Advanced physics-informed neural networks for numerical approximation of the coupled Schrödinger-KdV equation (Q6590978)

scientific article; zbMATH DE number 7899937

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English	Advanced physics-informed neural networks for numerical approximation of the coupled Schrödinger-KdV equation	scientific article; zbMATH DE number 7899937

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title

Advanced physics-informed neural networks for numerical approximation of the coupled Schrödinger-KdV equation (English)

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Communications in Nonlinear Science and Numerical Simulation

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publication date

21 August 2024

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zbMATH Keywords

coupled Schrödinger-KdV system

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\(H_1\) loss function

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parallel PINNs

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Publication

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cites work

A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System

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Existence of bound and ground states for a system of coupled nonlinear Schrödinger-KdV equations

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Solitons of the coupled Schrödinger-Korteweg-de Vries system with arbitrary strengths of the nonlinearity and dispersion

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A complex ansatz method applied to nonlinear equations of Schrödinger type

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On the solution of the coupled Schrödinger-KdV equation by the decomposition method

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Numerical and approximate solutions for coupled time fractional nonlinear evolutions equations via reduced differential transform method

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The tanh method: a tool for solving some mathematical models

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The finite element method for the coupled Schrödinger-KdV equations

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Numerical studies on a novel split-step quadratic B-spline finite element method for the coupled Schrödinger-KdV equations

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A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations

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Convergence of a numerical scheme for a coupled Schrödinger-KdV system

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Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrödinger-KdV equation

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Homotopy perturbation method for coupled Schrödinger-KdV equation

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A meshless method for numerical solution of the coupled Schrödinger-KdV equations

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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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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

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NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations

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Discretizationnet: a machine-learning based solver for Navier-Stokes equations using finite volume discretization

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Adversarial uncertainty quantification in physics-informed neural networks

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Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks

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\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition

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

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Physics-informed neural networks for high-speed flows

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PPINN: parareal physics-informed neural network for time-dependent PDEs

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NAS-PINN: neural architecture search-guided physics-informed neural network for solving PDEs

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fPINNs: Fractional Physics-Informed Neural Networks

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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

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SPINN: sparse, physics-based, and partially interpretable neural networks for PDEs

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ModalPINN: an extension of physics-informed neural networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Parallel physics-informed neural networks via domain decomposition

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On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks

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Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method

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

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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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Multi-hump bright solitons in a Schrödinger-mKdV system

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.CNSNS.2024.108229

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Mathematics(1 entry)

mardi Publication:6590978