Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs

While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains be big challenge. This is manifested by the “frequency principle” that neural networks tend learn low frequency components first. Novel architectures such as network (MscaleDNN) were proposed alleviate this problem some extent. In paper, we construct subspace decomposition based DNN (dubbed SD2NN) architecture for class of combining MscaleDNN with traditional numerical analysis ideas. The includes one normal submodule, and (or few) high submodule(s), which are designed capture smooth part oscillatory solutions simultaneously. We SD2NN outperforms existing models MscaleDNN, through several benchmark regular or perforated domains.