Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks

Understand

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.