VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient
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Publication:6069931
DOI10.1016/j.physd.2023.133945zbMath1527.35500arXiv2305.07479MaRDI QIDQ6069931
Publication date: 17 November 2023
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2305.07479
Inverse problems for PDEs (35R30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)
Related Items (2)
Parallel physics-informed neural networks method with regularization strategies for the forward-inverse problems of the variable coefficient modified KdV equation ⋮ Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations
Cites Work
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- Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- Borel summability of the heat equation with variable coefficients
- Perturbation of topological solitons due to sine-Gordon equation and its type
- Weak adversarial networks for high-dimensional partial differential equations
- One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada-Kotera equation
- Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning
- Painlevé analysis and new analytic solutions for variable-coefficient Kadomtsev-Petviashvili equation with symbolic computation
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra
- DGM: a deep learning algorithm for solving partial differential equations
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning
- Data-driven discoveries of Bäcklund transformations and soliton evolution equations via deep neural network learning schemes
- Self-adaptive physics-informed neural networks
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- Parallel physics-informed neural networks via domain decomposition
- DeepM\&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
- A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
- When and why PINNs fail to train: a neural tangent kernel perspective
- Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
- Meta-learning PINN loss functions
- \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm
- CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
- Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
- Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions
- A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
- Slowly varying solitary waves. I. Korteweg-de Vries equation
- Solitons in Shallow Seas of Variable Depth and in Marine Straits
- Decay estimates for wave equations with variable coefficients
- N-soliton solutions, Bäcklund transformation and Lax pair for a generalized variable-coefficient fifth-order Korteweg–de Vries equation
- Auto-Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg–de Vries equation. I
- A variable coefficient Korteweg–de Vries equation: Similarity analysis and exact solution. II
- Integrable Nonlinear Equations for Water Waves in Straits of Varying Depth and Width
- Neural‐network‐based approximations for solving partial differential equations
- Method for Solving the Korteweg-deVries Equation
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Physics-Informed Neural Networks with Hard Constraints for Inverse Design
- Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
- fPINNs: Fractional Physics-Informed Neural Networks
- Approximation by superpositions of a sigmoidal function
- Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations
- Solving second-order nonlinear evolution partial differential equations using deep learning
- Deep learning soliton dynamics and complex potentials recognition for 1D and 2D \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equations
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