Learning Green's Function Efficiently Using Low-Rank Approximations

• URL: http://arxiv.org/abs/2308.00350v1
• Date: Tue, 1 Aug 2023 07:43:46 GMT
• Title: Learning Green's Function Efficiently Using Low-Rank Approximations
• Authors: Kishan Wimalawarne, Taiji Suzuki, Sophie Langer
• Abstract summary: 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.
• Score: 44.46178415547532
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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