4 papers · 1 filter
Building Trust in PINNs: Error Estimation through Finite Difference Methods
Aleksander Krasowski, René P. Klausen, Aycan Celik +3
Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat con…
LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries
René P. Klausen, Ivan Timofeev, Jonas Naujoks +4
Initial-boundary value problems (IBVPs) provide the essential framework for modelling a wide range of phenomena in physics and engineering. We introduce a novel method for efficien…
Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks
Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker +5
Physics-informed neural networks (PINNs) offer a powerful approach to solving partial differential equations (PDEs), which are ubiquitous in the quantitative sciences. Applied to b…
PINNfluence: Interpreting PINNs through Influence Functions
Aleksander Krasowski, Jonas R. Naujoks, Moritz Weckbecker +5
Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their beh…