Session R12: Computational Materials Design - Machine Learning

Extensive deep neural networks for 2d materials

We present a procedure for training and evaluating a deep neural network which can efficiently infer extensive parameters of arbitrarily large systems, doing so with O(N) complexity. We use a form of domain decomposition for training and inference, where each sub-domain (tile) is comprised of a non-overlapping focus region surrounded by an overlapping context region. The relative sizes of focus and context are physically motivated and depend on the locality length scale of the problem. Extensive deep neural networks (EDNN) are a formulation of convolutional neural networks which provide a flexible and general approach, based on physical constraints, to describe multi-scale interactions. They are well suited to massively parallel inference, as no inter-thread communication is necessary during evaluation. Example uses for graphene, hexagonal boron nitride (hBN), as well as their 2d alloys are demonstrated.   

What can one learn about material structure given a single first-principles calculation?

We extract a variable X from electron orbitals Psi_nk and energies E_nk in the parent high-symmetry structure of a wide range of complex oxides (perovskites, rutiles, pyrochlores, cristobalites). Even though X was calculated in the parent structure we show that its value dictates material's (potentially lower-symmetry) ground state structure. We propose using Wannier functions to extract concealed variables such as X both for material structure prediction and for high-throughput approaches.   

Utilizing Convolutional Neural Networks to Predict Properties of Inorganic Compounds

Incorporating structural information in machine learning (ML) models of materials properties has been shown to improve the predictive accuracy of the resulting models. In this study, we demonstrate a novel use of convolution neural networks (CNN) to extract information about the crystal structure of inorganic compounds. The CNN-extracted structural properties are then combined with composition-dependent elemental properties to form the material representation for our ML model. We illustrate this method using datasets consisting of high-throughput density functional theory (DFT) data of formation energies of compounds. We critically examine the accuracy of different representations of the compound crystal structure as input for the CNN. We train ML models on ~200,000 entries taken from the Open Quantum Materials Database and evaluate the predictive accuracy on a test set of 20,000 compounds. We compare the predictive accuracy of our CNN model for formation energies with other recently-proposed structural representations, e.g., those based on Voronoi tessellation.
  

Machine Learning and Materials Discovery

The relative accuracy and speed of density functional calculations have transformed computational materials science and enabled the creation of large databases of computed materials properties. But true "materials by design" or in-silico materials discovery has not yet been realized, though there are isolated success stories. It seems likely that into make computional discovery of new materials possible, or to discover materials engineering routes to improve already-deployed materials, a brute force approach will not be practical---some other paradigm will be required. Machine learning, so successful in some other application areas, is an intriguing and promising idea, but there are hurdles to overcome. There are two important differences between the standard machine learning problems of image recognition, voice recognition, etc., and materials prediction. In the first instance, we cannot afford the typical accuracy tradeoff---materials predictions are not useful without meeting a high accuracy target; the energy difference of competing phases is often very small, requiring high fidelity in the models. The second difference is the amount of training data---we don't have "big data''. How do we move forward? In this talk I will review the state of the art in this emerging discipline and show some results from BYU's Materials Simulation Group efforts in this area.   

Accelerated Discovery of Quaternary Heusler with High-Throughput Density Functional Theory and Machine Learning

Discovering many-component crystalline materials is a complex task owing to the large composition space. Here, we employ machine learning to find 55 previously unknown, thermodynamically stable quaternary Heusler (QH) compounds in a search space of over 2M compounds after performing only 303 Density Functional Theory (DFT) calculations. Our ML model predicts the stability of a material based on attributes derived from the Voronoi tessellation of its crystal structure, and we trained the model using 450k entries from the OQMD. We find that including data from many types of crystal structures when training ML models leads to better accuracy than when using a carefully curated dataset containing only a single family of material (i.e., only Heuslers). This means that large datasets, such as OQMD, are particularly valuable for materials discovery. We also find that the models trained using our method perform 10x better at identifying new stable QHs than existing heuristics and about 30% better than other machine learning methods. Given the fact that our method does not require a specially-developed training set and its excellent performance, we propose it can be used to discover materials with many other types of crystal structures.   

Statistical Learning of Kinetic Monte Carlo Models of Complex Chemistry from Molecular Dynamics

Complex chemical processes, such as the decomposition of energetic materials or the adsorption of water on titania nanoparticles, are typically studied using large-scale molecular dynamics (MD) simulations. These computations may involve thousands of atoms forming hundreds of molecular species and undergoing thousands of reactions. It is natural to wonder whether this wealth of data can be utilized to build more efficient, interpretable, and predictive models. In this talk, we will use techniques from statistical learning to develop a framework for constructing kinetic Monte Carlo (KMC) models from MD data. We will show that our KMC models can not only extrapolate the behavior of the chemical system by as much as an order of magnitude in time, but can also be used to study the dynamics of entirely different chemical trajectories with a high degree of fidelity. Importantly, our KMC models require only minutes to simulate systems and timescales that typically require weeks using MD. The ability of our trained KMC models to quickly extrapolate to different chemistries suggests a path forward for accelerating the simulation of novel materials.   

