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

Author name not available (Why is that?)

Publication date: 16 March 2022

Abstract: 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.

Has companion code repository: https://github.com/martenlienen/finite-element-networks

This page was built for publication: Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6393897)