{"title":"SchrödingerNet: A Universal Neural Network Solver for The Schrödinger Equation","authors":"Yaolong Zhang, Bin Jiang, Hua Guo","doi":"arxiv-2408.04497","DOIUrl":null,"url":null,"abstract":"Recent advances in machine learning have facilitated numerically accurate\nsolution of the electronic Schr\\\"{o}dinger equation (SE) by integrating various\nneural network (NN)-based wavefunction ansatzes with variational Monte Carlo\nmethods. Nevertheless, such NN-based methods are all based on the\nBorn-Oppenheimer approximation (BOA) and require computationally expensive\ntraining for each nuclear configuration. In this work, we propose a novel NN\narchitecture, Schr\\\"{o}dingerNet, to solve the full electronic-nuclear SE by\ndefining a loss function designed to equalize local energies across the system.\nThis approach is based on a rotationally equivariant total wavefunction ansatz\nthat includes both nuclear and electronic coordinates. This strategy not only\nallows for the efficient and accurate generation of a continuous potential\nenergy surface at any geometry within the well-sampled nuclear configuration\nspace, but also incorporates non-BOA corrections through a single training\nprocess. Comparison with benchmarks of atomic and molecular systems\ndemonstrates its accuracy and efficiency.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":"77 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Computational Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.04497","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Recent advances in machine learning have facilitated numerically accurate
solution of the electronic Schr\"{o}dinger 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, Schr\"{o}dingerNet, 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 rotationally equivariant total wavefunction ansatz
that includes both nuclear and electronic coordinates. This strategy not only
allows for the 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 molecular systems
demonstrates its accuracy and efficiency.
通过将各种基于神经网络(NN)的波函数解析与变异蒙特卡洛方法相结合,机器学习的最新进展促进了电子薛定谔方程(SE)的精确数值求解。然而,这些基于神经网络的方法都是基于天生-奥本海默近似(BOA)的,需要对每个核构型进行昂贵的计算训练。在这项工作中,我们提出了一种新颖的 NN 架构--Schr\"{o}dingerNet,通过定义一个旨在均衡整个系统局部能量的损失函数来求解全电子-核 SE。这种策略不仅可以在采样良好的核构型空间内的任何几何形状上高效、准确地生成连续势能面,还可以通过单一训练过程纳入非BOA 修正。与原子和分子系统基准的比较证明了它的准确性和效率。