Session M39: Machine Learning for Quantum Matter II

Materials discovery through artificial intelligence

New, suitable materials are almost always at the core of new technologies. This endeavor now is spurred by exciting developments at the intersection of artificial intelligence (AI) and materials science. In this talk, I will present new AI tools developed at TRI for end-to-end material discovery systems. Using these tools, codified agents of research can incorporate machine-learning, physics, chemistry, logic or heuristics to make decisions to meet their goals, for example, on which structures to simulate using high-fidelity quantum mechanics. New agent designs can also be simulated a priori, projecting their performance in real-world discovery campaigns. Examples of simulations and executions of stable material discovery campaigns will be shown.   

Working without data: overcoming gaps in deep learning and physics-based extrapolation

Despite its many recent successes, several fundamental issues remain with the application of deep learning to experimental data and first-principles based simulation.

These problems include the ability to extrapolate to unseen experimental conditions, transfer knowledge across length-scales, and the challenge of interpreting results within a physically motivated framework. Other challenges include the lack of a standardized methodology for reporting and understanding model errors as well as the frequent requirement for large quantities of data.

I will outline some of our ongoing efforts to address some of these challenges, with special attention paid to the concept of extrapolation (including the physical conditions of study and across length scales). To explore these ideas, we explore model spin-systems, 2d materials, and optical lattices.   

Machine learning models of properties of hybrid 2D materials as potential super lubricants

The screening of novel materials is an important topic in the field of materials science. Although traditional computational modeling, especially first-principles approaches, is a very useful and accurate tool to predict the properties of novel materials, it still demands extensive and expensive state-of-the-art computational resources. Additionally, they can be often extremely time-consuming. We describe a time and resource-efficient machine learning approach to create a large dataset of structural properties of van der Waals layered structures. In particular, we focus on the interlayer energy and the elastic constant of layered materials composed of two different 2-dimensional (2D) structures, that are important for novel solid lubricant and super-lubricant materials. We show that machine learning models can recapitulate results of computationally expansive approaches (i.e. density functional theory) with high accuracy.   

Charge Density Prediction through 3D-CNN for Fast Convergence of Self-Consistent DFT calculation

The electronic charge density plays an important role in understanding the physical properties of quantum materials. Although the charge density can be obtained by solving the Kohn-Sham equation of density functional theory (DFT), one needs to solve a self-consistent equation which takes time until convergence. Recent studies have tried to directly predict the charge density using machine-learning methods, but the target materials are limited to slabs or organic molecules because they only considered local electronic features [1,2,3].
In this study, we propose a machine-learning algorithm to predict the charge densities of crystals using a three-dimensional convolutional neural network (3DCNN). To deal with the periodicity of crystals, we use FFT grid-based representation and a periodic convolution filter. We demonstrate that our model can predict the charge densities of ABO₃-type crystalline compounds without solving the self-consistent equation. It will accelerate the high-throughput DFT calculations for materials discovery.
[1] F. Brockherde et al. Nat. Commun. 8, 872 (2017)
[2] A. Chandrasekaran et al. npj Comput. Mater. 4, 25 (2018)
[3] Anton V. Sinitskiy and Vijay S. Pande. arXiv:1809.02723, 2018.   

Data-driven studies of the magnetic anisotropy of two-dimensional magnetic materials

Two-dimensional materials with intrinsic ferromagnetic order are at the forefront of condensed matter research. How many of these materials exist in nature? What is the relationship between thier crystal structure and magnetic properties? Remarkably, atomically-thin magnetic structures can exhibit novel spin properties which do not exist in the corresponding bulk materials. We use first-principles calculations, based on density functional theory, and machine learning to study the magnetocrystalline anisotropy of monolayer transition metal trichalcogenides of the form A₂B₂X₆. That is, we created permutations of the chemical composition of the ferromagnetic semiconductor Cr₂Ge₂Te₆. Specifically, we identify trends in their magnetocrystalline anisotropy data. We find that the X site dominates the machine learning prediction of the magnetocrystalline anisotropy of an A₂B₂X₆ monolayer. Our data-driven study aims to uncover physical insights into the microscopic origins of magnetism in reduced dimensions and to demonstrate the success of a high-throughput computational approach for the targeted design of quantum materials with potential applications from sensing to data storage.   

