We propose a new method for spatio-temporal forecasting on arbitrarily
distributed points. Assuming that the observed system follows an unknown
partial differential equation, we derive a continuous-time model for the
dynamics of the data via the finite element method. The resulting graph neural
network estimates the instantaneous effects of the unknown dynamics on each
cell in a meshing of the spatial domain. Our model can incorporate prior
knowledge via assumptions on the form of the unknown PDE, which induce a
structural bias towards learning specific processes. Through this mechanism, we
derive a transport variant of our model from the convection equation and show
that it improves the transfer performance to higher-resolution meshes on sea
surface temperature and gas flow forecasting against baseline models
representing a selection of spatio-temporal forecasting methods. A qualitative
analysis shows that our model disentangles the data dynamics into their
constituent parts, which makes it uniquely interpretable.

本文提出了一种用于任意分布的点的时空预测的新方法，该模型可以利用偏微分方程来推导数据动态的连续时间模型，通过有限元方法，在空间域的网格化中估计未知动态对每个单元格的瞬时影响，我们的模型可以通过假设方程的形式来将先前知识纳入其中，并从对流方程导出一个运输变体，该模型对比基准模型，表现了更好的海面温度和气体流量预测的转移性能。此外，我们的模型具有独特的可解释性。