  Owing to the remarkable development of deep learning technology, there have
been a series of efforts to build deep learning-based climate models. Whereas
most of them utilize recurrent neural networks and/or graph neural networks, we
design a novel climate model based on the two concepts, the neural ordinary
differential equation (NODE) and the diffusion equation. Many physical
processes involving a Brownian motion of particles can be described by the
diffusion equation and as a result, it is widely used for modeling climate. On
the other hand, neural ordinary differential equations (NODEs) are to learn a
latent governing equation of ODE from data. In our presented method, we combine
them into a single framework and propose a concept, called neural diffusion
equation (NDE). Our NDE, equipped with the diffusion equation and one more
additional neural network to model inherent uncertainty, can learn an
appropriate latent governing equation that best describes a given climate
dataset. In our experiments with two real-world and one synthetic datasets and
eleven baselines, our method consistently outperforms existing baselines by
non-trivial margins.
