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.

翻译：我们建议使用轨迹数据建立数量保存网络(VPNets),以学习未知的无源动态系统;我们提出三个模块,并把它们结合起来,以获得两个网络结构,即R-VPNet和LA-VPNet。拟议模型的明显特征是它们本身具有数量保存能力。此外,相应的近似理论得到了证明,从理论上保证了拟议VPNets的表达性,以学习无源动态。数字实验显示了VP-Net的有效性、一般化能力和结构保护特性。