Data-driven solutions and parameter discovery of the Sasa-Satsuma equation via the physics-informed neural networks method

DOI10.1016/j.physd.2022.133489zbMath1498.35157OpenAlexW4292489282WikidataQ113866667 ScholiaQ113866667MaRDI QIDQ2083739

Ya-Bin Zhang, Lei Wang, Jing-Jing Su, Yinchuan Zhao, Hao-Tian Luo, Gui Lu

Publication date: 11 October 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2022.133489

zbMATH Keywords

machine learningphysics-informed neural networkappropriate learnable parametersparameter discovery

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (1)

A two-component Sasa-Satsuma equation: large-time asymptotics on the line

Uses Software

• PMTK

Cites Work

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• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• On the limited memory BFGS method for large scale optimization
• Machine learning of linear differential equations using Gaussian processes
• Hidden physics models: machine learning of nonlinear partial differential equations
• Multilayer feedforward networks are universal approximators
• Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
• Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning
• Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Sasa-Satsuma equation, unstable plane waves and heteroclinic connections
• Human-level concept learning through probabilistic program induction
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Method for Solving the Korteweg-deVries Equation
• Large Sample Properties of Simulations Using Latin Hypercube Sampling
• New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
• Soliton solutions for a perturbed nonlinear Schrodinger equation
• The Riemann problem method for solving a perturbed nonlinear Schrodinger equation describing pulse propagation in optic fibres
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• An Algorithm for the Machine Calculation of Complex Fourier Series

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