Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm

•We explore a deep learning method for solving coupled nonlinear Schrödinger equation.•We propose an improved PINN algorithm by error measurement, multistage training and adaptive weights techniques.•The data-driven vector soliton and two-soliton solutions are derived by the proposed method. In this...

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Veröffentlicht in:Physics letters. A Jg. 421; S. 127739
Hauptverfasser: Mo, Yifan, Ling, Liming, Zeng, Delu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 06.01.2022
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ISSN:0375-9601, 1873-2429
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Abstract •We explore a deep learning method for solving coupled nonlinear Schrödinger equation.•We propose an improved PINN algorithm by error measurement, multistage training and adaptive weights techniques.•The data-driven vector soliton and two-soliton solutions are derived by the proposed method. In this work, we explore a deep learning algorithm for vector solitons of the coupled nonlinear Schrödinger equation (CNLSE). Based on the original physics-informed neural networks (PINN), we propose a pre-fixed multi-stage training algorithm by combining the ideas of error measurement, multi-stage training and adaptive weights. The result of numerical simulation demonstrates that the improved algorithm not only can recover different dynamical behaviors of solitons in the coupled equation but also has better approximation ability and faster convergence rate.
AbstractList •We explore a deep learning method for solving coupled nonlinear Schrödinger equation.•We propose an improved PINN algorithm by error measurement, multistage training and adaptive weights techniques.•The data-driven vector soliton and two-soliton solutions are derived by the proposed method. In this work, we explore a deep learning algorithm for vector solitons of the coupled nonlinear Schrödinger equation (CNLSE). Based on the original physics-informed neural networks (PINN), we propose a pre-fixed multi-stage training algorithm by combining the ideas of error measurement, multi-stage training and adaptive weights. The result of numerical simulation demonstrates that the improved algorithm not only can recover different dynamical behaviors of solitons in the coupled equation but also has better approximation ability and faster convergence rate.
ArticleNumber 127739
Author Mo, Yifan
Ling, Liming
Zeng, Delu
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  surname: Ling
  fullname: Ling, Liming
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  givenname: Delu
  surname: Zeng
  fullname: Zeng, Delu
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Keywords Deep learning
Two-soliton solutions
Nondegenerate vector soliton
Data-driven solutions
Coupled nonlinear Schrödinger equation
Language English
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Snippet •We explore a deep learning method for solving coupled nonlinear Schrödinger equation.•We propose an improved PINN algorithm by error measurement, multistage...
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SubjectTerms Coupled nonlinear Schrödinger equation
Data-driven solutions
Deep learning
Nondegenerate vector soliton
Two-soliton solutions
Title Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm
URI https://dx.doi.org/10.1016/j.physleta.2021.127739
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