Learning Green's Function Efficiently Using Low-Rank Approximations

2023/08/01 by Kishan Wimalawarne, Taiji Suzuki, Wimalawarne, Kishan +3 · 2 citations
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2308.00350

openalex publication_date 2023/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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