Session Y32: Material Science and Machine Learning II

Data-driven estimation of transfer integrals in undoped cuprates

For magnetic insulators such as undoped cuprates, band-structure calculations

based on density-functional theory (DFT) are a reliable source of information

on the microscopic magnetic model. Yet, estimation of the transfer integrals

remains cumbersome, as it requires projections on a carefully crafted Wannier

basis. We demonstrate how an artificial neural network (ANN), trained on

results of high-throughput DFT calculations, can be

employed for the estimation of transfer integrals based exclusively on the

structural information. In particular, the ANN maps the local crystal

environment of two copper sites onto the real value of the respective transfer

integral.  The crystal environment representation is based on the three-dimensional Zernike functions,

which is a truncated expansion in orthogonal multinomials of site positions

functions [1]. It encrypts the spatial configuration of atoms and the chemical

composition, expressed by the oxidation number and the ionicity radius. Our

approach can be employed for a rapid assessment of the spin models of new

cuprate materials.

[1] M. Novotni and R. Klein, Comput. Aided Des. 36, 1047 (2004).   

High-Throughput Screening of Semiconductors for Artificial Photosynthesis with Data-Mining and First Principles Calculations

We propose an algorithm for efficient design of semiconductor structures with a selected set of physical properties. We deploy our algorithm to produce semiconductor candidates for artificial photosynthesis, i.e. photocatalytic water splitting. Our candidate structures are composed of earth-abundant elements, capable of trapping sunlight, suitable for H₂ and/or O₂ production, and stable to reduction and oxidation in aqueous media. First, we predict thousands of undiscovered semiconductors compositions using an ionic translation model trained on a large experimental database. Then, we screen the predicted semiconductors compositions for redox stability under HER or OER conditions. Finally, we generate thermodynamically stable crystal structures and calculate accurate band gap values for these compounds. Ultimately we produce dozens of promising semiconductor candidates with ideal properties for artificial photosynthesis.   

Accelerated materials discovery of complex multicomponent alloys and ceramics with deep reinforcement learning

In recent years  the study of multicomponent alloys and ceramics including disordered rock salt cathodes for Li-ion batteries, metal halide perovskite solar absorbers, alloys for thermoelectrics, ultra-high-temperature ceramics for aerospace applications has seen rapid growth due to their superior mechanical, thermal, and magnetic properties. The immense configurational space offers unique opportunities for discovery of new materials with unprecedented qualities. However, discovery of materials with targeted properties is challenging due to  the huge number of distinct atomic configurations available  . We employ multidimensional scaling (MDS) strategies to reduce the size of the configurational manifold.  We use the distribution of local environments of elements in a given configuration as descriptors of the configuration.  The atomic environments are described  using features such as bond length and order parameter.  The dimensionality reduction is beneficial for the reinforcement learning (RL) approach, which scales poorly for large numbers of space states. We compare the number of exploration steps needed to reach the target configuration before training (random walk) and after training the deep RL model. We demonstrate the approach to discover configurations for ternary compounds such as (Al_xGa_yIn_z)_2NO_3N and high-entropy ceramics. Deep RL is implemented on the reduced 3D and 2D manifold in order to achieve target physical property.   

A neural network potential for high throughput screening of the energetics and thermodynamical stabilities of non-stoichiometric Chromium Sulfides

Machine learning potentials (MLPs) have recently become a powerful tool in computational materials science due to their ability to bridge the quantum-mechanical accuracy of ab initio methods to large systems with a linear scaling. We present a neural network potential (NNP) trained on data generated using density functional theory (DFT) to predict the energies and stabilities for a wide range of stoichiometries of Cr-S structures with Cr vacancies. A preliminary investigation of the stable phases is performed using the cluster expansion method (CE). Crystal structures are exhaustively enumerated for a more fine-grained stoichiometry range. The NNP shows an excellent transferability to unseen stoichiometries, which is utilized in identifying the crystal structures of the stable and metastable phases for the full stoichiometric space. The phonon bandstructures are then predicted with an excellent agreement with DFT over the full stoichiometry space. Furthermore, the dynamical stabilities of some phases are evaluated using classical molecular dynamics (MD) driven by the NNP. The employed methodology acts as a systematic approach using (MLPs) to search the structure space and investigate the phonon and dynamical stabilities for a wide range of stoichiometries of a given material.   

