Neural differential equations have recently emerged as a flexible data-driven/hybrid approach to model time-series data. This work experimentally demonstrates that if the data contains oscillations, then standard fitting of a neural differential equation may result in a flattened out trajectory that fails to describe the data. We then introduce the multiple shooting method and present successful demonstrations of this method for the fitting of a neural differential equation to two datasets (synthetic and experimental) that the standard approach fails to fit. Constraints introduced by multiple shooting can be satisfied using a penalty or augmented Lagrangian method.

翻译：神经差异方程式最近作为一种灵活的数据驱动/混合方法出现,用于模拟时间序列数据。这项工作实验性地证明,如果数据含有振动,那么神经差异方程式的标准安装可能导致轨迹平坦,无法描述数据。然后,我们引入了多种射击方法,并成功演示了这种方法,将神经差异方程式安装到两种(合成和实验)标准方法不符合的数据集(合成和实验)上。多枪射击带来的限制可以通过罚款或增强拉格兰加法来满足。