Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity

Erpai Luo, Xinran Wei, Lin Huang, Yunyang Li, Han Yang, Zaishuo Xia, Zun Wang, Chang Liu, Bin Shao, Jia Zhang

TL;DR: SPHNet, an efficient and scalable equivariant network, which introduces adaptive SParsity into Hamiltonian prediction networks.

Abstract: Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this domain, their substantial computational cost—driven by high-order tensor product (TP) operations—restricts their scalability to large molecular systems with extensive basis sets. To address this challenge, we introduce **SPH**Net, an efficient and scalable equivariant network, that incorporates adaptive **SP**arsity into **H**amiltonian prediction. SPHNet employs two innovative sparse gates to selectively constrain non-critical interaction combinations, significantly reducing tensor product computations while maintaining accuracy. To optimize the sparse representation, we develop a Three-phase Sparsity Scheduler, ensuring stable convergence and achieving high performance at sparsity rates of up to 70\%. Extensive evaluations on QH9 and PubchemQH datasets demonstrate that SPHNet achieves state-of-the-art accuracy while providing up to a 7x speedup over existing models. Beyond Hamiltonian prediction, the proposed sparsification techniques also hold significant potential for improving the efficiency and scalability of other SE(3) equivariant networks, further broadening their applicability and impact.

Lay Summary:

Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While existing methods have achieved remarkable success in this domain, their substantial computational cost—driven by high-order tensor product (TP) operations—restricts their scalability to large molecular systems with extensive basis sets.

To address this challenge, we introduce **SPH**Net, an efficient and scalable equivariant network, that incorporates adaptive **SP**arsity into **H**amiltonian prediction. SPHNet employs two innovative sparse gates to selectively constrain non-critical interaction combinations in the tensor product operation, significantly reducing the computation cost while maintaining accuracy. To optimize the sparse representation, we develop a Three-phase Sparsity Scheduler, ensuring stable convergence and achieving high performance at sparsity rates of up to 70\%.

Extensive evaluations on different scale datasets demonstrate that SPHNet achieves state-of-the-art accuracy while providing up to a 7x speedup over existing models. Beyond Hamiltonian prediction, the proposed sparsification techniques also hold significant potential for improving the efficiency and scalability of other SE(3) equivariant networks, further broadening their applicability and impact.

Link To Code: https://github.com/microsoft/SPHNet

Primary Area: Applications->Chemistry, Physics, and Earth Sciences

Keywords: Equivariant network, Hamiltonian Matrix, Computational Chemistry, Efficiency

Submission Number: 3882