  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.
