期刊
OPTICS COMMUNICATIONS
卷 222, 期 1-6, 页码 331-339出版社
ELSEVIER
DOI: 10.1016/S0030-4018(03)01570-0
关键词
neural networks; numerical simulation; solution of equations; numerical approximation and analysis; nonlinear Schrodinger equation
类别
We present a practical method for estimating the upper error bound in the neural network (NN) solution of the nonlinear Schrodinger equation (NLSE) under different degrees of nonlinearity. The error bound is a function of the nonnegative energy E value that is minimized when the NN is trained to solve the NLSE. The form of E is derived from the NLSE expression and the NN solution becomes identical with the true NLSE solution only when the E value is reduced exactly to zero. In practice, machines with finite floating-point range and accuracy are used for training and E is not decreased exactly to zero. Knowledge of the error bound permits the estimation of the maximum average error in the NN solution without prior knowledge of the true NLSE solution - a crucial factor in the practical applications of the NN technique. The error bound is verified for both the linear time - independent Schrodinger equation for a free particle, and the NLSE. We also discuss the conditions where the error bound formulation is valid. (C) 2003 Elsevier Science B.V. All rights reserved.
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