Harmonizing Covariance and Expressiveness for Deep Hamiltonian Regression in Crystalline Material Research: a Hybrid Cascaded Regression Framework

Deep learning for Hamiltonian regression of quantum systems in material research necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the expressiveness capability of networks remains an elusive challenge due to the restriction to non-linear mappings on guaranteeing theoretical equivariance. To alleviate the covariance-expressiveness dilemma, we propose a hybrid framework with two cascaded regression stages. The first stage, i.e., a theoretically-guaranteed covariant neural network modeling symmetry properties of 3D atom systems, predicts baseline Hamiltonians with theoretically covariant features extracted, assisting the second stage in learning covariance. Meanwhile, the second stage, powered by a non-linear 3D graph Transformer network we propose for structural modeling of atomic systems, refines the first stage's output as a fine-grained prediction of Hamiltonians with better expressiveness capability. The combination of a theoretically covariant yet inevitably less expressive model with a highly expressive non-linear network enables precise, generalizable predictions while maintaining robust covariance under coordinate transformations. Our method achieves state-of-the-art performance in Hamiltonian prediction for electronic structure calculations, confirmed through experiments on six crystalline material databases. The codes and configuration scripts are available in the supplementary material.

Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective

Predicting molecular properties (e.g., atomization energy) is an essential issue in quantum chemistry, which could speed up much research progress, such as drug designing and substance discovery. Traditional studies based on density functional theory (DFT) in physics are proved to be time-consuming for predicting large number of molecules. Recently, the machine learning methods, which consider much rule-based information, have also shown potentials for this issue. However, the complex inherent quantum interactions of molecules are still largely underexplored by existing solutions. In this paper, we propose a generalizable and transferable Multilevel Graph Convolutional neural Network (MGCN) for molecular property prediction. Specifically, we represent each molecule as a graph to preserve its internal structure. Moreover, the well-designed hierarchical graph neural network directly extracts features from the conformation and spatial information followed by the multilevel interactions. As a consequence, the multilevel overall representations can be utilized to make the prediction. Extensive experiments on both datasets of equilibrium and off-equilibrium molecules demonstrate the effectiveness of our model. Furthermore, the detailed results also prove that MGCN is generalizable and transferable for the prediction.