared Error Loss while maximizing the Pearson’s Correlation Coefficient.
For experiments on PDbbind v.2016 and v.2019 datasets containing 16,179 and 21,382 protein-ligand complexes respectively, the core set splits are used for testing purposes while the rest is used for training. During training, each sample in the input space is rotated to all the 24 combinations possible and has been added random translation to make our model center-invariant. Our experiments showed that single-headed attention performs much better than multi-head attention because of the long input sequences; hence, both used transformers are single-headed and have 6 encoder and 6 decoder layers with feed-forward dimension of 2048. To prevent overfitting, weight decay is applied. We report 1.184 Root Mean Squared Error and 0.878 Pearson’s Correlation Coefficient on PDBbind v.2016 dataset which, to our knowledge, is above the current state-of-the-art.
Our MR-Net achieves state-of-the-art performance on both PDbbind v.2016 and v.2019 datasets, greatly reducing the need for computational resources and accurately predicting the protein-ligand binding affinity. We are also planning on more optimization approaches to further extend the capability of MR-Net . Experiments with the preprocessing pipeline of our model are to be conducted for the atomic feature descriptors and grid resolution. To learn embeddings from a larger dataset, we are working on an extended version of the Word2Vec algorithm for protein-ligand complexes.
This work is supported by the Garcia High School Program. The numerical calculations reported were partially performed at TUBITAK ULAKBIM, High Performance and Grid Computing Center.

Over the years, computational materials science has greatly contributed to novel materials search, adding to the experimental search which is inherently low-throughput compared to computational search. Computational exploration of unknown materials has two key components: crystal structure generation algorithms, and energy evaluation of the generated crystal structures. The latter is critical as the energy of the crystal structure is directly related to synthesizability. Conventionally, the energy evaluation has been carried by quantum mechanical calculations, notably density functional theory (DFT). However, when it comes to ternary or higher (multinary) phases search, DFT shows its limitation, as the size of the materials space grows exponentially with the increase of the complexity and DFT is still too slow to evaluate the immense number of crystal structures that can appear during the crystal structure search. In addition, as previous researches are more focused on crystal structure search of unary and binary phases, an efficient crystal structure generation algorithm optimized on multinary phases is still lacking.
In this presentation, we introduce SPINNER, an efficient crystal structure search framework that can carry more than 10⁵ energy evaluations and has optimized crystal structure generation algorithms for multinary phases. The high efficiency of the SPINNER framework is realized by adopting machine-learning (ML) based interatomic potentials for crystal energy evaluations. ML potentials can evaluate the energy and force of given atomic structures at low computational costs while maintaining an accuracy comparable to that of DFT. With the newly developed SPINNER framework, we aim to find novel military crystals which have high Li-ion conductivity and suggest some of the promising new compounds.

The degredation and eventual failure of a specimen through fracture, fatigue or creep represents an extremely challenging test-case for atomistic materials modelling, since there is a simultaneous requirement for high accuracy in the anharmonic region near a crack tip or dislocation core where chemical bonds break, and for large length- and time-scales to correctly capture elastic relaxation associated with long-range stress fields. I will demonstrate how the Gaussian Approximation Potential (GAP) framework has been succesfully applied to this problem using models trained on ab initio data for silicon [1], silicon carbide [2] and diamond [3,4], as well as considering how the approach could be further leveraged in future, for example as part of QM/ML (quantum mechanics/machine learning) multiscale schemes and/or to carry out active learning [5].

[1] A. P. Bartók, J. R. Kermode, N. Bernstein, and G. Csányi, Machine Learning a General-Purpose Interatomic Potential for Silicon, Phys. Rev. X 8, 041048 (2018)
[2] H. Tunstall, J. R. Kermode and G. Sosso, In Prep (2021)
[3] P. Rowe, V. L. Deringer, P. Gasparotto, G. Csányi, and A. Michaelides, An Accurate and Transferable Machine Learning Potential for Carbon, J. Chem. Phys. 153, 034702 (2020)
[4] J. Brixey and J. R. Kermode, In Prep (2021)
[5] Z. Li, J. R. Kermode, and A. De Vita, Molecular Dynamics with On-the-Fly Machine Learning of Quantum-Mechanical Forces, Phys. Rev. Lett. 114, 096405 (2015)

With exascale super computers arriving in the near future, it is timely to ask whether our simulation software is capable of matching this unprecedented computing capability. While many research challenges in material physics, chemistry and biology lie just out of reach on peta-scale machines due to length and time restrictions inherent to Molecular Dynamics(MD), questions of the accuracy of our simulations will continue to linger. Simply running the same peta-scale simulations with more atoms on a larger computer (weak scaling) does not advance the accessible timescales, nor does it avoid the pitfalls of empirically developed constitutive models. This talk will overview the U.S. Department of Energy* EXAALT (EXascale Atomistics for Accuracy, Length and Time) project and our efforts to provide software tools for MD that not only scale efficiently to huge atom counts, but also enable efficient MD simulations for smaller systems too. Central to this effort are machine learned models via the Spectral Neighborhood Analysis Potential(SNAP) which demonstrate both tunable accuracy and computational cost, a highly advantageous trait for MD on exascale resources.
*This work is funded through the Exascale Computing Project (No. 17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration

Normal mode analysis is a powerful technique for understanding the motions of chemical and biological systems, with applications in molecular design and fingerprinting. The number of operations required to compute the normal modes of such a system scales cubically with the size of the system, making such analyses computationally intractable. In order to make this technique more accessible to the broader scientific community, prior work produced a data-driven model that relied on geometric and structural properties to predict protein normal modes with high accuracy. In this work, we experimented with creating fully end-to-end models in two ways: first, we investigated multiple architectures for predicting normal modes from amino acid sequences alone, and second, we investigated graph-based architectures. Success in this project will enable faster and more sophisticated applications in functional protein design and recognition, such as screening and inhibiting novel coronavirus spike proteins.

