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Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger · James Morrill · James Foster · Terry Lyons

Thu Dec 10 08:20 AM -- 08:30 AM (PST) @ Orals & Spotlights: Deep Learning

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.

Author Information

Patrick Kidger (University of Oxford)
James Morrill (University of Oxford)
James Foster (University of Oxford)
Terry Lyons (University of Oxford)

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