Solving Schr\"{o}dinger Equation Using Tensor Neural Network

Hehu Xie; Jianghao Liu; Mingfeng He; Qingyuan Sun; Teng Wu; Yangfei Liao; Yifan Wang; Zhongshuo Lin

Solving Schr\"{o}dinger Equation Using Tensor Neural Network

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arxiv 2209.12572 v4 pith:N22SG6S3 submitted 2022-09-26 physics.comp-ph physics.chem-ph

Yangfei Liao , Zhongshuo Lin , Jianghao Liu , Qingyuan Sun , Yifan Wang , Teng Wu , Hehu Xie , Mingfeng He This is my paper · ORCID

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keywords tensorequationnetworkneuralnumericalaccuracymany-bodyschrodinger

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In this paper, we introduce a novel approach to solve the many-body Schrodinger equation by the tensor neural network. Based on the tensor product structure, we can do the direct numerical integration by using fixed quadrature points for the functions constructed by the tensor neural network within tolerable computational complexity. Especially, we design several types of efficient numerical methods to treat the variable-coupled Coulomb potentials with high accuracy. The corresponding machine learning method is built for solving many-body Schrodinger equation. Some numerical examples are provided to validate the accuracy and efficiency of the proposed algorithms.

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An adaptive neural network subspace method, using tensor neural networks and a posteriori error estimators, solves 2D elliptic PDEs with singularities and interface discontinuities to relative errors as low as 1e-9.

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