In many multi-scale and reactive Molecular Dynamics (MD) simulations, ab-initio quantum calculations such as Density Functional Theory (DFT) or post-Hartree-Fock (post-HF) methods constitute a bottleneck in simulation workflows which prevents exact predictions for long time-scales or large system sizes due to its prohibitively expensive computation costs. In the past years, machine learning has emerged as a tool to enable fast and accurate energy predictions with so-called neural network potentials [1]. A set of neural networks trained on a sufficiently large amount of quantum data offer differentiable energy predictions at constant evaluation times. Here, we adapted this methodology to develop the Python Rapid Artificial Intelligence Ab Initio Molecular Dynamics (PyRAI²MD) software for photodynamics simulations investigating the cis–trans isomerization of trans-hexafluoro-2-butene and the 4π-electrocyclic ring-closing of a norbornyl hexacyclodiene [2]. The active learning approach of the neural network photodynamics simulations is capable of revealing reaction pathways like the low-yielding syn-product, which was absent in the quantum chemical trajectories, and the subsequent thermal reactions within 1 ns for the norbornyl cyclohexadiene. Additionally, we integrated the machine learning model in multi-scale simulations for organic semiconductors to compute the complete distribution of energy levels in a MD simulation to support more accurate charge transport models [3]. We find that static disorder and thus the distribution of shallow traps is highly asymmetrical for many materials, impacting the widely considered Gaussian disorder models. We furthermore analyze characteristic energy level fluctuation times and compare them to typical hopping rates to evaluate the importance of dynamic disorder for charge transport.

[1] J Behler 2014. Representing potential energy surfaces by high-dimensional neural network potentials. J. Phys.: Condens. Matter 26 183001.
[2] Li, J., Reiser, P., Boswell, B.R., Eberhard, A., Burns, N.Z., Friederich, P. and Lopez, S.A., 2021. Automatic discovery of photoisomerization mechanisms with nanosecond machine learning photodynamics simulations. Chemical Science, 12(14), pp.5302-5314.
[3] Reiser P., Konrad M., Fediai A., Léon S., Wenzel W. and Friederich P., 2021. Analyzing Dynamical Disorder for Charge Transport in Organic Semiconductors via Machine Learning. J. Chem. Theory Comput., 17, 3750−3759.

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use existing machine learning methodologies to train the model. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena even for simple PDEs. In particular, we analyze several distinct situations of widespread physical interest, including learning differential equations with convection, reaction, and diffusion operators. We provide evidence that the soft regularization in PINNs, which involves differential operators, can introduce a number of subtle problems, including making the problem ill-conditioned. Importantly, we show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize. We then describe two promising solutions to address these failure modes. The first approach is to use curriculum regularization, where the PINN's loss term starts from a simple PDE regularization, and becomes progressively more complex as the NN gets trained. The second approach is to pose the problem as a sequence-to-sequence learning task, rather than learning to predict the entire space-time at once. Extensive testing shows that we can achieve up to 1-2 orders of magnitude lower error with these methods as compared to regular PINN training.

Molecular dynamics simulations are used to realistically simulate the material properties. The interatomic potential energy function (PEF) is critical in determining the validity of the results. We use density functional theory (DFT) to parameterize the interatomic PEF. Usually, interatomic PEF is a multi-body function whose functional form is non-trivial to determine. Therefore, estimating the functional form is very critical in determining the interatomic PEF and hence the material properties. Herein, we use a graph neural network with multi-message passing to model the interatomic PEF. Further, we use the Euler-Lagrange equation to determine the acceleration of the atomic system. Finally, we train the GNN against the simulation trajectories of unary and binary Lennard Jones (LJ) systems created from traditional molecular dynamics (MD) simulations. The trained GNN is then used to do MD simulations and demonstrate energy conservation.

Data-driven materials discovery requires the automated interpretation of large volumes of materials characterization data and its onward use in materials modeling. Thereby, materials can be designed with properties that suit a given functional application. This data-science approach is enabled by a range of methods from artificial intelligence (AI): machine learning and natural language processing. This talk will show how such AI-based methods can be employed to source materials characterization data from the academic literature, automatically interpret these data, and use them to model and predict materials properties in a molecular-engineering fashion.

Homogeneous metallic nanoparticles form highly stable colloids because of the strong electrostatic repulsions. Coating with metal chalcogenide complexes and with changes to solvent polarity, the colloidal stability can be altered to result in the formation of highly ordered aggregates with diverse applications in energy storage, photonics and electronics. The structure of the self-assembled aggregates depends on the delicate interplay between the dispersion and the electrostatic interactions governed by the design parameters such as temperature, size-charge-dielectric constant of the nanoparticle and the dielectric strength of the solvent. To aid in the rational design of engineered materials composed of polarizable nanoparticles, we have established a computational and machine learning framework to efficiently screen the experimental design space, identify regimes leading to spontaneous and triggerable self-assembly, and extract microscopic design rules for engineered assembly.

We perform high-throughput virtual screening of the particle design space using a coarse-grained simulation model implementing an image-charge formalism that rigorously accounts for the many-body polarization interactions. We efficiently sample the design space and identify self-assembly phase boundaries using a data-driven active learning approach to optimally guide the deployment of computational resources. Our computational phase boundaries are in good agreement with experimental scattering measurements, and predict the structure of self-assembled aggregates become more ordered with decreasing nanoparticle size and increasing solvent dielectric constant. Finally, we use our computational models to design switchable materials systems composed of polarizable nanoparticles that are capable of triggered assembly and disassembly upon changes in temperature and solvent quality.

