%0 Conference Paper %1 pmlr-v277-dulny25a %A Dulny, Andrzej %A Heinisch, Paul %A Hotho, Andreas %A Krause, Anna %B Proceedings of the 2nd ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications" %D 2025 %E Coelho, Cecı́lia %E Zimmering, Bernd %E Costa, M. Fernanda P. %E Ferrás, Luı́s L. %E Niggemann, Oliver %I PMLR %K myown deep-learning author:krause symbolic-regression neural-ode from:adulny author:dulny physics author:heinisch author:hotho %P 26--46 %T TaylorNet: Learning PDEs from Non-Grid Data %U https://proceedings.mlr.press/v277/dulny25a.html %V 277 %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 TaylorNet - 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. TaylorNet 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.

@inproceedings{pmlr-v277-dulny25a, 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 TaylorNet - 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. TaylorNet 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 = {2026-01-27T12:43:41.000+0100}, author = {Dulny, Andrzej and Heinisch, Paul and Hotho, Andreas and Krause, Anna}, biburl = {https://www.bibsonomy.org/bibtex/226735525aa2584bae29018a0738bc8e9/dmir}, booktitle = {Proceedings of the 2nd ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"}, editor = {Coelho, Cecı́lia and Zimmering, Bernd and Costa, M. Fernanda P. and Ferrás, Luı́s L. and Niggemann, Oliver}, interhash = {ff74f7644586c5e705d623cc382ed5f2}, intrahash = {26735525aa2584bae29018a0738bc8e9}, keywords = {myown deep-learning author:krause symbolic-regression neural-ode from:adulny author:dulny physics author:heinisch author:hotho}, month = {26 Oct}, pages = {26--46}, pdf = {https://raw.githubusercontent.com/mlresearch/v277/main/assets/dulny25a/dulny25a.pdf}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, timestamp = {2026-01-27T12:43:41.000+0100}, title = {TaylorNet: Learning PDEs from Non-Grid Data}, url = {https://proceedings.mlr.press/v277/dulny25a.html}, volume = 277, year = 2025 }