While deep learning algorithms demonstrate a great potential in scientific\ncomputing, its application to multi-scale problems remains to be a big\nchallenge. This is manifested by the "frequency principle" that neural networks\ntend to learn low frequency components first. Novel architectures such as\nmulti-scale deep neural network (MscaleDNN) were proposed to alleviate this\nproblem to some extent. In this paper, we construct a subspace decomposition\nbased DNN (dubbed SD$^2$NN) architecture for a class of multi-scale problems by\ncombining traditional numerical analysis ideas and MscaleDNN algorithms. The\nproposed architecture includes one low frequency normal DNN submodule, and one\n(or a few) high frequency MscaleDNN submodule(s), which are designed to capture\nthe smooth part and the oscillatory part of the multi-scale solutions,\nrespectively. In addition, a novel trigonometric activation function is\nincorporated in the SD$^2$NN model. We demonstrate the performance of the\nSD$^2$NN architecture through several benchmark multi-scale problems in regular\nor irregular geometric domains. Numerical results show that the SD$^2$NN model\nis superior to existing models such as MscaleDNN.\n
Discussion(0)
No comments yet. Be the first to comment.