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

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