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Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs
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DOI：10.1016/j.jcp.2023.112242.png)
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摘要
En 中文
While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the frequency principle that neural networks tend to learn low frequency components first. Novel architectures such as multi-scale deep neural network (MscaleDNN) were proposed to alleviate this problem to some extent. In this paper, we construct a subspace decomposition based DNN (dubbed SD2NN) architecture for a class of multi-scale problems by combining MscaleDNN algorithms with traditional numerical analysis ideas. The proposed architecture includes one low frequency normal DNN submodule, and one (or a few) high frequency MscaleDNN submodule(s), which are designed to capture the smooth part and the oscillatory part of the multi-scale solutions simultaneously. We demonstrate that the SD2NN outperforms existing models such as MscaleDNN, through several benchmark multi-scale problems in regular or perforated domains. & COPY; 2023 Elsevier Inc. All rights reserved.
Keyword:
Multi-scale
DNN
Fourier
Subspace-decomposed
Activation function
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期刊
IF:
3.8
论文数:
1.6W
被引数:
7.7W
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