  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.