In Situ Multiobjective Genetic-Algorithm Workflow for Training and Uncertainty Quantification of Reactive Molecular-Dynamics Force Fields

The conventional approach of training a ReaxFF reactive force field parameters by fitting to a quantum-mechanical database is tedious and time consuming, and requires a considerable degree of prior experience. For fast and automated development of ReaxFF force fields, we propose a dynamic approach of directly fitting ReaxFF based reactive molecular dynamics (RMD) trajectories against a quantum molecular dynamics (QMD) trajectory on the fly. Here, we present a scalable in situ MOGA (iMOGA) workflow that eliminates the file I/O bottleneck involving file base communication between RMD, QMD and genetic algorithm computations, using inter-process communications but with minimal modification of the original parallel RMD code. The iMOGA workflow has been used to tune ReaxFF parameters for the sulfidation of MoO₃ by H₂S, while providing uncertainty quantification (UQ) of the force field.   

3D Scattering Transform Representation of Materials: From Molecules to Crystals

Computational materials scientists have generated huge databases of quantum accurate calculations for materials and their properties. These large databases have been mined to find correlations between structure and macroscopic properties in order to find new interesting materials. Machine learning potentials are gradually replacing more expensive first-principles calculations as surrogate models to obtain information on stability and properties of a material based on the microscopic arrangement of its atoms. In order for these machine learning potentials to be effective, the representations must be invariant to permutation, isometric transformations, and stable to deformation. In this talk, we present a 3D scattering transform representation that satisfies these properties. We apply this representation to molecules and crystal systems to show the robustness of this representation.   

Determining Nanoscale Structures from Pair Distribution Function and Density Functional Theory via Multi-Objective Optimization

The structures of nanoparticles are challenging to determine. Various techniques have been proposed, each with its own limitations. Computational predictions require approximations and extensive sampling to find low-energy structures, and lowest-energy structures are not guaranteed. Experimental characterization, such as pair distribution function (PDF), provides information on the specific structure, but the inversion of such data is non-trivial.

Combining experimental and computational data into one framework to solve for nanostructures can reduce or eliminate these difficulties. We report our development of a framework that uses multi-objective genetic algorithm to optimize the structure by simultaneously minimizing the energy calculated by density functional theory (DFT) and the PDF residual. We benchmark this framework on gold nanoclusters, compare them to a one that minimizes one data type (i.e. the energy or PDF only), and show that the multi-modal optimization approach is more often able to find the target structures.   

GAtor: A First Principles Genetic Algorithm for Molecular Crystal Structure Prediction

We present the implementation of GAtor, a massively parallel, first principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and performs local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented by using machine learning to perform clustering on the fly and then employing a cluster-based fitness function. The best structures generated by GAtor are re-relaxed and re-ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. The experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z’=2 structure with P1bar symmetry and a scaffold packing motif, which has not been reported previously.
  

Bayesian optimization of layered transition metal dichalcogenide hetero-structures

Vertical hetero-structures made from stacked monolayers of transition metal dichalcogenides (TMDC) are promising candidates for the next generation optoelectronic and thermoelectric devices. Identification of optimal layered materials for specific applications requires estimation of several physical properties, including electronic band structure and thermal transport coefficients. However, exhaustive screening of the material structure space using ab initio calculations is currently outside the bounds of existing computational resources. Furthermore, the functional form of how each physical property relates to the structures is often unknown, making gradient-based optimization unsuitable. Here, we present a model based on the Bayesian optimization to expedite the discovery of optimal N-layered hetero-structures. As specific exmaples, we consider the electronic band gap and thermoelectric figure of merit. With high probability, the Bayesian optimization discovered the optimal hetero-structure after evaluation of only ~15% of all possible 3- or 4-layered structures.   

Genetic Algorithms and DFT in the Search for Novel Stable and Metastable Crystal Structures of the Uranium Oxides

The existence of non-stoichiometric uranium oxides is well known. However, many of these possible structures are not well-characterized experimentally because traditional analysis tools fail to easily characterize the structure of systems with low or no translational symmetry. Even stoichiometric uranium oxides such as U₃O₈, U₄O₉, and UO₃ exhibit complex crystal phases when varying temperature and pressure. Using a combination of genetic algorithms and DFT calculations, we have searched the uranium–oxygen system for novel stable and metastable UO_x states. Several structure prediction codes already exist that implement genetic algorithms for this purpose, such as the Genetic Algorithm for Structure Prediction and the Universal Structure Predictor: Evolutionary Xtallography (USPEX) codes. USPEX can do additional searches for metastable states from a well-converged starting structure using an evolutionary metadynamics algorithm. By further calculating experimental observables such as the vibrational spectra of low-energy predicted structures, direct comparisons to experimentally obtained data of unknown compounds can be made, and unknown experimental samples can potentially be assigned to a predicted crystal structure.   

Prediction of novel metallic carbon and silicon allotropes using an inverse material design method

Carbon has a rich variety of structural allotropes due to its ability of forming sp, sp², and sp³ hybridized bonds. Graphene, a single layer of graphite, consists of all-sp² bonds and exhibits a semimetallic band structure with Dirac points. The cubic diamond phase of Si is semiconducting and this material is widely used as the key element in the semiconductor technology. Although many metastable forms of Si have been observed, no metallic phase at ambient conditions has been reported to date. In this work, we report novel metallic carbon and silicon allotropes using an inverse material design method based on evolutionary global optimization and first-principles DFT calculations. The new carbon allotrope, termed m-C₈, consists of five-membered rings with sp³ bonding interconnected by sp²-bonded graphitic carbon networks. Analyzing the electronic band structure, we identify that m-C₈ belongs to the class of topological nodal line semimetals. The new Si allotrope, termed P6/m-Si₆, contains open channels embedded in a simple hexagonal lattice. We find that the P6/m-Si₆ clathrate is superconducting with the critical temperature of about 12 K at zero pressure.