%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 }