  Neural Ordinary Differential Equations (NODEs) use a neural network to model
the instantaneous rate of change in the state of a system. However, despite
their apparent suitability for dynamics-governed time-series, NODEs present a
few disadvantages. First, they are unable to adapt to incoming data points, a
fundamental requirement for real-time applications imposed by the natural
direction of time. Second, time series are often composed of a sparse set of
measurements that could be explained by many possible underlying dynamics.
NODEs do not capture this uncertainty. In contrast, Neural Processes (NPs) are
a family of models providing uncertainty estimation and fast data adaptation
but lack an explicit treatment of the flow of time. To address these problems,
we introduce Neural ODE Processes (NDPs), a new class of stochastic processes
determined by a distribution over Neural ODEs. By maintaining an adaptive
data-dependent distribution over the underlying ODE, we show that our model can
successfully capture the dynamics of low-dimensional systems from just a few
data points. At the same time, we demonstrate that NDPs scale up to challenging
high-dimensional time-series with unknown latent dynamics such as rotating
MNIST digits.
