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1. 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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2. 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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3. Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry

   https://doi.org/10.21468/SciPostPhysCodeb.10  

   Gao, Yang; Helms, Phillip; Chan, Garnet Kin-Lic; Solomonik, Edgar (February 2023, SciPost Physics Codebases)

   Tensor contractions are ubiquitous in computational chemistry andphysics, where tensors generally represent states or operators andcontractions express the algebra of these quantities. In this context,the states and operators often preserve physical conservation laws,which are manifested as group symmetries in the tensors. These groupsymmetries imply that each tensor has block sparsity and can be storedin a reduced form. For nontrivial contractions, the memory footprint andcost are lowered, respectively, by a linear and a quadratic factor inthe number of symmetry sectors. State-of-the-art tensor contractionsoftware libraries exploit this opportunity by iterating over blocks orusing general block-sparse tensor representations. Both approachesentail overhead in performance and code complexity. With intuition aidedby tensor diagrams, we present a technique, irreducible representationalignment, which enables efficient handling of Abelian group symmetriesvia only dense tensors, by using contraction-specific reduced forms.This technique yields a general algorithm for arbitrary group symmetriccontractions, which we implement in Python and apply to a variety ofrepresentative contractions from quantum chemistry and tensor networkmethods. As a consequence of relying on only dense tensor contractions,we can easily make use of efficient batched matrix multiplication viaIntel’s MKL and distributed tensor contraction via the Cyclops library,achieving good efficiency and parallel scalability on up to 4096 KnightsLanding cores of a supercomputer. 

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4. Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

   Yu, Haiyang; Xu, Zhao; Qian, Xiaofeng; Qian, Xiaoning; Ji, Shuiwang (October 2023, Proceedings of the 40th International Conference on Machine Learning)

   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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5. Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

   Yu, Haiyang; Xu, Zhao; Qian, Xiaofeng; Qian, Xiaoning; Ji, Shuiwang (October 2023, Proceedings of Machine Learning Research)

   Andreas Krause, Emma Brunskill (Ed.)

   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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