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 work experimentally demonstrates that if the data contains oscillations, then standard fitting of neural equation may result in flattened out trajectory fails describe We introduce multiple shooting method and present successful demonstrations this for two datasets (synthetic experimental) fit. Constraints introduced by can be satisfied using penalty or augmented Lagrangian method.