Deep finite volume method for partial differential equations
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Publication:6615033
DOI10.1016/j.jcp.2024.113307MaRDI QIDQ6615033
Publication date: 8 October 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)
Cites Work
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- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- Weak adversarial networks for high-dimensional partial differential equations
- Analysis of linear and quadratic simplicial finite volume methods for elliptic equations
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations
- Learning phase field mean curvature flows with neural networks
- A derivative-free method for solving elliptic partial differential equations with deep neural networks
- PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries
- MIM: a deep mixed residual method for solving high-order partial differential equations
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Solving many-electron Schrödinger equation using deep neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Adaptive deep neural networks methods for high-dimensional partial differential equations
- DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations
- Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients
- The Divergence Theorem
- Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
- Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
- Learning representations by back-propagating errors
- Failure-Informed Adaptive Sampling for PINNs
- wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws
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