Data-driven discoveries of Bäcklund transformations and soliton evolution equations via deep neural network learning schemes
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Publication:2081273
DOI10.1016/j.physleta.2022.128373OpenAlexW4294959391WikidataQ114949327 ScholiaQ114949327MaRDI QIDQ2081273
Zijian Zhou, Zhenya Yan, Li Wang
Publication date: 12 October 2022
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.09489
Artificial neural networks and deep learning (68T07) NLS equations (nonlinear Schrödinger equations) (35Q55) Biology and other natural sciences (92-XX) Statistical mechanics, structure of matter (82-XX)
Related Items (3)
VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient ⋮ Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions ⋮ A new method for solving nonlinear partial differential equations based on liquid time-constant networks
Uses Software
Cites Work
- Rogue waves in the ocean
- Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning
- On the limited memory BFGS method for large scale optimization
- Applications of symmetry methods to partial differential equations
- Bäcklund transformations and their applications
- Bäcklund transformations, the inverse scattering method, solitons, and their applications. NSF research workshop on contact transformations
- Hidden physics models: machine learning of nonlinear partial differential equations
- DGM: a deep learning algorithm for solving partial differential equations
- Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning
- A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
- \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm
- Physics-informed neural networks for high-speed flows
- Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Darboux transformations in integrable systems. Theory and their applications to geometry
- Human-level concept learning through probabilistic program induction
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
- Large Sample Properties of Simulations Using Latin Hypercube Sampling
- The Korteweg–deVries Equation: A Survey of Results
- Neural‐network‐based approximations for solving partial differential equations
- Method for Solving the Korteweg-deVries Equation
- Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
- Solving high-dimensional partial differential equations using deep learning
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Learning data-driven discretizations for partial differential equations
- Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
- fPINNs: Fractional Physics-Informed Neural Networks
- Integrals of nonlinear equations of evolution and solitary waves
- The partial differential equation ut + uux = μxx
- On a quasi-linear parabolic equation occurring in aerodynamics
- Symmetries and differential equations
- Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves
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