Here we propose a new design method using reinforcement learning to solve bioinspired composite materials in a complex system. Biological structural materials are made by a stiff matrix and a compliance glue to exhibit extraordinary mechanical properties which synthetic materials do not possess. The reason for this excellent performance is because a particular order makes them of microstructures. To imitate the exceptional material properties of biomaterials, the idea of bioinspired structural material has been proposed. However, the number of combinations of design space is usually intractable. Therefore, we offer a new design method by using reinforcement learning to solve the problem. Here we developed a hierarchical design paradigm. The hierarchical design process starts from a design space with limited combinations. After obtaining the best design of the current system size, we expanded the design system and searched for the best design with higher resolution. We searched for the best crack resistance by using the hierarchical reinforcement learning from a lower resolution. By comparing the design results in the two design systems, the hierarchical design can effectively increase the convergence rate. We further discussed the results obtained from each hierarchical level. It can be observed that the best structure obtained from a high-resolution design space shows a significant improvement by depressing the stress concentration at the crack tip. The best composition was examined through 3D printing. The experimental results show that there is an excellent agreement with our AI design. The design framework proposed in this research can be used as an alternative method for optimization in a complex design system with various constraints. This research can be potentially applied to bionic structural design, nanoengineering, and material design in the future.

The organic-inorganic mixed-ion perovskite materials are one of the promising active materials in the photovoltaic and optoelectronic applications because of their high absorption coefficient, high power conversion efficiency, easy processing and low fabrication cost. The microstructures of the mixed ion perovskites are vital for the device performance. However, experimental characterization of the microstructures of mixed-ion perovskites is still considered to be a challenging task; furthermore, the chemical complexity in conjunction with the huge permutation degrees of freedom makes extensive samplings over the composition space using conventional ab-initio calculations intractable. In the present study, a machine learning-enabled potential model for MA_yFA_1–yPb(Br_xI_1-x)₃ mixed-ion perovskite was trained for extensive exploration over both the composition and permutation space to access the energetics and microstructure properties¹. Subsequent correlation analysis of low energy structures over the composition space allowed us to construct the process-structure-property (PSP) relationship of mixed ion perovskites, namely, to reveal the correlations among chemical compositions, ion mixing energies, chemical short-range orderings, atomic strains as well as the device performance. Our analysis suggest that the lattice distortion is the primary factor impacting material performance – in the high MA/Br concentration regime, strong lattice distortion induces high mixing energy, resulting in phase segregation and introducing defects such as domain boundaries. Hence, mitigating the lattice distortion to retain the single-phase solid solution phase is one necessary condition of the optimal composition of mixed-ion perovskite material. The present study therefore demonstrate the capability of machine-learned potential in evaluating the energetics and microstructures of mixed-ion perovskites, and can be readily extended to studying other chemically complex materials such as the high entropy materials.

¹Chen, H. A., Tang, P. H., Chen, G. J., Chang, C. C., & Pao, C. W. (2021). Microstructure Maps of Complex Perovskite Materials from Extensive Monte Carlo Sampling Using Machine Learning Enabled Energy Model. The Journal of Physical Chemistry Letters, 12(14), 3591-3599.

Lattice thermal conductivity is of central importance in engineering field, as insulator for silicon-on-insulator devices needs sufficiently high thermal conductivity to dissipate heat effectively during operation, for example. A fast and accurate estimation of lattice thermal conductivity can be helpful to product designers. A reliable approach for the theoretical evaluation of lattice thermal conductivity exploits ab initio calculations to decide the harmonic and anharmonic factors of Boltzmann transport equation solution. However, the anharmonic effect requires exhaustive amount of ab initio calculations, which is the most time-consuming process and hence the main bottleneck of this approach.
One of the emerging alternatives is to replace the fully ab initio approach with neural network potential (NNP), which has an accuracy comparable to ab initio calculations at a significantly reduceed computation time. In this study, we employed NNP to calculate harmonic and anharmonic factors to evaluate lattice thermal conductivity. Results were in good agreements with the ab initio results. Three types of datasets for NNP training were tested, where molecular dynamics trajectories outperformed the superposition of phonon modes and random displacements. We then discussed the framework to make this approach efficient and how to obtain reliable and high-precision results. We finally showed the total computation time compared to the fully ab initio approach.

Gaussian process regression has become increasingly popular in machine learning based materials research, quantum dynamics, and other applications. Advantages include the non-parametric nature of the method, and, by ricochet, ease of use with high-dimensional data, as increase in dimensionality does not lead to a rapid increase in the number of non-linear parameters (contrary for example to neural networks) except a small number of hyperparameters. However with very high-dimensional data, especially when some features are subject to uncertainty, commonly used product kernels (of the Matern family) can lead to a failure of the method. We will show how this phenomenon arises and propose possible solutions based on the use of high-dimensional model representations (HDMR). We will demonstrate the advantages of imposing HDMR structure on the entire function model or on the GPR kernel. In particular, we will show how the use of HDMR allows working with very sparse data and obtaining physical insight with an otherwise general ML method. Examples from modeling of kinetic energy densities, potential energy surfaces, and electricity demand prediction will be discussed.

Polycrystals are thermodynamically unstable; hence, their properties are path-dependent. Polycrystals prepared using different methods should exhibit different microstructures and properties. Although most polycrystalline metals are formed via solidification of the liquid phase, there are vast, continuous, thermal processing strategies available during solidification (temperature, cooling rates, etc.). Identifying the optimal approach to obtain a given microstructure—e.g., small average grain size, narrow grain size distribution, high density of coherent twin boundaries, and a high proportion of coincident-site-lattice boundaries—can be quite challenging. Using molecular dynamics simulations, we investigated the grain boundary properties and microstructures of nanocrystalline FCC and HCP metals formed using different strategies. Based on our simulation results, we circumvent conventional trial-and-error methods via reinforcement learning to find the most efficient pathway toward desirable microstructures and properties. Our work shows a path towards tailoring polycrystalline microstructures in a controllable and efficient manner.

