Multiple Shooting for Training Neural Differential Equations on Time Series

Neural differential equations have recently emerged as a flexible data-driven/hybrid approach to model time-series data. This letter 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.