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Physics > Computational Physics
Title: Harmonizing SO(3)-Equivariance with Neural Expressiveness: a Hybrid Deep Learning Framework Oriented to the Prediction of Electronic Structure Hamiltonian
(Submitted on 1 Jan 2024 (v1), last revised 16 Apr 2024 (this version, v8))
Abstract: 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.
Submission history
From: Shi Yin [view email][v1] Mon, 1 Jan 2024 12:57:15 GMT (259kb,D)
[v2] Tue, 2 Jan 2024 08:36:58 GMT (259kb,D)
[v3] Wed, 3 Jan 2024 02:17:26 GMT (259kb,D)
[v4] Mon, 15 Jan 2024 14:31:50 GMT (1580kb,D)
[v5] Thu, 25 Jan 2024 09:16:15 GMT (1586kb,D)
[v6] Fri, 2 Feb 2024 08:45:25 GMT (1584kb,D)
[v7] Mon, 8 Apr 2024 07:51:57 GMT (1728kb,D)
[v8] Tue, 16 Apr 2024 02:04:29 GMT (1359kb,D)
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