  Neural ordinary differential equations are an attractive option for modelling
temporal dynamics. However, a fundamental issue is that the solution to an
ordinary differential equation is determined by its initial condition, and
there is no mechanism for adjusting the trajectory based on subsequent
observations. Here, we demonstrate how this may be resolved through the
well-understood mathematics of \emph{controlled differential equations}. The
resulting \emph{neural controlled differential equation} model is directly
applicable to the general setting of partially-observed irregularly-sampled
multivariate time series, and (unlike previous work on this problem) it may
utilise memory-efficient adjoint-based backpropagation even across
observations. We demonstrate that our model achieves state-of-the-art
performance against similar (ODE or RNN based) models in empirical studies on a
range of datasets. Finally we provide theoretical results demonstrating
universal approximation, and that our model subsumes alternative ODE models.
