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Poster
in
Workshop: The Synergy of Scientific and Machine Learning Modelling (SynS & ML) Workshop

Learning Green's Function Efficiently Using Low-Rank Approximations

Kishan Wimalawarne · Taiji Suzuki · Sophie Langer

Keywords: [ Green function ] [ PDE ] [ low rank ]


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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