Open AccessSolving the nonlinear Schrodinger equation with an unsupervised neural network
Author(s) -
Christopher Monterola,
Caesar Saloma
Publication year - 2001
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.9.000072
Subject(s) - artificial neural network , nonlinear system , position (finance) , schrödinger equation , energy (signal processing) , boundary value problem , differential equation , nonlinear schrödinger equation , mathematics , physics , mathematical analysis , computer science , artificial intelligence , quantum mechanics , finance , economics
We solve the nonlinear Schrodinger equation with an unsupervised neural network with the optical axis position z and time t as inputs. The network outputs the real and imaginary components of the solution. Unsupervised training aims to minimize a non-negative energy function derived from the equation and the boundary conditions. The trained network is generalizing - a solution value is determined at any (z, t)-combination including those not considered during training. Solutions with normalized mean-squared errors of order 10;-2, are obtained when the average energy is reduced to 10;-2 from order 10;4. The NN method is universal and applies to other complex differential equations.