SchrödingerNet: A Universal Neural Network Solver for The Schrödinger Equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910741619015680 |
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| author | Zhang, Yaolong Jiang, Bin Guo, Hua |
| author_facet | Zhang, Yaolong Jiang, Bin Guo, Hua |
| contents | Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born-Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wavefunction ansatz that includes both nuclear and electronic coordinates. This strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SchrödingerNet: A Universal Neural Network Solver for The Schrödinger Equation Zhang, Yaolong Jiang, Bin Guo, Hua Chemical Physics Computational Physics Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born-Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wavefunction ansatz that includes both nuclear and electronic coordinates. This strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency. |
| title | SchrödingerNet: A Universal Neural Network Solver for The Schrödinger Equation |
| topic | Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2408.04497 |