Abstract

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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, NOD Es 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, which could be explained by many possible underlying dynamics. NOD Es do not capture this uncertainty. To this end, 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.