Neural Controlled Differential Equations for Irregular Time Series

TL;DR

This paper introduces neural controlled differential equations, a novel approach for modeling irregular time series that overcomes limitations of neural ODEs by incorporating observations for trajectory adjustment, achieving state-of-the-art results.

Contribution

It proposes neural controlled differential equations for irregular time series, enabling trajectory adjustment based on observations and efficient backpropagation, with theoretical guarantees.

Findings

Achieves state-of-the-art performance on multiple datasets.

Demonstrates universal approximation capabilities.

Subsumes existing ODE-based models.

Abstract

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.