Transferable neural networks for partial differential equations
DOI10.1007/S10915-024-02463-YarXiv2301.11701MaRDI QIDQ6123346
Lili Ju, Zezhong Zhang, Feng Bao, Guannan Zhang
Publication date: 4 March 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2301.11701
Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Numerical computation of solutions to systems of equations (65H10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Cites Work
- Weak adversarial networks for high-dimensional partial differential equations
- Solving differential equations of fractional order using an optimization technique based on training artificial neural network
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- Neural operator prediction of linear instability waves in high-speed boundary layers
- Nonlinear approximation and (deep) ReLU networks
- Transfer learning based multi-fidelity physics informed deep neural network
- PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- The Random Feature Model for Input-Output Maps between Banach Spaces
- Neural‐network‐based approximations for solving partial differential equations
- MIONet: Learning Multiple-Input Operators via Tensor Product
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
- On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions
- Approximation by superpositions of a sigmoidal function
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