2D organic-inorganic Ruddlesden-Popper perovskite material is a promising alternative for optoelectronic and photovoltaic applications because of its long-term stability in ambient conditions relative to its 3D perovskite counterparts. Furthermore, the band gap and exciton binding energies of 2D perovskite materials are directly correlated with the number of anionic inorganic perovskite layers, indicating tunable optoelectronic properties by adjusting the proper stoichiometric ratio of the methylammonium (MA) and butylammonium (BA) spacer cations during synthesis. However, it has been shown recently that the quantum well width distribution is not uniform for selected MA to BA cation ratio¹. Furthermore, it has been reported that 2D Ruddlesden-Popper perovskites with principle number n > 5 are thermodynamically unstable relative to their 3D counterparts, namely, higher 2D perovskite members would segregate into lower members and 3D like-phase². Therefore, comprehensive insights into the stability and microstructure of 2D perovskite, in particular, the distribution of quantum well width are critical for enhancing the performance of 2D perovskite materials. In this work, a machine-learned potential energy model based on the Spectral Neighbor Analysis Potential (SNAP) was trained using images obtained from ab-initio molecular dynamics simulations 2D perovskite of a variety of members. The trained potential energy model possesses high fidelity in both energies and atomic forces relative to ab initio calculations, and the potential model is stable during regular molecular dynamics simulations under canonical ensemble. The potential energy model allows us to perform a series of large-scale atomistic Monte Carlo simulations of 2D perovskite slabs containing several tens of quantum wells to examine the quantum well width distribution and their impacts on the optoelectronic properties of 2D perovskites. Furthermore, this way, it is also possible to extract the properties of an active layer in a working device for the different initial stoichiometric ratio of MA and BA cations during synthesis.

1. Quintero-Bermudez, R. et al. Compositional and orientational control in metal halide perovskites of reduced dimensionality. Nat. Mater. 17, 900–907 (2018).
2. Soe, C. M. M. et al. Structural and thermodynamic limits of layer thickness in 2D halide perovskites. Proc. Natl. Acad. Sci. 116, 58 LP – 66 (2019).

The increasing demands for developing novel chemically complex alloys have imposed a significant challenge to the modeling and simulation community. The mechanical properties of these complex alloys are essential for their applications; however, the length scale required for studying the plasticity of these alloys is beyond the reach of quantum chemistry calculations. In this study, we harnessed the power of machine learning and trained a potential model for the chemically complex Ni/Co/Ti/Zr/Hf alloy system by combining the spectral neighbor analysis potential (SNAP) model and the Bayesian optimization based on a large data set of training images labeled with energies and atomic forces computed from the density functional theory (DFT). We demonstrate that the trained potential model can predict the energies and atomic forces of this chemically complex alloy with high fidelity to the DFT calculations. A series of large-scale (over 10⁵ atoms) molecular dynamics simulations were performed to examine the deformation and dislocation dynamics of both nanowires and bulk structures, and the formation of amorphous, shear band-like region following dislocation pinning was observed, which is in excellent agreement with experiments. Hence, the present study demonstrates that the machine-learned SNAP model yields quantum accuracy even for complex alloy comprised of five constituents, allowing for investigating the plasticity deformation of chemically complex alloys with atomistic insights.

In this work, we present the development and application of the Chebyshev Interaction Model for Efficient Simulations (ChIMES) to the study of hydrazoic acid (HN₃) under detonation. Computational study of HN₃ is challenging due to its ultrafast detonation, i.e. the chemical decomposition to stable products is complete in less than 10 ps, and the system evolves through multiple thermodynamics (ambient and extreme conditions) and electronic (metal and insulator) states. We show that ChIMES, a generalized many-body reactive force field machine-learned to density-functional theory molecular dynamics (DFT-MD) trajectories, is able to retain the accuracy of DFT simulation in describing structural properties and chemistry for a wide range of unreactive and decomposition conditions of liquid HN₃ while increasing orders of magnitude in computational efficiency. The techniques and recipes for MD model creation here allow for direct simulation of nanosecond shock compression experiments and calculation of the detonation properties of materials with the accuracy of Kohn-Sham DFT.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

The atomic structure of glassy materials lacks long-range order; glassy materials do, however, possess short- and medium-range order imposed by nature's thermodynamic drive towards an energetic minimum. So, while the space of local atomic configurations that appear in a glass is in some sense "larger" than one would find in a crystalline material, that space is nonetheless constrained to a manifold by energetics, with the details of that manifold depending on the chemistry of the glass. We generated molecular dynamics samples of a silicate glass and a generic binary metallic glass, extracted the local atomic environments from each, and applied diffusion maps and an autoencoder architecture to identify the low-dimensional manifold underpinning the local structure of both exemplar materials. The resulting structural parameterizations are partially interpretable in terms of intuitive physical quantities, and enable identification of both outliers and reoccurring structural motifs. Comparison of the structural parameterizations between the covalent glass and the metallic glass illuminates the relative local structural complexity of these materials, reflecting the inflexibility of bonds in the covalent glass compared to bonds in the metallic glass. This presentation will cover our methods and analysis, and will look forward to applications of our structural parameterizations in computational statistical mechanics and as structural state variables in mesoscale and continuum models.
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525 (SAND2021-7304 A).

When modeling materials at the atomic scale, achieving a realistic level of complexity and making quantitative predictions are usually conflicting goals. Data-driven techniques have made great strides towards enabling simulations of materials in realistic conditions with uncompromising accuracy.
In this talk I will summarize the core concepts that have driven the extraordinarily fast progress of the field and discuss some of the most promising modeling techniques that combine physics-inspired and data-driven paradigms. I will focus in particular on "integrated" models that combine a prediction of the interatomic potential and that of functional properties, that open up a new dimension to the simulation of materials in realistic conditions. I will present several compelling examples ranging from water to semiconductors and from metals to molecular solids, and indicate the most pressing open challenges in the field

To power microelectronics of IoT (internet-of-things) applications, high-performance microbatteries are critically important. Given their limited size, the three-dimensional design of microbatteries is key to maximize their performance. To design the 3D microbattery architecture following the power-sources requirements of a variety of IoT devices, a computational strategy to identify the target battery architecture is vital. In this talk, we propose a 3D battery optimization system which consists of the automatic geometry generator [1] and highly accurate machine-learning (ML) based performance simulators that utilize a small number of performance data obtained from the continuum simulations. As the ML-based performance simulators evaluate the energies of the 3D battery with much smaller computational cost and with comparable accuracy, as compared with the continuum simulations, it is possible to find the best geometries from a huge number of randomly generated 3D battery geometries. We demonstrate the effectiveness of our approach by designing a set of microbatteries having higher energy than the simplest 3D battery (i.e., an interdigitated plates configuration which is characterized by the shortest ion-transport distance) without reducing the power. Compared with the simplest geometry, one of the designed geometries displayed 1.4 times higher energy at low current density and the other showed 6.5 times higher energy at high current density. The best geometry changes with the applied current, indicating that there exists a particular optimal geometry for each electronic device. This work is an important first step toward the realization of such a tailor-made 3D microbattery design.

