On generalized residual network for deep learning of unknown dynamical systems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:438

Article

Chen, Zhen¹  Xiu, Dongbin¹ 

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

关键词: Deep neural network;    Residual network;    Governing equation discovery;    Model correction;   

DOI  :  10.1016/j.jcp.2021.110362

来源: Elsevier

【 摘 要 】

We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified residual network (ResNet) as an effective neural network learning structure. In this paper, we present a generalized ResNet framework and broadly define residue as the discrepancy between observation data and prediction made by another model, which can be an existing coarse model or reduced order model. In this case, the generalized ResNet serves as a model correction to the existing model and recovers the unresolved/missing dynamics. When an existing coarse model is not available, we present numerical strategies for fast creation of coarse models, to be used in conjunction with the generalized ResNet. These coarse models are constructed using the same data set and thus do not require additional resource. The generalized ResNet is capable of learning the underlying unknown dynamics and producing predictions with accuracy higher than the standard ResNet structure. This is demonstrated via several numerical examples, including long-term prediction of a chaotic system. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free