Solving Schrödinger Equation Using Tensor Neural Network
Fuente:
arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910844370026496 |
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| author | Liao, Yangfei Lin, Zhongshuo Liu, Jianghao Sun, Qingyuan Wang, Yifan Wu, Teng Xie, Hehu He, Mingfeng |
| author_facet | Liao, Yangfei Lin, Zhongshuo Liu, Jianghao Sun, Qingyuan Wang, Yifan Wu, Teng Xie, Hehu He, Mingfeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12572 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solving Schrödinger Equation Using Tensor Neural Network Liao, Yangfei Lin, Zhongshuo Liu, Jianghao Sun, Qingyuan Wang, Yifan Wu, Teng Xie, Hehu He, Mingfeng Computational Physics Chemical Physics 65N25, 65L15, 65B99, 68T07 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. |
| title | Solving Schrödinger Equation Using Tensor Neural Network |
| topic | Computational Physics Chemical Physics 65N25, 65L15, 65B99, 68T07 |
| url | https://arxiv.org/abs/2209.12572 |