[1] Miyamoto et al., iScience, 23, 101317 (2020).

Typically, 3D atomic models are required for physics-based simulations of materials. Within the specific area of polymer science, an automatic engine for generating such polymer models is needed. We have developed a python toolkit named Polymer Structure Predictor (PSP) for suggesting a hierarchy of polymer models, ranging from oligomer/infinite polymer chains to sophisticated amorphous models[1], which can be used downstream in physics-based simulations. The only input of PSP is the simplified molecular-input line-entry system (SMILES) string of the repeat unit of a polymer. The performance of PSP was tested by comparing the generated models with the known experimental data of several polymers. The output files can be directly used with several computational software, such as VASP, ORCA, LAMMPS, and GAMESS, allowing automation for computing properties. PSP has already been used in the polymer version of computational autonomy for materials discovery (CAMD) [2], establishing extensive databases for polymer bandgap and charge injection barriers that power the Polymer Genome platform (www.polymergenome.org).

PSP is expected to benefit a wide number of academic and industrial research activities, realizing automation in polymer discovery. In the context of the emerging polymer informatics ecosystem, this toolkit will substantially reduce efforts to develop extensive databases of computed polymer properties. Besides, simpler visual models of polymeric materials would likely aid in polymer synthesis research, benefiting experimental polymer scientists.

Reference
[1] H. Sahu, T. D. Huan, K.-H. Shen, J. H. Montoya, R. Ramprasad, PSP: A python toolkit for predicting 3D models of polymers, in preparation.
[2] J. H. Montoya, K. T. Winther, R. A. Flores, T. Bligaard, J. S. Hummelshøj, M. Aykol, Autonomous intelligent agents for accelerated materials discovery, Chem. Sci., 2020, 11, 8517-8532.

The ability to readily design novel materials with chosen functional properties on-demand represents a next frontier in materials discovery. However, thoroughly and efficiently sampling the entire design space in a computationally tractable manner remains a highly challenging task. To tackle this problem, we propose an inverse design framework (MatDesINNe) utilizing invertible neural networks which can map both forward and reverse processes between the design space and target property. This approach can be used to generate materials candidates for a designated property, thereby satisfying the highly sought-after goal of inverse design. We then apply this framework to the task of band gap engineering in two-dimensional materials, starting with MoS₂. We show the framework can generate novel, high fidelity, and diverse candidates with near-chemical accuracy. We extend this generative capability further to provide insights regarding metal-insulator transition, important for memristive neuromorphic applications among others, in MoS₂ which is not otherwise possible with brute force screening. This approach is general and can be directly extended to other materials and their corresponding design spaces and target properties.

The task of finding the mechanism and estimating the rate of an atomic rearrangement in a material typically involves finding a minimum energy path and first order saddle point on the energy surface. When such calculations are combined with electronic structure calculations, the computational effort can be large. Furthermore, in order to carry out simulations of long time scale dynamics, all relevant saddle points on the energy rim surrounding a given initial state minimum need to be found, a significant challenge when electronic structure calculations are involved. Machine learning using Gaussian process regression can accelerate these tasks and reduce the computational effort by an order of magnitude [1,2]. An approximate energy surface is generated and most of the iterations in the path optimization and saddle point searches are carried on this faster, approximate surface, which is updated when new electronic structure calculations have been perormed. By using a kernel based on pairwise distances between atoms and introducing a length scale or each type of atom pair, and working with inverse distances in a non-stationary kernel, a robust algorithm has been developed for rate calculations and long time scale simulations [3,4]. Examples of diffusion in and on the surface of solids, as well as reactions at solids surfaces will be presented as examples of such calculations where density functional theory is used to evaluate the atomic forces.


[1] 'Minimum energy path calculations with Gaussian process regression', O-P. Koistinen, E. Maras, A. Vehtari, H. Jónsson. Nanosystems: Physics, Chemistry, Mathematics, 7, 925 (2016).

[2] 'Nudged Elastic Band Calculations Accelerated with Gaussian Process Regression', O-P. Koistinen, F. Dagbjartsdóttir, V. Ásgeirsson, A. Vehtari, and H. Jónsson, J. Chem. Phys. 147, 152720 (2017).

[3] 'Nudged Elastic Band Calculations Accelerated with Gaussian Process Regression Based on Inverse Inter-atomic Distances', O-P. Koistinen, V. Ásgeirsson, A. Vehtari and H. Jónsson. J. Chem. Theo. Comput. 15, 6738 (2019).

[4] 'Minimum Mode Saddle Point Searches Using Gaussian Process Regression with Inverse-distance Covariance Function', O-P. Koistinen, V. Ásgeirsson, A. Vehtari and H. Jónsson. J. Chem. Theo. Comput. 16, 499 (2020)

While compositional disorder can generate exciting properties in perovskites, it is often challenging to predict the formability of such materials using ab initio methods such as density functional theory (DFT). Target-driven discovery of disordered perovskite materials can be accelerated by applying experimental data powered machine learning methods. Here, we demonstrate that an unsupervised deep learning strategy can find fingerprints of disordered materials that embed perovskite formability and underlying crystal structure information by learning only from the chemical composition, manifested in (A_1-xA’_x)BO₃ and A(B_1-xB’_x)O₃ formulae. The unsupervised model learns the crystal system of disordered solid solutions at a 72% success rate even though no information on the crystal structures was originally supplied to the model. Material fingerprints extracted by the model facilitates inverse exploration of promising perovskites based on similarity investigation with known materials, identified as analogical materials discovery. Quantifying materials analogies can further provide insights on possible phase transitions and significantly reduce the computational time required by DFT in predicting the properties of disordered materials. We demonstrate analogical materials discovery can also assist in finding a plausible experimental geometry required to initialise DFT computations by modelling six novel lead-free perovskites.

