VPNets: Volume-preserving neural networks for learning source-free dynamics
This work addresses the challenge of modeling dynamical systems without external sources, which is important for physics and engineering applications, but it appears incremental as it builds on existing neural network methods with a specific structural constraint.
The authors tackled the problem of learning unknown source-free dynamical systems from trajectory data by proposing volume-preserving neural networks (VPNets), which are intrinsically volume-preserving, and demonstrated their effectiveness through numerical experiments.
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.