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.
Description
[2306.14511] TaylorPDENet: Learning PDEs from non-grid Data
%0 Generic
%1 heinisch2023taylorpdenet
%A Heinisch, Paul
%A Dulny, Andrzej
%A Krause, Anna
%A Hotho, Andreas
%D 2023
%K Taylornet app_physics author:Dulny author:Hotho author:Krause deep-implicit-learning deep-learning from:adulny from:martinr myown neural-ode research_knowledge
%T TaylorPDENet: Learning PDEs from non-grid Data
%U http://arxiv.org/abs/2306.14511
%X 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.
@misc{heinisch2023taylorpdenet,
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.},
added-at = {2023-09-20T08:39:08.000+0200},
author = {Heinisch, Paul and Dulny, Andrzej and Krause, Anna and Hotho, Andreas},
biburl = {https://www.bibsonomy.org/bibtex/2b153f655a14cc69d59e98ca8b133443f/dmir},
description = {[2306.14511] TaylorPDENet: Learning PDEs from non-grid Data},
interhash = {1d31286712579fe200abec994ad593a0},
intrahash = {b153f655a14cc69d59e98ca8b133443f},
keywords = {Taylornet app_physics author:Dulny author:Hotho author:Krause deep-implicit-learning deep-learning from:adulny from:martinr myown neural-ode research_knowledge},
note = {cite arxiv:2306.14511},
timestamp = {2024-01-18T10:31:52.000+0100},
title = {TaylorPDENet: Learning PDEs from non-grid Data},
url = {http://arxiv.org/abs/2306.14511},
year = 2023
}