  Deep learning inspired by differential equations is a recent research trend
and has marked the state of the art performance for many machine learning
tasks. Among them, time-series modeling with neural controlled differential
equations (NCDEs) is considered as a breakthrough. In many cases, NCDE-based
models not only provide better accuracy than recurrent neural networks (RNNs)
but also make it possible to process irregular time-series. In this work, we
enhance NCDEs by redesigning their core part, i.e., generating a continuous
path from a discrete time-series input. NCDEs typically use interpolation
algorithms to convert discrete time-series samples to continuous paths.
However, we propose to i) generate another latent continuous path using an
encoder-decoder architecture, which corresponds to the interpolation process of
NCDEs, i.e., our neural network-based interpolation vs. the existing explicit
interpolation, and ii) exploit the generative characteristic of the decoder,
i.e., extrapolation beyond the time domain of original data if needed.
Therefore, our NCDE design can use both the interpolated and the extrapolated
information for downstream machine learning tasks. In our experiments with 5
real-world datasets and 12 baselines, our extrapolation and interpolation-based
NCDEs outperform existing baselines by non-trivial margins.
