The defocusing action ground state of the nonlinear Schrodinger equation can be characterized via three different but equivalent minimization formulations.In this work,we propose some deep neural network(DNN)approache...The defocusing action ground state of the nonlinear Schrodinger equation can be characterized via three different but equivalent minimization formulations.In this work,we propose some deep neural network(DNN)approaches to compute the action ground state through the three formulations.We first consider the unconstrained formulation,where we propose the DNN with a shift layer and demonstrate its necessity towards finding the correct ground state.The other two formulations involve the L^(p+1)-normalization or the Nehari manifold constraint.We enforce them as hard constraints into the networks by further proposing a normalization layer or a projection layer to the DNN.Our DNNs can then be trained in an unconstrained and unsupervised manner.Systematical numerical experiments are conducted to demonstrate the effectiveness and superiority of the approaches.展开更多
基金supported by the National Natural Science Foundation of China No.12271413the Natural Science Foundation of Hubei Province No.2019CFA007the Fundamental Research Funds for the Central Universities No.2042024kf0016。
文摘The defocusing action ground state of the nonlinear Schrodinger equation can be characterized via three different but equivalent minimization formulations.In this work,we propose some deep neural network(DNN)approaches to compute the action ground state through the three formulations.We first consider the unconstrained formulation,where we propose the DNN with a shift layer and demonstrate its necessity towards finding the correct ground state.The other two formulations involve the L^(p+1)-normalization or the Nehari manifold constraint.We enforce them as hard constraints into the networks by further proposing a normalization layer or a projection layer to the DNN.Our DNNs can then be trained in an unconstrained and unsupervised manner.Systematical numerical experiments are conducted to demonstrate the effectiveness and superiority of the approaches.
