Equivariant Deep Learning in Direct-Product Space for Electronic-Structure Hamiltonian Prediction
Researchers propose DP-Learner, an equivariant learning framework that performs message passing directly on Hamiltonian-like operator blocks in direct-product space rather than direct-sum spaces of irreducible spherical tensors. The method introduces Lie-generator-based directional embedding and invariantly weighted left-right products and contractions intended to preserve equivariance to SO(3), SU(2), and spatial inversions without explicit Clebsch-Gordan decomposition. It is instantiated as a Transformer architecture and accompanied by MP-HAM-110K, a dataset of more than 110,000 material structures covering 68 elements with Hamiltonian and wavefunction data. Experiments on MP-HAM-110K and Materials-HAM-SOC report improved Hamiltonian prediction accuracy and inference efficiency over the state-of-the-art method.