Session X43: Computational design and discovery of novel materials VII: Machine learning and high throughput computing

Density Functional Theory Calculations on Surface Oxygen Vacancy Formation in Metal Oxides

Properties of materials may be significantly changed from intrinsic ones by making small physical and chemical changes in the form of defects. As a result, various point and extended defects are intentionally introduced to govern their chemical reactivity, catalytic, electrical, optical, and mechanical properties. One mechanism important in catalysis is the Mars-Van Krevelen mechanism that is frequently encountered. An example is where O vacancy sites on a metal oxide catalyst surface acts as the reaction site.

Accurate calculation of the surface vacancy formation energy based on first principles calculations require calculation of a surface model and is much more computationally expensive than a bulk calculation. Catalysts typically require a certain physical quantity to be within a certain range, hence rapid judgement of whether a candidate material is viable or not based on quantities (descriptors) that are easy to calculate can significantly accelerate the screening process. We report on correlations between descriptors that can be calculated at low cost and the O vacancy formation energy of various insulating binary oxide materials [Hinuma et al., J. Phys. Chem. C 2018, 122, 29435] as well as spinel oxides containing zinc.   

Genarris 2.0: A Random Structure Generator for Molecular Crystals

Genarris 2.0 is an open-source Python code, parallilized with mpi4py, that performs configuration space screening of molecular crystals by random structure generation. It may be used for generating initial populations to seed other structure search algorithms (such as genetic algorithms) or for generating datasets to train machine learning models. The target unit cell volume is estimated from the single molecule structure by a machine-learned model trained on data from the Cambridge Structural Database (CSD). Crystal structures are then generated in all space groups compatible with the requested number of molecules per cell (Z) with one molecule in the asymmetric unit (Z’=1), including those with special Wyckoff positions. To avoid unphysically close intermolecular distances, structures undergo a cascade of three increasingly rigorous checks. Special settings are applied for strong hydrogen bonds, which are automatically detected. Once an initial dataset of several thousand structures is generated, a smaller dataset may be selected based on quality and diversity criteria via user-defined workflows. For clustering Genarris uses the affinity propagation machine learning algorithm with a relative coordinate descriptor (RCD) or a radial symmetry function (RSF) representation.   

Exploring the quantum chemical space of small molecules: QM7-X database

Robust and extensive databases of molecular properties are required to enable rational exploration of chemical space. Most databases created so far either include only equilibrium structures of molecules or do not use sufficiently high level of quantum mechanics. Here, we introduce the QM7-X database created with the goal of sampling the vast chemical space for small organic molecules. As basis for QM7-X, we used all molecules within the GDB7 database. All possible enantiomers and diastereomers were also added. Then, to have a sufficient sampling of the potential energy surface, we have considered 100 non-equilibrium conformations around every conformer of a molecule, producing a database of approximately 4.2 million structures in total. Several physicochemical properties were subsequently computed by performing quantum mechanics calculations using FHI-AIMS code at the PBE0-MBD level of theory. As a first attempt for predicting molecular properties, we have applied neural networks in the form of the SchNet package. We also demonstrate that the exploration of the QM7-X chemical space breaks traditional textbook notions of chemical correlations and enables building robust and transferable machine learning models for molecular property prediction.   

Matching Crystal Structures Atom-to-Atom: Applications to Phase Transitions and Interface Structures

Finding an optimal match between two different crystal structures underpins many important materials science problems including describing solid-solid phase transitions, developing models for interface and grain boundary structures, finding suitable substrates and their orientation, etc. We designed and implemented an algorithm that tackles this problem by finding the atom-to-atom map and alignment that minimizes a chosen distance function. We demonstrate its capacity to describe transformation pathways of several solid-solid transformations. In particular we show its ability to seamlessly predict important experimentally observed characteristics of the martensitic transformation of steel. Next, we study several interfaces and show our method's relevance in predicting interfacial planes and their orientation relationships. Finally, from our findings, we define a rigorous metric for measuring distances between crystal structures and use it as a tool to screen the Inorganic Crystal Structure Database.   

Predicting h-BCN Geometric Structures Using Clustering and Regression Methods

Despite the fact that hexagonal graphene-like boron–carbon–nitrogen (h-BCN) monolayer, a synthesized material that has received a great deal of attention thanks to its intriguing properties and its potential application, there is no consensus on its geometric structure. We report here results of our machine learning approach that utilizes clustering and neural networks to find the lowest energy structure of h-BCN. Our dataset consists of 300 randomly generated h-BCN structures, optimized using density functional theory based calculations. To characterize the atomic environment of the atoms, a pattern recognition scheme based on neighbors was developed. We found that our model accurately predicts the total energy of h-BCN structure with a R-squared score as high as 0.85, depending on the number of k-means clusters used. We will also discuss the improvement of our predictions using a deep neural network.   

