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
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:41368-41390, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-luo25l, title = {Efficient and Scalable Density Functional Theory {H}amiltonian Prediction through Adaptive Sparsity}, author = {Luo, Erpai and Wei, Xinran and Huang, Lin and Li, Yunyang and Yang, Han and Xia, Zaishuo and Wang, Zun and Liu, Chang and Shao, Bin and Zhang, Jia}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {41368--41390}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/luo25l/luo25l.pdf}, url = {https://proceedings.mlr.press/v267/luo25l.html}, 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.} }
Endnote
%0 Conference Paper %T Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity %A Erpai Luo %A Xinran Wei %A Lin Huang %A Yunyang Li %A Han Yang %A Zaishuo Xia %A Zun Wang %A Chang Liu %A Bin Shao %A Jia Zhang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-luo25l %I PMLR %P 41368--41390 %U https://proceedings.mlr.press/v267/luo25l.html %V 267 %X 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.
APA
Luo, E., Wei, X., Huang, L., Li, Y., Yang, H., Xia, Z., Wang, Z., Liu, C., Shao, B. & Zhang, J.. (2025). Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:41368-41390 Available from https://proceedings.mlr.press/v267/luo25l.html.

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