Learning Green's Function Efficiently Using Low-Rank Approximations
Abstract
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.
Cite
Text
Wimalawarne et al. "Learning Green's Function Efficiently Using Low-Rank Approximations." ICML 2023 Workshops: SynS_and_ML, 2023.Markdown
[Wimalawarne et al. "Learning Green's Function Efficiently Using Low-Rank Approximations." ICML 2023 Workshops: SynS_and_ML, 2023.](https://mlanthology.org/icmlw/2023/wimalawarne2023icmlw-learning/)BibTeX
@inproceedings{wimalawarne2023icmlw-learning,
title = {{Learning Green's Function Efficiently Using Low-Rank Approximations}},
author = {Wimalawarne, Kishan and Suzuki, Taiji and Langer, Sophie},
booktitle = {ICML 2023 Workshops: SynS_and_ML},
year = {2023},
url = {https://mlanthology.org/icmlw/2023/wimalawarne2023icmlw-learning/}
}