SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Zhang, Yaolong [University of New Mexico, Albuquerque, NM (United States)] (ORCID:0000000246010461); Jiang, Bin [University of Science and Technology of China, Anhui (China)] (ORCID:0000000326965436); Guo, Hua [University of New Mexico, Albuquerque, NM (United States)] (ORCID:000000019901053X)

doi:10.1021/acs.jctc.4c01287

DOE OSTI · 3011596

SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Zhang, Yaolong [University of New Mexico, Albuquerque, NM (United States)] (ORCID:0000000246010461)·Jiang, Bin [University of Science and Technology of China, Anhui (China)] (ORCID:0000000326965436)·Guo, Hua [University of New Mexico, Albuquerque, NM (United States)] (ORCID:000000019901053X)

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Abstract

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function 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 wave function ansatz that includes both nuclear and electronic coordinates. Furthermore, 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.

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Zhang, Yaolong [University of New Mexico, Albuquerque, NM (United States)] (ORCID:0000000246010461), Jiang, Bin [University of Science and Technology of China, Anhui (China)] (ORCID:0000000326965436), Guo, Hua [University of New Mexico, Albuquerque, NM (United States)] (ORCID:000000019901053X). 2025-01-07. SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation. https://doi.org/10.1021/acs.jctc.4c01287

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