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arXiv · 2204.13843

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

Aiqing Zhu·Beibei Zhu·Jiawei Zhang·Yifa Tang·Jian Liu
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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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Aiqing Zhu, Beibei Zhu, Jiawei Zhang, Yifa Tang, Jian Liu. 2022-04-29. VPNets: Volume-preserving neural networks for learning source-free dynamics. https://arxiv.org/abs/2204.13843

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