Keywords: differential equations, neural processes, dynamics, deep learning, neural ode
Abstract: 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 new class of stochastic processes 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.
One-sentence Summary: Neural Processes with time-awareness
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Code: [![github](/images/github_icon.svg) crisbodnar/ndp](https://github.com/crisbodnar/ndp) + [![Papers with Code](/images/pwc_icon.svg) 1 community implementation](https://paperswithcode.com/paper/?openreview=27acGyyI1BY)