Voxelized Representations of Atomic Systems for Machine Learning Applications

The behavior of a materialHomogenization or chemical system is determined by complex physical phenomena taking place over a hierarchy of length scales. Atomic systems are typically considered to be the smallest relevant length scale in materials modeling and thus form the basis of hierarchical multiscaleMultiscale materials modeling. This chapter presents a detailed overview of voxelized representations of the atomic structureAtomic structure that can be used in machine learning (ML) applications not only at the atomic length scale, but also as the foundation of a hierarchical multiscaleMultiscale materials modeling framework. We first present a theoretical development of the continuous microstructure functionMicrostructure function as a mathematical definition of material structureMaterial structure. We then show that the mathematical definition of the discrete (i.e., voxelized) microstructure function is consistent for any length scale. Furthermore, we show that the microstructure functionMicrostructure function (both discrete and continuous) can be used both to quantify the local material structureMaterial structure directly by systematically selecting the reference axis of the material system and to statistically quantify the global material structure using n-point spatial correlation functionsSpatial correlation function. We then present practical methods for computing microstructure functions and numerically quantifying the material structureMaterial structure. Finally, we present theVoxelized atomic structure (VASt) discovery voxelized atomic structureAtomic structure (VASt) frameworkVoxelized atomic structure (VASt) framework forVoxelized atomic structure (VASt) potential developing both ML-based interatomic potentialsChemical potential andVoxelized atomic structure (VASt) potential ML models supporting materials discoveryMaterials discovery for desired effective properties.