The presence of multiple elements in large proportions poses a major computational challenge to understand and predict defect properties in high entropy alloys (HEAs) using conventional atomistic methods. To overcome this challenge, we have developed a machine learning (ML) model to predict the defect properties such as vacancy formation energies, migration energies, and stacking fault energy (SFE) in HEAs. Using the support vector machine model and local nearest-neighbor information of only the binary constituents’ alloys, we predict the defect energies in ternary, quaternary, and quinary alloys with high level of accuracy. Similarly, using linear regression and bond lengths, we predict SFEs in HEAs. Our scheme utilizes density functional theory and atomistic simulations database of binary alloys fed to ML models. The relative importance of various descriptors, both electronic and atomic, and the accuracy of various algorithms are discussed. The work is performed in Ni-based HEAs towards the development of high-temperature materials for extreme environments. A key benefit of this approach is that once the binary database is built and the model is trained, defect energies can be predicted with little computational expense thereby bypassing a large number of calculations that would be otherwise needed every time a new composition is discovered in the HEA phase space.

Gaining transformative insight into dynamic materials processes at the nanoscale is extremely desirable but has largely remained elusive. Emerging characterization techniques such as coherent imaging methods (e.g. Ptychography), nano-CT and Lorentz TEM are providing an unprecedented view of materials structure and properties at the nanoscale. However, these methods that rely on algorithmic inversion of measured data are not typically suited to in-situ or operando imaging. This is because the successful inversion of raw data requires enormous online computing power which is projected to increase even more with faster detectors and next generation x-ray and electron sources (> PFLOPS). I will describe our work in applying AI to both accelerate current methods and create new imaging modalities from various X-ray and electron imaging techniques. Our AI-enabled methods are hundreds of times faster than traditional algorithms used for image reconstruction, opening up the prospect of real-time 3D imaging at the nanoscale.

Materials-by-design is new paradigm to develop novel high-performance materials. However, finding materials with superior properties is often computationally or experimentally intractable because of the astronomical number of possible combinations in the design space. Especially for composite materials, the heterogeneity and structural complexity really hinder us from calculating materials properties and searching for optimal designs at low costs. Fortunately, with the recent advances in artificial intelligence (AI) or machine learning (ML), new approaches and perspectives are provided to solve the puzzles. This study is proposed to leverage deep learning methods to bridge the gap between a material’s microstructure – the design space – and the physical performance. Specifically, it will answer research questions about how to use AI for fast predictions on physical fields of composite materials like stress or strain directly from the input materials geometry. Using a game-theory based conditional generative adversarial networks (cGANs), an end-to-end deep learning approach are developed to give accurate predictions on not only physical fields data but also derivative global properties such as modulus and recoverability. Furthermore, the proposed approach offers extensibility by predicting complex materials behaviors regardless of component shapes, boundary conditions and geometrical hierarchy, providing new perspectives of performing physical modeling and simulations. The method outperforms some conventional numerical methods such as finite element analysis (FEA) and is able to vastly improves the efficiency of evaluating physical properties of hierarchical materials directly from the geometry of its structural makeup. In addition, the idea of geometry-to-field translation can also be applied to other areas in the sciences, such as density functional theory fields, fluid mechanical fields, or electromagnetism.

The inverse elasticity problem of identifying elastic modulus distribution based on measured displacement/strain fields plays a key role in various non-destructive evaluation (NDE) techniques used in geological exploration, quality control and medical diagnosis (e.g., elastography). Conventional methods in this field are often computationally costly and cannot meet the increasing demand for real-time and high-throughput solutions for advanced manufacturing and clinical practices. Here, we propose a deep learning (DL) approach to address this challenge. By constructing representative sampling spaces of shear modulus distribution and adopting a conditional generative adversarial net (cGAN), we demonstrate that the DL model can learn the high-dimensional mapping between strain and modulus via training over a limited portion of the sampling space. The proposed DL approach bypasses the costly iterative solver in conventional methods and can be rapidly deployed with high accuracy, making it particularly suitable for applications such as real-time elastography and high-throughput NDE techniques.

Body-centered cubic (bcc) refractory multicomponent alloys are of great interest due to their remarkable strength at high temperatures. Optimizing the chemical compositions of these alloys to achieve a combination of high strength and room-temperature ductility remains challenging. We first analyzed the electronic structures of crystalline defects in BCC refractory alloys. The interactions between solute atoms and crystalline defects such as vacancies, dislocations, and grain boundaries are essential in determining alloy properties. Here we present a general linear correlation between two descriptors of local electronic structures and the solute-defect interaction energies in binary alloys of body-centered-cubic (bcc) refractory metals (such as W and Ta) with transition-metal substitutional solutes. One electronic descriptor is the bimodality of the d-orbital local density of states for a matrix atom at the substitutional site, and the other is related to the hybridization strength between the valance sp- and d-bands for the same matrix atom. For a particular pair of solute-matrix elements, this linear correlation is valid independent of types of defects and the locations of substitutional sites. These results provide the possibility to apply local electronic descriptors for quantitative and efficient predictions on the solute-defect interactions and defect properties in alloys. At the second step, with these local/global electronic descriptors and a simple bond-counting model, we developed regression models to accurately and efficiently predict the unstable stacking fault energy (γ_usf) and surface energy (γ_surf) for refractory multicomponent alloys. We performed first-principles calculations with the special quasi-random structure (SQS) method to predict γ_usf and γ_surf for 106 individual binary, ternary and quaternary bcc solid-solution alloys with constituent elements among Ti, Zr, Hf, V, Nb, Ta, Mo, W, Re, and Ru. Then we developed surrogate models based on statistical regression to accurately and efficiently predict γ_usf and γ_surf for refractory multicomponent alloys in the 10-element compositional space. Building upon binary and ternary data, the surrogate models show outstanding predictive capability in the high-order multicomponent systems. The ratio between γ_usf and γ_surf can be used to populate a model of intrinsic ductility based on the Rice model of crack-tip deformation. Therefore, using the surrogate models, we performed a systematic screening of γ_usf, γ_surf, and their ratio over 112,378 alloy compositions to search for alloy candidates that may have enhanced strength-ductility synergies. Search results were also validated by additional first-principles calculations and reported experimental results.

