Solving Schrodinger Equation with Soft Constrained Monotonic Neural Network  

用软约束单调神经网络求解薛定谔方程

作　　者：LIU Xuan LI Hanlin PU Kaifang PANG Longgang 刘轩;李汉林;蒲开放;庞龙刚(武汉科技大学理学院,武汉430065;华中师范大学粒子物理研究所和夸克与轻子物理教育部重点实验室,武汉430079)

机构地区：[1]College of Science,Wuhan University of Science and Technology,Wuhan 430065,China [2]Key Laboratory of Quark and Lepton Physics(MOE)and Institute of Particle Physics,Central China Normal University,Wuhan 430079,China

出　　处：《原子核物理评论》2024年第1期379-384,共6页Nuclear Physics Review

基　　金：国家自然科学基金资助项目(12035006,12075098);湖北省科技厅基金资助项目(2019CFB563,2021BLB171)。

摘　　要：Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.人工神经网络(Artificial Neural Network,ANN)以其强大的信息封装能力和方便的变分优化方法成为科学研究领域的有力工具。特别是最近在计算物理解决变分问题方面取得了许多进展。用深度神经网络(DNN)表示波函数来求解变分优化的量子多体问题时,使用一种新的物理信息神经网络(PINN)来表示量子力学中一些经典问题的累积分布函数(CDF),并通过CDF获得它们的基态波函数和基态能量。通过对精确解的基准测试,可以将结果的误差控制在很小范围。这种新的网络结构和优化方法为解决量子多体问题提供了新的选择。

关 键 词：deep neural network variational problem Cumulative distribution function ground state wave function 

分 类 号：O571.6[理学—粒子物理与原子核物理]