Towards a Crystalline Organic Superconductor Database

A database of layered organic crystalline materials containing structural information, experimentally determined properties, and electronic band structure is proposed. Layered organic crystals have a rich electronic phase diagram and exhibit numerous electronic ground states including traditional and unconventional superconductivity, charge and spin density waves, Dirac points, and spin liquid states. The proposed database will be a versatile tool for scientists studying quantum materials and will pave the way towards new discoveries and materials via machine learning methods. We will present a computer algorithm for analyzing the crystal structure of layered organic crystals and storing the extracted structure parameters in the database. The algorithm analyzes molecular conformation, dimerization, packing types, and intermolecular interactions of cations that form the conductive layer of these materials. We will discuss the challenges of inputting experimentally determined material properties from scientific articles into the database, and the best methods to do it. We will also show a Python based system for automatically initializing, executing, and analyzing WIEN2k DFT calculations for materials in the database.   

Accelerated enumeration of derivative structures using zero-suppressed binary decision diagram

The enumeration of “derivative structures” [1], which are unique substitutional atomic configurations derived from a given parent lattice, plays an essential role in searching for the ground states in multi-component systems. The possible size of supercells to enumerate the derivative structures, however, is limited because the number of the derivative structures increases exponentially as the number of sites in a substitutional lattice increases. In the present study, we apply a compressed data structure of the zero-suppressed binary decision diagram (ZDD) [2] to enumerate the derivative structures much more efficiently. We also employ an efficient procedure [3] to build the ZDD representing the derivative structures without listing all substitutional structures. The present study shows simple applications of the procedure to enumerate the derivative structures for the face-centered cubic and hexagonal close-packed parent lattices in binary, ternary, and quaternary systems. The present procedure with the ZDD should significantly contribute to computational approaches based on the derivative structures.
[1] G. L. W. Hart and R. W. Forcade, Phys. Rev. B 77, 224115 (2008).
[2] S. Minato, DAC ’93 (1993).
[3] T. Horiyama, et al., CCCG (2018).   

Multifidelity Learning and Statistical Analysis of Material Properties

There are many examples of materials data where the coexistence of two types of datasets occur: a smaller, higher-fidelity (higher accuracy) dataset, and a larger, lower-fidelity dataset. Here, we investigate a statistical modeling approach for materials properties in these cases of varying fidelity. Kriging based multi-fidelity learning is an approach suited to these cases, and we demonstrate its usefulness by applying it to model and predict the chemical properties of compounds in the Open Quantum Materials Database (OQMD). Specifically, we focus datasets of DFT-calculated bandgaps, and consider a case of high-fidelity data from computationally expensive hybrid HSE calculations and low-fidelity PBE GGA calculations. The multifidelity model is trained on a database containing 1100 HSE bandgaps and combined with results from the OQMD which contains a much larger set of PBE bandgaps. We demonstrate the utility of this multifidelity approach in predicting HSE bandgaps for all materials in OQMD, analyze the predicted results for various material classes, and compare the multifidelity approach with multiple single-fidelity machine learning models trained on the same dataset.   

Symbolic Regression in Materials Science

One of the fundamental research objectives of materials science is to design new materials with optimal performance. Typical machine learning models could be powerful predictors but not ideal in terms of interpretability. Here we present on an alternative to machine-learning models: symbolic regression (SR), which simultaneously searches for the optimal form of a function and set of parameters to the given problem, and is a powerful regression technique when little if any a-priori knowledge of the data distribution is available. We present how SR can learn the Landau free energy expansion describing the structural phase transition in LaNiO₃ using existing computational data [1]. Our model is able to capture the coupling of the temperature and order parameter, and we successfully predicted the structural phase transition at high temperature. We encourage materials scientists to utilize SR to open challenges in materials research, which could potentially unearth hidden governing laws in materials science from a data-driven approach.

[1] Wang, Y.; Wagner, N.; Rondinelli, J. M. Symbolic Regression in Materials Science. MRS Communications 2019, 9 (3), 793–805.   

DFT-45B---a fertile soil (data) for your seeds (machine learning algorithms)

Machine-learning (ML) models have become the new paradigm in computational materials science for predicting properties of materials with the accuracy of quantum mechanics at a fraction of the cost. Accurate data (fertile soil) is crucial and helps us to build better ML models (healthier plants) using any ML algorithms (seeds). The inconsistencies in the materials data extracted from existing material repositories---less than a few hundred calculations for each alloy system, varied sizes of prototypes, and varying k-point density for different cell sizes---make it challenging to develop effective ML models. We created a DFT-based materials dataset (DFT-45B) consisting of 45 binary alloys (all binary combinations of 10 different elements---Ag, Al, Co, Cu, Fe, Mg, Nb, Ni, Ti, and V) with over 71775 calculations free of such inconsistencies. Each alloy system includes all possible enumerated crystal structures until 8 atoms for fcc, bcc and hcp crystal types. As the data encompasses the space of 10 elements and all their binary combinations, it is helpful to understand the similarity between various elements and alloys. In this talk, we present the methodology and heuristics of the dataset.   

