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Parallel physics-informed neural networks method with regularization strategies for the forward-inverse problems of the variable coefficient modified KdV equation - MaRDI portal

Parallel physics-informed neural networks method with regularization strategies for the forward-inverse problems of the variable coefficient modified KdV equation (Q6130986)

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scientific article; zbMATH DE number 7827315

Language	Label	Description	Also known as
English	Parallel physics-informed neural networks method with regularization strategies for the forward-inverse problems of the variable coefficient modified KdV equation	scientific article; zbMATH DE number 7827315

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scholarly article

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Parallel physics-informed neural networks method with regularization strategies for the forward-inverse problems of the variable coefficient modified KdV equation (English)

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10.1007/s11424-024-3467-7

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Journal of Systems Science and Complexity

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publication date

3 April 2024

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

data-driven forward-inverse problems

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parallel physics-informed neural networks

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regularization strategies

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variable coefficient modified KdV equation

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s11424-024-3467-7

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Mathematical physiology. I: Cellular physiology

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Generalized \(x\)-dependent modified Korteweg-de Vries equation: Painlevé analysis, Bäcklund transformation and soliton solutions

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The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions

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The exact solution and integrable properties to the variable-coefficient modified Korteweg-de Vries equation

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Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach

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Solitary wave solutions for a generalized KdV-mKdV equation with variable coefficients

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Painlevé property, Lax pair and Darboux transformation of the variable-coefficient modified Kortweg-de Vries model in fluid-filled elastic tubes

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\(N\)-fold Darboux transformation and double-Wronskian-typed solitonic structures for a variable-coefficient modified Kortweg-de Vries equation

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Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber

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Nondegenerate solitons and collision dynamics of the variable-coefficient coupled higher-order nonlinear Schrödinger model via the Hirota method

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High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation

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Variable-coefficient higher-order nonlinear Schrödinger model in optical fibers: variable-coefficient bilinear form, Bäcklund transformation, Brightons and symbolic computation

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Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations

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Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method

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Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

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Solving second-order nonlinear evolution partial differential equations using deep learning

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A deep learning method for solving third-order nonlinear evolution equations

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PINN deep learning method for the Chen-Lee-Liu equation: rogue wave on the periodic background

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A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions

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Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions

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Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning

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Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers \textit{via} the modified PINN

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

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Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning

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VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient

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On the limited memory BFGS method for large scale optimization

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