TaylorPDENet: Learning PDEs from non-grid Data

• URL: http://arxiv.org/abs/2306.14511v1
• Date: Mon, 26 Jun 2023 08:40:24 GMT
• Title: TaylorPDENet: Learning PDEs from non-grid Data
• Authors: Paul Heinisch, Andrzej Dulny, Anna Krause, Andreas Hotho
• Abstract summary: TaylorPDENet is 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. 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.
• Score: 2.0550543745258283
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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