VPNets: Volume-preserving neural networks for learning source-free dynamics

2022/04/29 by Aiqing Zhu, Beibei Zhu, Zhu, Aiqing +7 · 1 citation
Computer Science · #Time Series Analysis and Forecasting #Neural Networks and Applications #Gaussian Processes and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2204.13843

Abstract

We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two network architectures, coined R-VPNet and LA-VPNet. The distinct feature of the proposed models is that they are intrinsic volume-preserving. In addition, the corresponding approximation theorems are proved, which theoretically guarantee the expressivity of the proposed VPNets to learn source-free dynamics. The effectiveness, generalization ability and structure-preserving property of the VP-Nets are demonstrated by numerical experiments.

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