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.

本研究介绍了一个新的神经模型：神经控制微分方程模型，解决了利用常规微分方程对时间动态进行建模时无法针对后续观察调整轨迹的问题，并通过实验和理论结果展示其在较多数据集上实现了与其他神经网络模型相当的最佳性能