Harmonizing SO(3)-Equivariance with Neural Expressiveness: a Hybrid Deep Learning Framework Oriented to the Prediction of Electronic Structure Hamiltonian
arxiv(2024)
摘要
Deep learning for predicting the electronic structure Hamiltonian of quantum
systems necessitates satisfying the covariance laws, among which achieving
SO(3)-equivariance without sacrificing the non-linear expressive capability of
networks remains unsolved. To navigate the harmonization between equivariance
and expressiveness, we propose a deep learning method synergizing two distinct
categories of neural mechanisms as a two-stage cascaded regression framework.
The first stage corresponds to group theory-based neural mechanisms with
inherent SO(3)-equivariant properties prior to the parameter learning process,
while the second stage is characterized by a non-linear 3D graph Transformer
network we propose featuring high capability on non-linear expressiveness. The
novel combination lies in the point that, the first stage predicts baseline
Hamiltonians with abundant SO(3)-equivariant features extracted, assisting the
second stage in empirical learning of equivariance; and in turn, the second
stage refines the first stage's output as a fine-grained prediction of
Hamiltonians using powerful non-linear neural mappings, compensating for the
intrinsic weakness on non-linear expressiveness capability of mechanisms in the
first stage. Our method enables precise, generalizable predictions while
maintaining robust SO(3)-equivariance under rotational transformations, and
achieves state-of-the-art performance in Hamiltonian prediction on six
benchmark databases.
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