Multiscale Neural Networks for Approximating Green's Functions Article Swipe

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Wenrui Hao , Ruipeng Li , Yuanzhe Xi , Tianshi Xu , Yahong Yang ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2410.18439

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green's functions. However, Green's functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this paper, we address these challenges by leveraging multiscale NNs to learn Green's functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2410.18439
PDF: https://arxiv.org/pdf/2410.18439
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4404313112

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DOI: https://doi.org/10.48550/arxiv.2410.18439

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Title: Multiscale Neural Networks for Approximating Green's Functions

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-10-24

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Authors: Wenrui Hao, Ruipeng Li, Yuanzhe Xi, Tianshi Xu, Yahong Yang

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Landing page: https://arxiv.org/abs/2410.18439

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PDF URL: https://arxiv.org/pdf/2410.18439

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Concepts: Artificial neural network, Mathematics, Computer science, Artificial intelligence

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