Data driven machine learning methods in materials science are emerging as one of the promising tools for expanding the discovery domain of materials to unravel useful knowledge. The power of these methods will be illustrated by covering three major aspects, namely, development of prediction models, establishment of hidden connections and scope of new algorithmic developments. For the first aspect, we have developed accurate prediction models for various computationally expensive physical properties such as band gap, band edges and lattice thermal conductivity. The prediction model for band gap and band edges are developed on 2D family of materials -MXene, which are very promising for a wide range of electronic to energy applications, which rely on accurate estimation of band gap and band edges. These models are developed with GW level accuracy, and hence can accelerate the screening of desired materials. For the lattice thermal conductivity prediction model, an exhaustive database of bulk materials is prepared. By employing the high-throughput approach, several ultra-low and ultra-high lattice thermal conductivity compounds are predicted. The property map is generated from the high-throughput approach and four simple features directly related to the physics of lattice thermal conductivity are proposed. For the second aspect, we have connected the otherwise independent electronic and thermal transport properties. The role of bonding attributes in establishing this relationship is unraveled by machine learning. An accurate machine learning model for thermal transport properties is proposed, where electronic transport and bonding characteristics are employed as descriptors. In the third aspect, we have proposed a new algorithm to develop highly transferable prediction models. The approach is named as guided patchwork kriging, which is applied for prediction of lattice thermal conductivity.
Ref: Chem. Mater. 31, 14, 5145 (2019), J. Mater. Chem. A, 8, 8716 (2020), Chem. Mater. 32, 15, 6507 (2020)

We present two methods to predict the crystal structure, given the chemical composition, by combining machine learning and high-throughput density functional theory (DFT) methods.
In our work, initially, a classification model predicts the point groups of the given stoichiometries. Based on the predicted point group, a series of high-throughput DFT calculations determine the ground state of non-centrosymmetric crystal structures. Using this framework, we also extended our analysis to predict new ferroelectric compounds. In addition to the ground state structure, identifying metastable polymorphs that might get stabilized by controlling the synthetic conditions is of great importance as they can exhibit different functionalities. Then, using the example of bismuth ferrite, we illustrate how crystal structure, decomposed into distortion modes, can be implemented as a feature to explore the energy surface leading to the identification of metastable polymorphs. Therefore, we studied BiFeO₃ as a multifunctional compound with a rich low-energy phase space. A training set is constructed by mapping the phase space based on possible distortion modes starting from the cubic perovskite structure. A machine learning model is built using the generated training set predicting new metastable phases of BiFeO₃.

Many real-world systems, such as moving planets, can be considered as multi agent dynamical systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture. Understanding and predicting the dynamics based on observed trajectories of objects become a critical research problem in many domains. In this talk, we propose to treat dynamical systems as evolving graphs, and design graph neural network (GNN)-based ODEs to approximate system dynamics via the observed signals. In particular, we provide solutions to two challenging scenarios. First, we propose to learn system dynamics from irregularly-sampled partial observations with underlying graph structure. To tackle the above challenge, we present LG-ODE, a latent ordinary differential equation generative model for modeling multi-agent dynamical system with known graph structure, which is the first Graph ODE model in this direction. Second, we propose to learn system dynamics where both node features and edges are evolving. We present a dual Graph ODE, CG-ODE, where both node and edge dynamics are modeled. Experiments on motion capture, spring system, charged particle datasets, COVID-19, and simulated social dynamical systems demonstrate the effectiveness of our approaches.

Multicrystalline Si (mc-Si) is widely used as a material for solar cells. Mc-Si can be usually produced at a low cost by the directional solidification (DS) method. However, many crystal defects exist in mc-Si ingot and among them, especially the dislocation cluster leads to lower solar cell efficiency than that of monocrystalline Si solar cells. For the growth of multicrystalline materials, the mechanism of crystal defect generation has not yet been elucidated due to the complexity of the structure caused by the diversity of crystal orientations and grain boundaries. We aim to elucidate the universal mechanism by combining experiments, theories, simulations, and machine learning using realistic data-driven models collected from actual multicrystals. In this study, a realistic 3D mc-Si model including the dislocation cluster generation region was created by image processing and machine learning on a large amount of PL and optical images collected from actual mc-Si ingots. In addition, finite element stress analysis was performed on the model to investigate the effect of stress on dislocation cluster generation.
We used high-performance (HP) mc-Si in this research. The ingot was sliced into 729 wafers of 156 mm x 156 mm x 180µm. First, Photo Luminescence (PL) images of the sequentially numbered as-slice wafers on the top of the ingot were taken. From the PL image, the distribution of dislocation clusters in HP mc-Si ingot is obtained [1], and taking a look at this distribution, we determined the 9.18 mm×9.18 mm×3.60 mm region to be modeled, in which a dislocation cluster is generated. Then, the wafers were alkali etched and taken their optical images. By taking the optical images while changing the position of the light source, a vector reflecting the crystal orientation can be obtained for each pixel. These vectors were used to analyze crystal orientation by originally developed crystal orientation estimation model using machine learning [2], and crystal grain segmentation at the region by Mean Shift Clustering. Finally, the mc-Si model for finite element stress analysis was then created by stacking sequentially numbered sections with corrections. The model consists of 53816 nodes and 48373 hexahedral elements, and each grain is given the orientation of a representative point obtained by orientation prediction. Then, finite element stress analysis was performed on this model. From the distribution of dislocation clusters, we expect that dislocation clusters are generated during crystal growth, not in the cooling process. So the conditions for the analysis were the temperature and stress that reproduced the inside of the ingot during crystal growth by the DS method.
As a result, finite element stress analysis was successfully performed on the realistic model which reproduces the mc-Si structure well, and we could obtain the stress tensor at each node in this model. From these tensors, various analysis results can be obtained, such as the distribution of Mises equivalent stress. From the distribution of Mises equivalent stress, it was found that the stresses were concentrated at grain boundaries and grain boundary triple points as expected. On the other hand, there is no stress concentration near the dislocation cluster generation point. Therefore, the Mises equivalent stress is not likely to contribute to dislocation cluster generation. In the future, the stress tensors obtained from the analysis results should be used to investigate the resolved shear stress at the slip plane, which has a large impact on dislocation generation and to discuss its effect on the generation of dislocation clusters.
[1] Y. Hayama et al., Solar Energy Mat. and Solar Cells 189, pp. 239-244 (2019).
[2] T. Kojima et al., Abstr. of 68th JSAP Spring meeting, 2021, 18a-Z32-9.

