Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations
DOI10.1016/j.jcp.2023.112415arXiv2206.09299MaRDI QIDQ6078492
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Publication date: 27 September 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2206.09299
partial differential equationsLie symmetryinvariant surface conditionssymmetry-enhanced physics-informed neural network
Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)
Cites Work
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- Nonclassical potential symmetries for the Burgers equation
- On the limited memory BFGS method for large scale optimization
- Lie symmetry analysis and exact explicit solutions for general Burgers' equation
- Symmetry and integration methods for differential equations
- A (2+1)-dimensional breaking soliton equation: solutions and conservation laws
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- 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
- Neural networks enforcing physical symmetries in nonlinear dynamical lattices: the case example of the Ablowitz-Ladik model
- 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
- Classical and nonclassical symmetries analysis for initial value problems
- A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations
- A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
- Finding symmetries by incorporating initial conditions as side conditions
- Integrable (2+1)-dimensional and (3+1)-dimensional breaking soliton equations
- Large Sample Properties of Simulations Using Latin Hypercube Sampling
- A new hierarchy of Korteweg–de Vries equations
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Locally adaptive activation functions with slope recovery for deep and physics-informed 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
- fPINNs: Fractional Physics-Informed Neural Networks
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