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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
classification physics.comp-phphysics.chem-ph
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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

    math.NA 2024-12 conditional novelty 6.0 of 10

    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.

  2. Neural Network Element Method for Partial Differential Equations

    math.NA 2025-04 conditional novelty 4.0 of 10

    The paper constructs NN-enriched finite element spaces, proves a partition-of-unity error bound, and shows a 2D Laplace example with much smaller errors than standard FEM.

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