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Rapid discovery of stable materials by coordinate-free coarse graining.

ABSTRACT: A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating previously unidentified materials. Our approach solves this bottleneck by coarse-graining the infinite search space of atomic coordinates into a combinatorially enumerable search space. The key idea is to use Wyckoff representations, coordinate-free sets of symmetry-related positions in a crystal, as the input to a machine learning model. Our model demonstrates exceptionally high precision in finding unknown theoretically stable materials, identifying 1569 materials that lie below the known convex hull of previously calculated materials from just 5675 ab initio calculations. Our approach opens up fundamental advances in computational materials discovery.

SUBMITTER: Goodall REA

PROVIDER: S-EPMC9328671 | biostudies-literature | 2022 Jul

REPOSITORIES: biostudies-literature

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Rapid discovery of stable materials by coordinate-free coarse graining.

Goodall Rhys E A REA Parackal Abhijith S AS Faber Felix A FA Armiento Rickard R Lee Alpha A AA

Science advances 20220727 30

A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating previously unidentified mate ...[more]

PMID: 35895811

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Project description:Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth ε -dependent Hamiltonian vector field Xε possesses an approximate symmetry if the limiting vector field X0=limε→0Xε possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamics of the symmetry-invariant dependent variables. Deriving such reduced systems, or approximating them numerically, is an ongoing challenge. We demonstrate that WSINDy can successfully identify this reduced Hamiltonian system in the presence of large perturbations imparted in the ε>0 regime, while remaining robust to extrinsic noise. This is significant in part due to the nontrivial means by which such systems are derived analytically. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. The methodology is computationally efficient, often requiring only a single trajectory to learn the global reduced Hamiltonian, and avoiding forward solves in the learning process. In this way, we argue that weak-form equation learning is particularly well-suited for Hamiltonian coarse-graining. Using nearly-periodic Hamiltonian systems as a prototypical class of systems with approximate symmetries, we show that WSINDy robustly identifies the correct leading-order system, with dimension reduced by at least two, upon observation of the relevant degrees of freedom. While our main contribution is computational, we also provide a contribution to the literature on averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems. This provides theoretical justification for our approach as WSINDy's computations occur at the level of Hamiltonian vector fields. We illustrate the efficacy of our proposed method using physically relevant examples, including coupled oscillator dynamics, the Hénon-Heiles system for stellar motion within a galaxy, and the dynamics of charged particles.

Dataset Information

Rapid discovery of stable materials by coordinate-free coarse graining.

Publications

Rapid discovery of stable materials by coordinate-free coarse graining.

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