Strategies combining high-throughput (HT) and machine learning (ML) to accelerate the discovery of promising new materials have garnered immense attention in recent years. The knowledge of new guiding principles is usually scarce in such studies, essentially due to the “black-box” nature of the ML models. Therefore, we devised an intuitive method of interpreting such opaque ML models through SHapley Additive exPlanations (SHAP) values and coupling them with the HT approach for finding efficient two-dimensional (2D) water splitting photocatalysts. We developed a new database of 3099 2D materials consisting of metals of various oxidation states connected to six ligands in an octahedral geometry, termed the 2DO database. The first tier of the HT scheme screened 2DO materials with high thermodynamic and dynamic stabilities. The ML models were constructed using a combination of composition and chemical hardness-based features to gain insights into the thermodynamic and overall stabilities. Most importantly, it distinguished the target properties of the isocompositional 2DO materials differing in bond connectivities, since it combines the advantages of both elemental and structural features. The interpretable ML regression, classification, and data analysis lead to a new hypothesis that the highly stable 2DO materials follow the hard and soft acids and bases (HSAB) principle. The most stable 2DO materials were further screened based on suitable band gaps lying within the visible region and band alignments with respect to standard redox potentials using the GW method, resulting in 21 potential candidates. Moreover, HfSe₂ and ZrSe₂ were found to have high solar-to-hydrogen efficiencies reaching their theoretical limits. The proposed methodology will enable materials scientists and engineers to formulate predictive models, which will be accurate, physically interpretable, transferable, and computationally tractable.

Composites or heterogeneous materials have a wide range of applications in the fields of aerospace, structural materials, biomedical, energy conversion devices, high-temperature materials, etc. But the effective properties of composites, in particular, toughness and strength are hard to predict as a function of their constituent properties. By definition, heterogeneous materials contain different shapes, sizes, compositions, and material or phase distributions at different length scales, making iterative experiments inefficient, time-consuming, and expensive to use for this purpose. In this work, the toughness of heterogeneous brittle material is investigated using a combination of continuum scale simulations and machine learning techniques. Our goal is to predict the configurations (or different structural and material parameters) of the composite that optimize its effective toughness. The continuum simulations are based on the variational phase-field modeling of fracture, and we applied the novel surfing boundary condition, which allows adequate time for the crack to propagate, enabling evaluation of the critical energy release rate or toughness. In particular, we focus on understanding the criteria for deflection vs. penetration for a number of composite configurations and identify the structural or material descriptors that define the criteria. Using the descriptors, we develop supervised machine learning models for predicting the toughness of the composite. The models are trained using data sets, collected from continuum simulations and are used to ascertain the toughness-structure correlation for a number of unexplored variants of the configurations. This talk will discuss the findings and highlight the need for applying machine learning tools to predict the toughness of a composite, for an arbitrary choice of structural and material parameters.

There are increasing interests in using machine-learning (ML) interatomic potentials in molecular dynamics (MD) simulations to explore local structure and chemistry that governs key physical and chemical properties of materials for energy applications. A number of methodologies has been developed to train ML potentials (e.g., neural network potential, Gaussian approximation potential, etc.) using local atomic environments in structure data as feature inputs and energies, forces, and/or virial tensors of the structures as outputs. The training data are often collected from highly accurate ab-initio simulation and therefore the trained and validated ML potentials are capable of performing simulations with quantum-level accuracy while achieving thousands of times faster computational speed than ab-initio calculations. In this talk, we will discuss our recent development of ML interatomic potentials based on artificial neural network[1,2] to study ion transport phenomena in highly-disordered, garnet-type LLZO solid-electrolyte and establishment of local correlation between Li-ion transport kinetics and the structural and chemical features of disordered LLZO. The training data was collected from AIMD simulations at a wide range of temperatures and our developed ML potentials are able to predict energies and forces for both crystalline and amorphous LLZO with DFT level of accuracy. Our predicted elastic properties, ion diffusivities, radial distribution functions, and vibrational characteristics of atoms also show excellent agreement with those calculated by ab-initio simulations. Based on similar methodology, we will briefly discuss the development of ML force field for the LLZO/LiCoO₂ interfaces that are relevant for all-solid-state battery technologies, and illustrate how the ML force field can be applied to understand Li-ion transport at the interfaces and to probe the structural and chemical instabilities at the interfaces.

[1] A. Singraber, J. Behler, and C. Dellago, J. Chem. Theory Comput. 2019, 15, 1827−1840.
[2] A. Singraber, T. Morawietz, J. Behler, and C. Dellago, J. Chem. Theory Comput. 2019, 15, 3075−3092.

Acknowledgement:
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract number DEAC52-07NA27344. Authors acknowledge funding support from the Vehicle Technologies Office, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy and computational resource support from the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.

Materials informatics datasets and computational resources are growing rapidly. While machine learning offers a promising set of generic tools for extracting insight from large volumes of data, these tools are not inherently good at generalizing to new data. For this reason, tools that enable a seamless integration of physically informed priors with machine learning are crucial for building data-driven models that generalize in a useful way. I will talk about our recent work in this direction where we combine differentiable atomistic simulations with graph neural networks and meta-learning, with applications to materials modelling, optimization, and discovery.