  Time series with non-uniform intervals occur in many applications, and are
difficult to model using standard recurrent neural networks (RNNs). We
generalize RNNs to have continuous-time hidden dynamics defined by ordinary
differential equations (ODEs), a model we call ODE-RNNs. Furthermore, we use
ODE-RNNs to replace the recognition network of the recently-proposed Latent ODE
model. Both ODE-RNNs and Latent ODEs can naturally handle arbitrary time gaps
between observations, and can explicitly model the probability of observation
times using Poisson processes. We show experimentally that these ODE-based
models outperform their RNN-based counterparts on irregularly-sampled data.
