Bright-dark rogue wave transition in coupled ab system via the physics-informed neural networks method
DOI10.2140/camcos.2024.19.1zbMATH Open1545.65479MaRDI QIDQ6574264
Shilin Zhang, Yinchuan Zhao, Minhua Wang
Publication date: 18 July 2024
Published in: Communications in Applied Mathematics and Computational Science (Search for Journal in Brave)
Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Numerical methods for partial differential equations, boundary value problems (65N99) Soliton solutions (35C08) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weak adversarial networks for high-dimensional partial differential equations
- DGM: a deep learning algorithm for solving partial differential equations
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Self-adaptive physics-informed neural networks
- Multi-fidelity Bayesian neural networks: algorithms and applications
- Physics-informed semantic inpainting: application to geostatistical modeling
- Parallel physics-informed neural networks via domain decomposition
- A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
- Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
- Meta-learning PINN loss functions
- Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers \textit{via} the modified PINN
- Physics-informed neural networks for high-speed flows
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Bright-dark soliton solutions of the multi-component AB system
- Adversarial uncertainty quantification in physics-informed neural networks
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons
- Reducing the Dimensionality of Data with Neural Networks
- An example of soliton behaviour in a rotating baroclinic fluid
- The finite difference method at arbitrary irregular grids and its application in applied mechanics
- Evolution of baroclinic wave packets in a flow with continuous shear and stratification
- Algorithm 778: L-BFGS-B
- A coupled “AB” system: Rogue waves and modulation instabilities
- Envelope Solitary Waves and Periodic Waves in the AB Equations
- Periodic solutions and Whitham equations for the AB system
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements
- When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Finite-amplitude baroclinic instability of a mesoscale gravity current in a channel
- Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
- Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
- fPINNs: Fractional Physics-Informed Neural Networks
- Bright-dark soliton, breather and semirational rogue wave solutions for a coupled AB system
- Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations
- SLeNN-ELM: a shifted Legendre neural network method for fractional delay differential equations based on extreme learning machine
- Wave-packet behaviors of the defocusing nonlinear Schrödinger equation based on the modified physics-informed neural networks
- Error estimates for physics-informed neural networks approximating the Navier-Stokes equations
This page was built for publication: Bright-dark rogue wave transition in coupled ab system via the physics-informed neural networks method