Deep surrogate model for learning Green's function associated with linear reaction-diffusion operator

DOI10.4208/IJNAM2024-1028MaRDI QIDQ6648520

Junqing Jia, Xiaoping Zhang, Lili Ju

Publication date: 4 December 2024

Published in: International Journal of Numerical Analysis and Modeling (Search for Journal in Brave)

zbMATH Keywords

Green's functionfast solversurrogate modeldeep learningreaction-diffusion operator

Mathematics Subject Classification ID

Green's functions for ordinary differential equations (34B27) Numerical methods for partial differential equations, boundary value problems (65N99)

Cites Work

• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• DGM: a deep learning algorithm for solving partial differential equations
• Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
• A mesh-free method for interface problems using the deep learning approach
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• BI-GreenNet: learning Green's functions by boundary integral network
• Neural‐network‐based approximations for solving partial differential equations
• A Comparison Study of Deep Galerkin Method and Deep Ritz Method for Elliptic Problems with Different Boundary Conditions
• 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

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