A Framework of SO(3)-equivariant Non-linear Representation Learning and its Application to Electronic-Structure Hamiltonian Prediction

arXiv:2405.05722v1 Announce Type: new
Abstract: We present both a theoretical and a methodological framework that addresses a critical challenge in applying deep learning to physical systems: the reconciliation of non-linear expressiveness with SO(3)-equivariance in predictions of SO(3)-equivariant quantities, such as the electronic-structure Hamiltonian. Inspired by covariant theory in physics, we address this problem by exploring the mathematical relationships between SO(3)-invariant and SO(3)-equivariant quantities and their representations. We first construct theoretical SO(3)-invariant quantities derived from the SO(3)-equivariant regression targets, and use …

abstract application arxiv challenge covariant cs.lg deep learning electronic framework linear non-linear prediction predictions reconciliation representation representation learning systems type