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.

翻译：普通神经等同(NODs)使用神经网络来模拟一个系统状态的瞬时变化速度。然而,尽管它们显然适合动态管理的时间序列,但NODs有一些缺点。首先,它们无法适应进取的数据点,这是自然时间方向对实时应用施加的一项基本要求。第二,时间序列往往由一套稀少的测量组成,可以用许多潜在动态来解释。NODs并不能够捕捉这种不确定性。相比之下,神经进程(NPs)是一个提供不确定性估计和快速数据适应的模型组合,但缺乏对时间流的明确处理。为了解决这些问题,我们引入了神经模式进程(NDPs),这是由神经模式组织内分流分配决定的新型随机分析过程。通过在基本ODS上保持适应性的数据分布,我们表明我们的模型能够成功地从几个数据点捕捉到低度系统的动态。与此同时,我们证明NDPs向具有挑战性的高维时间序列,其潜在动态是未知的。