Learning Green's Function Efficiently Using Low-Rank Approximations
Not on the map. Why?
Abstract (arXiv)
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive Monte-Carlo integral approximations. We propose to learn the Green's function by low-rank decomposition, which results in a novel architecture to remove redundant computations by separate learning with domain data for evaluation and Monte-Carlo samples for integral approximation. Using experiments we show that the proposed method improves computational time compared to MOD-Net while achieving comparable accuracy compared to both PINNs and MOD-Net.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 16 of its 31 references that are in the map. First posted on arXiv 1 Aug 2023.
Builds on
16 of 31 references.
References · 16
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
- 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
- 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
- 2023Separable Physics-Informed Neural Networkscited by 64
- 2020DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problemscited by 61
- 2021Meta-learning PINN loss functionscited by 51
- 2021Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimalitycited by 40
- 2021Learning elliptic partial differential equations with randomized linear algebracited by 29
- 2022Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activationscited by 29
4 more
- 2022Learning Green's functions associated with time-dependent partial differential equationscited by 25
- 2021MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEscited by 24
- 2022Bounding the Rademacher Complexity of Fourier neural operatorscited by 16
- 2021Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solvercited by 15
Built on by
Citing papers per year: 2025: 1.
1 paper.