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.
@article{arxiv.2308.00350,
title = {Learning Green's Function Efficiently Using Low-Rank Approximations},
author = {Kishan Wimalawarne and Taiji Suzuki and Sophie Langer},
journal= {arXiv preprint arXiv:2308.00350},
year = {2023}
}