VPNets: Volume-preserving neural networks for learning source-free dynamics. (arXiv:2204.13843v2 [cs.LG] UPDATED)

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.

arxiv dynamics free learning lg networks neural networks