Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity

TL;DR

This paper introduces SPHNet, a scalable equivariant neural network that employs adaptive sparsity to predict Hamiltonian matrices efficiently, achieving high accuracy and significant speedups for large molecular systems.

Contribution

We propose SPHNet, a novel sparse, adaptive SE(3) equivariant network that reduces computational cost while maintaining accuracy in Hamiltonian matrix prediction.

Findings

Achieves up to 7x speedup over existing models.

Maintains state-of-the-art accuracy with 70% sparsity.

Demonstrates effectiveness on QH9 and PubchemQH datasets.

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 SPHNet, an efficient and scalable equivariant network, that incorporates adaptive SParsity into Hamiltonian 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. Our code can be found at https://github.com/microsoft/SPHNet.