5 papers
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…
Opportunities and limitations of explaining quantum machine learning
Elies Gil-Fuster, Jonas R. Naujoks, Grégoire Montavon +3
A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability o…
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…