Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

Haiyang Yu, Zhao Xu, Xiaofeng Qian, Xiaoning Qian, Shuiwang Ji
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:40412-40424, 2023.

Abstract

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-yu23i, title = {Efficient and Equivariant Graph Networks for Predicting Quantum {H}amiltonian}, author = {Yu, Haiyang and Xu, Zhao and Qian, Xiaofeng and Qian, Xiaoning and Ji, Shuiwang}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {40412--40424}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/yu23i/yu23i.pdf}, url = {https://proceedings.mlr.press/v202/yu23i.html}, abstract = {We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).} }
Endnote
%0 Conference Paper %T Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian %A Haiyang Yu %A Zhao Xu %A Xiaofeng Qian %A Xiaoning Qian %A Shuiwang Ji %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-yu23i %I PMLR %P 40412--40424 %U https://proceedings.mlr.press/v202/yu23i.html %V 202 %X We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).
APA
Yu, H., Xu, Z., Qian, X., Qian, X. & Ji, S.. (2023). Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:40412-40424 Available from https://proceedings.mlr.press/v202/yu23i.html.

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