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Abstract <p>The paper considers a method based on physics-informed neural networks (PINNs) for solving the problem of modelling the propagation of pulses in a nonlinear optical medium described by the generalized nonlinear Schrödinger equation (GNSE), including the case of 6th-order GNSE with 7th-order nonlinearity. Based on the analysis of problems with existing analytical solutions, a model has been proposed that includes a selected set of hyperparameters and modifications: modifications to the loss function, various optimization algorithms, and an advanced method for selecting collocation points. The proposed solution achieved accuracy 13.8 times higher compared to the classical PINNs. The obtained configuration was used to solve problems of modelling two and three sequentially propagating solitons, which do not have analytical solutions. The solution’s validity was verified using conservation laws. The obtained configuration of PINNs yields good results both for modelling single solitons and for multisoliton problems, and it allows achieving an average error on conservation laws of less than 1<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\%\)</EquationSource> <!--BPhysMGU2570301Moloshnikov-m1--> </InlineEquation>.</p>

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Neural Network Modeling of Optical Solitons Described by the Generalized Nonlinear Schrödinger Equation of the Sixth Order with High Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • I. A. Moloshnikov,
  • M. S. Kuvakin,
  • A. G. Sboev

摘要

Abstract

The paper considers a method based on physics-informed neural networks (PINNs) for solving the problem of modelling the propagation of pulses in a nonlinear optical medium described by the generalized nonlinear Schrödinger equation (GNSE), including the case of 6th-order GNSE with 7th-order nonlinearity. Based on the analysis of problems with existing analytical solutions, a model has been proposed that includes a selected set of hyperparameters and modifications: modifications to the loss function, various optimization algorithms, and an advanced method for selecting collocation points. The proposed solution achieved accuracy 13.8 times higher compared to the classical PINNs. The obtained configuration was used to solve problems of modelling two and three sequentially propagating solitons, which do not have analytical solutions. The solution’s validity was verified using conservation laws. The obtained configuration of PINNs yields good results both for modelling single solitons and for multisoliton problems, and it allows achieving an average error on conservation laws of less than 1 \(\%\) .