Bayesian Machine Learning in Metamaterial Design: Fragile Becomes Supercompressible

Designing future-proof materials goes beyond a quest for the best. The next generation of materials needs to be adaptive, multipurpose, and tunable. This is not possible by following the traditional experimentally guided trial-and-error process, as this limits the search for untapped regions of the solution space. Here, a computational data-driven approach is followed for exploring a new metamaterial concept and adapting it to different target properties, choice of base materials, length scales, and manufacturing processes. Guided by Bayesian machine learning, two designs are fabricated at different length scales that transform brittle polymers into lightweight, recoverable, and supercompressible metamaterials. The macroscale design is tuned for maximum compressibility, achieving strains beyond 94% and recoverable strengths around 0.1 kPa, while the microscale design reaches recoverable strengths beyond 100 kPa and strains around 80%. The data-driven code is available to facilitate future design and analysis of metamaterials and structures (https://github.com/mabessa/F3DAS).

Reference: Bessa, M. A., Glowacki, P., & Houlder, M. (2019). Bayesian Machine Learning in Metamaterial Design: Fragile Becomes Supercompressible. Advanced Materials, 1904845.   

A roadmap for machine learning in alloy modeling

Years before the data science craze, ideas of modern machine learning played an essential role in alloy modeling. Genetic algorithms (for both searching materials space and model construction), statistical learning methods based on Bayesian ideas, dimensionality reduction approaches (cluster expansion, compressive sensing, interatomic potentials, etc.) have contributed to a rich heritage of innovation in the field. Recent developments in data science, and the affordability of generating unprecedented volumes of high-quality training data, open up further avenues. New materials informatics approaches, machine-learned interatomic potentials (GAP, SNAP, MTP, genetic programs, atomic cluster expansion, and others), new thermodynamic approaches such as nested sampling, etc., provide unrivaled opportunities in computational alloy modeling and discovery. We highlight past successes and spotlight promising new approaches.
  

Leveraging machine learning to determine nanoscale structures from theory and experiments

Determining the atomistic details of nanoscale structures is a fundamental problem. Although there are both experimental and computational methods to determine these nanoscale structures, they both possess limitations. We develop the FANTASTX code (Fully Automated Nanoscale To Atomistic Structure from Theory and eXperiment) to overcome the limitations of either by combining both experimental and computational data using machine learning techniques. We demonstrate the effectiveness of FANTASTX by determining the structures of nanoparticles and solid interfaces from x-ray and electron microscopy data combined with atomistic and first principles energies, using multi-objective optimization and a variety of canonical and grand canonical sampling algorithms.   

Machine learning for novel and improved inorganic scintillators

Scintillators are detector materials with a wide range of applications, from medical imaging to radiation detection. These materials convert a fraction of the energy deposited by high energy radiation into visible or ultraviolet photons. An ideal scintillator may have high light output, fast response time, and emission at suitable wavelengths. However, no single scintillator is ideal for all uses; there is a need to design custom scintillators optimized for each application. Currently, the discovery and design of new scintillators relies on a laborious, time-intensive approach, yielding little physical insight and leaving a vast space of potentially revolutionary materials unexplored. To accelerate the discovery of optimal scintillator materials, we are developing a closed loop machine learning driven adaptive design framework based on literature data, experiments and calculations. This talk presents an overview of this framework, focusing on the screening of complex chemistries with high band-gaps to identify promising materials amenable to band-gap/band-edge engineering to yield custom scintillation properties. The framework is general and is expected to prove useful for applications beyond scintillator discovery such as photovoltaic and semi-conductor materials.   

Exploring Information Density in Crystalline and Amorphous Configurations using Deep Neural Networks

Predicting the properties of amorphous systems is one of the grand challenges for computational material science. Deep neural network potentials (DNP) promise to recreate the chemical fidelity of DFT while scaling to much larger systems, enabling more realistic simulations of amorphous materials. DNPs also provide a tool to analyze large quantities of DFT data by selective training and evaluation. We trained a DNP on the crystalline polymorphs for SiO2 from the Materials Project. This DNP successively predicted the total energies of several DFT computed quasi-amorphous configurations suggesting that the local atomic environments encoded in amorphous compounds are also present in the potential energy space covered by polymorphism. More importantly, a DNP trained on just the amorphous configurations was able to predict the energies of polymorphs, including the ground state configuration over 100 meV/atom below the lowest included amorphous configuration. This suggests that DNPs trained on quasi-amorphous configurations may be an effective means of identifying ground state configurations as well as polymorphism in never before explored systems.