Robust cluster expansion of multicomponent systems using machine learning with structured sparsity

Identifying a suitable set of descriptors for modeling physical systems often utilizes either deep physical insights or statistical methods. In machine learning, a class of methods known as structured sparsity regularization combines both physics- and statistics-based approaches. We present group lasso as an efficient method for obtaining robust cluster expansions (CE) of multicomponent systems, a popular computational technique for modeling the thermodynamic properties of such systems. Via convex optimization, group lasso selects the most predictive set of atomic clusters as descriptors in accordance with the physical insight that if a cluster is selected, so should its subclusters. These selection rules avoid spuriously large fitting parameters by redistributing them among lower order terms, resulting in more physical, accurate, and robust CEs. We showcase these features of group lasso using the CE of bcc ternary alloy Mo-V-Nb. These results are timely given the growing interests in applying CE to increasingly complex systems, which demand a more reliable machine learning method to handle the larger parameter space.   

Generalizing an Energy Predictor based on Wavelet Scattering for 3D Atomic Systems

The dream of machine learning in quantum matter is for a neural network to learn the underlying physics of an atomic system, allowing it to move beyond interpolation of the training set to the prediction of properties that were not present in the original training data. Achieving this ambitious goal will require a method to convert a 3D atomic system into neural-network-friendly features that preserve rotational and translational symmetry, smoothness under small perturbations, and invariance under re-ordering. The atomic orbital wavelet scattering transform preserves these symmetries by construction, and has achieved great success as a featurization method for machine learning energy prediction. Both in small molecules and in the amorphous Li_xSi system, neural networks using wavelet scattering coefficients as features have demonstrated a comparable accuracy to Density Functional Theory at a small fraction of the computational cost. In this work, we test the generalizability of our Li_xSi energy predictor to properties that were not included in the training set, such as elastic constants and migration barriers. We also discuss the potential for future improvements in generalizability through automatic training-set expansion based on active learning.   

Using Machine Learning Models to Predict Higher-Level Quantities from Energy Models

Machine learning methods are now used more and more as a substitute for Density Functional Theory calculations due to their low computational costs. However, in some cases, relevant datasets are not available, and the effort that would be necessary to generate this data suppresses the advantages of using machine learning to speed up the calculations. Furthermore, the process of training a reliable model is not trivial and can also be expensive. For those reasons, we are developing a python package named ML_Calc_Driver¹, which goal is to allow to use portable trained models to make predictions easily. Energy datasets are numerous and, through the use of implemented finite difference workflows, can be used to predict higher-level quantities such as forces, phonon energies, and infrared intensities. As of now, the package is interfaced to use SchNetPack² trained models, and more model types can easily be added as our workflows are independent of the actual calculators.

1. https://github.com/OMalenfantThuot/ML_Calc_Driver
2. Schütt, K. T. And al. https://doi.org/10.1021/acs.jctc.8b00908.   

AI-guided engineering of nanoscale topological materials

Nanoscale organic materials have long been known to host topologically protected excitations. Inspired by recent progress in classifying topological phases in armchair, cove-edged and chevron graphene nanoribbons, we develop a high-throughput framework based on the computation of the Zak phase and the Z2 invariants using tight-binding and density functional theory to explore the topology of low-symmetry 1D and 2D periodic organic compounds. As of today, we have identified 224,071 new topological nanoribbons using our framework. Training deep neural networks on the graphs of these Hamiltonians, we analyze the graphical features conducive to topological excitations in these systems. We show how this workflow can help the atomic assembly of topologically non-trivial artificial lattices.   

Motif-based machine learning for crystalline materials

With the development of advanced algorithms and improvements in computational power, machine learning (ML) has been widely successful in predicting various physical and chemical properties of materials. The success of any ML model mainly depends on the good representation of the input data, and there have been surging interests in identifying effective representations for crystalline materials. In this talk, we propose a novel representation of crystalline solid-state materials (such as complex metal oxides) as graphs composed of structure motifs. This motif-based representation serves as input to a graph convolutional network for the learning and prediction of material properties, such as bandgaps and formation energies. Our test results indicate that, when combined with atomic information and related networks, the inclusion of motif information in the network architecture improves the prediction performance, especially for complex oxide materials.
  

Machine learning powered kinetic energy functional finding in solid state physics

Kinetic energy functional is crucial to speed up the density functional theory calculation. However, deriving it directly from first principle is challenging, and existing approximations all have significant flaw. In this work, we use machine learning method to build a kinetic energy functional for 1D extended system, our solution combines the dimensionality reduction method with the Gauss process regression, and use a simple scaling trick to generalize the functional to 1D lattice with arbitrary lattice constant. Besides reaching chemical accuracy in kinetic energy calculation, our solution also performs well in functional derivative prediction, and integrating it into the current orbital free density functional theory scheme provide us with expected ground state electron density.