Our paper "TaylorPDENet: Learning PDEs from non-grid Data" has been accepted at th ECML Workshop "ML meets Explicit Knowledge"

Our paper presents a novel method of approximating differential operators from non-grid data using the taylor approximation with the objective to learn explicit representations of PDEs describing the data.

Abstract

Modeling data obtained from dynamical systems has gained attention in recent years as a challenging task for machine learning models. Previous approaches assume the measurements to be distributed on a grid. However, for real-world applications like weather prediction, the observations are taken from arbitrary locations within the spatial domain. In this paper, we propose TaylorPDENet - a novel machine learning method that is designed to overcome this challenge. Our algorithm uses the multidimensional Taylor expansion of a dynamical system at each observation point to estimate the spatial derivatives to perform predictions. TaylorPDENet is able to accomplish two objectives simultaneously: accurately forecast the evolution of a complex dynamical system and explicitly reconstruct the underlying differential equation describing the system. We evaluate our model on a variety of advection-diffusion equations with different parameters and show that it performs similarly to equivalent approaches on grid-structured data while being able to process unstructured data as well.