  Smooth dynamics interrupted by discontinuities are known as hybrid systems
and arise commonly in nature. Latent ODEs allow for powerful representation of
irregularly sampled time series but are not designed to capture trajectories
arising from hybrid systems. Here, we propose the Latent Segmented ODE
(LatSegODE), which uses Latent ODEs to perform reconstruction and changepoint
detection within hybrid trajectories featuring jump discontinuities and
switching dynamical modes. Where it is possible to train a Latent ODE on the
smooth dynamical flows between discontinuities, we apply the pruned exact
linear time (PELT) algorithm to detect changepoints where latent dynamics
restart, thereby maximizing the joint probability of a piece-wise continuous
latent dynamical representation. We propose usage of the marginal likelihood as
a score function for PELT, circumventing the need for model complexity-based
penalization. The LatSegODE outperforms baselines in reconstructive and
segmentation tasks including synthetic data sets of sine waves, Lotka Volterra
dynamics, and UCI Character Trajectories.
