Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method
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Publication:2113241
DOI10.1016/j.chaos.2022.112118zbMath1505.35316arXiv2204.06311OpenAlexW4224033936MaRDI QIDQ2113241
Yin Fang, Yue-Yue Wang, Nikolay A. Kudryashov, Chao-Qing Dai, Gang-Zhou Wu
Publication date: 12 January 2023
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.06311
neural networknonlinear Schrödinger equationconservation-law constraintflexible learning rateKorteweg-de Vries and modified Korteweg-de Vries equations
Related Items (3)
Two-dimensional rogue wave clusters in self-focusing Kerr-media ⋮ A linearly implicit energy-preserving exponential time differencing scheme for the fractional nonlinear Schrödinger equation ⋮ Prediction of optical solitons using an improved physics-informed neural network method with the conservation law constraint
Cites Work
- Nonlinear stability of MKdV breathers
- Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
- Dark-bright soliton interactions in coupled nonautonomous nonlinear Schrödinger equation with complex potentials
- Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg-de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma
- Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers \textit{via} the modified PINN
- Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
- Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
- Numerical preservation of multiple local conservation laws
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Exp-function method for a generalized MKdV equation
- New solutions to mKdV equation
- Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
- A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
- Conserved quantities and symmetries of KP hierarchy
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
- A deep learning method for solving third-order nonlinear evolution equations
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