Data driven governing equations approximation using deep neural networks

JOURNAL OF COMPUTATIONAL PHYSICS

卷:395

Article

Qin, Tong¹  Wu, Kailiang¹  Xiu, Dongbin¹ 

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

关键词: Deep neural network;    Residual network;    Recurrent neural network;    Governing equation discovery;   

DOI  :  10.1016/j.jcp.2019.06.042

来源: Elsevier

【 摘 要 】

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation approximation. We demonstrate that the ResNet block can be considered as a one-step method that is exact in temporal integration. We then present two multi-step methods, recurrent ResNet (RT-ResNet) method and recursive ReNet (RS-ResNet) method. The RT-ResNet is a multi-step method on uniform time steps, whereas the RS-ResNet is an adaptive multi-step method using variable time steps. All three methods presented here are based on integral form of the underlying dynamical system. As a result, they do not require time derivative data for equation recovery and can cope with relatively coarsely distributed trajectory data. Several numerical examples are presented to demonstrate the performance of the methods. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free