46 citations · 81 across the 8 of their papers we have counts for
8 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…
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…
Hypergeometric Feynman Integrals
René Pascal Klausen
In this thesis we will study Feynman integrals from the perspective of A-hypergeometric functions, a generalization of hypergeometric functions which goes back to Gelfand, Kapranov…
Kinematic singularities of Feynman integrals and principal A-determinants
René Pascal Klausen
We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A-hypergeometric functions introduced by Gelfand,Kapranov and Zelevinsk…
Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems
René Pascal Klausen
We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of Horn hypergeometric functions.…
The number of master integrals as Euler characteristic
Thomas Bitoun, Christian Bogner, René Pascal Klausen +1
We give a brief introduction to a parametric approach for the derivation of shift relations between Feynman integrals and a result on the number of master integrals. The shift rela…