Predicting oxygen vacancy formation energy in metal oxides

The oxygen vacancy formation energy is a key quantity determining materials chemical and thermodynamic properties, and plays a fundamental role in a variety of energy applications. Large scale prediction of this quantity is therefore a particularly attractive endeavour, and high-throughput DFT and machine learning can be powerful tools to this end.

By performing high throughput DFT studies within the Open Quantum Materials Database (OQMD), we produced a dataset comprising thousands of oxygen vacancy formation energy calculations of materials with a broad range of compositions and structures. Here, we first present the results of such studies, and then utilize the dataset to train multiple machine learning models. We compare the performance of the different models, and analyze the influence of various descriptors, identifying the ones playing the largest role in maximizing the predictive accuracy.   

Superconductor and Critical Temperature Predictions Using Machine Learning

We used superconductors from the SuperCon database to perform

supervised machine learning to predict their critical temperatures. Using

only chemical composition as the predictor, our calculations

achieved a coefficient of determination R$^{2} \simeq 0.93$, which is

comparable to, and in some cases higher than, similar estimates using

other artificial intelligence techniques. Based on this machine

learning model, we predicted several new superconductors with

high critical temperatures. We also used unsupervised machine

learning to find possible clustering structure in the

superconducting materials data. Conventional clustering methods

like k-means, hierarchical or Gaussian mixtures, as well a clustering

method based on self-organizing maps (a type of artificial neural network),

were used. Our results indicate that machine learning can achieve,

and in some cases exceed, human level performance in clustering

superconductors.   

Crystal Diffusion Variational Autoencoder for Periodic Material Generation

Generating the periodic structure of stable materials is a long-standing challenge for the inverse design of solid-state materials. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. Our approach opens exciting new opportunities for the property-guided inverse design of solid-state materials for various important applications.   

Predicting elastic properties of crystal structures using rotationally equivariant graph neural networks

The advent of machine learning (ML) enables data-driven approaches for computational materials science. With sufficient data from first principles, e.g. density functional theory, well-developed ML models can predict properties of unseen materials with high accuracy. Despite its empirical success, standard black box ML models lack explainability, and often are uninformed of material physics. In this work, we apply the recently developed ML model that is aware of symmetry groups possessed by crystal structures, to predict the elastic property of crystalline solids. Specifically, we train graph neural networks designed to learn rotational equivariance of three-dimensional objects to predict the strain energy tensors computed from the elastic tensors of crystalline solids. Although the strain energy tensor has 6 x 6 components, the number of independent components crucially depend on the symmetries of the crystals. Our physics-informed ML model can predict the strain energy tensor of unseen crystal structures rather accurately, and symmetry-induced tensor components are considerably differentiated. Our work is a stepping stone towards the data-driven discovery of materials with desirable properties.   

Machine learning to establish zero point energy as a screening parameter for identifying vibrationally stable perovskites

The present calculations show that scanning the potential energy surface of any compositional space (i.e. perovskites, in this context) using formation energy calculations i.e. with E_hull analysis is not sufficient to comment on vibrational stability of compounds. Machine learning is used to classify the vibrationally stable perovskites from the unstable ones, which shows the zero point energy (ZPE), i.e. thermal energy content of the system at 0 K, has a strong implication on thermal stability of compounds. Below a threshold value of ZPE (∼ 40 kJmol⁻¹), 90 % of compounds are found to be vibrationally stable. This is very advantageous, since ZPE can be absolutely quantitatively calculated for each structure individually. However, it suffers lengthy vibration calculation, which can not be performed for large scale high throughput screening. Thus, one of the compress sensing techniques (SISSO) is used to provide a highly accurate regression model for the ZPE using only elemental and simple compound descriptors. This model, while providing computationally inexpensive means to predict the vibrational stability of compounds, also establishes ZPE as a reference free screening parameter for predicting the vibrational stability of the compounds, which can be extended to different compound classes and even to elevated temperatures.