Sparse expansions of multicomponent oxide configuration energy using coherency & redundancy

TL;DR

This paper introduces a novel frame-based compressed sensing approach for modeling the energy of complex oxide materials, overcoming strict sampling requirements and achieving more accurate and sparse models than traditional methods.

Contribution

It develops a redundant frame from occupancy-based cluster expansion bases, enabling effective sparse energy modeling without strict sampling constraints.

Findings

Sparse energy models outperform standard cluster expansions.

Redundant frames improve prediction accuracy.

Method is effective for complex oxide materials.

Abstract

Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.