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   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). 

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2. Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

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   We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equiv- ariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant net- work, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the inno- vative design of QHNet architecture, which not only obeys the underlying symmetries, but also en- ables the reduction of number of tensor products by 92%. In addition, QHNet prevents the expo- nential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular sys- tems. 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 mem- ory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). 

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3. A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

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   We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). 

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4. A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

   Yan, Keqiang; Saxton, Alexandra; Qian, Xiaofeng; Qian, Xiaoning; Ji, Shuiwang (June 2024, The Forty-first International Conference on Machine Learning)

   We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). 

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5. A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

   Yan, Keqiang; Saxton, Alexandra; Qian, Xiaofeng; Qian, Xiaoning; Ji, Shuiwang (July 2024, Proceedings of Machine Learning Research)

   We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). 

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