3 papers
cs.CE2026
Modeling isotropic polyconvex hyperelasticity by neural networks -- sufficient and necessary criteria for compressible and incompressible materials
Gian-Luca Geuken, Patrick Kurzeja, David Wiedemann +3
This work investigates different sufficient and necessary criteria for hyperelastic, isotropic polyconvex material models, focusing on neural network implementations for compressib…
cs.CE2025
Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies
Gian-Luca Geuken, Patrick Kurzeja, David Wiedemann +1
This paper presents a novel framework of neural networks for isotropic hyperelasticity that enforces necessary physical and mathematical constraints while simultaneously satisfying…
cs.CE2023
Incorporating sufficient physical information into artificial neural networks: a guaranteed improvement via physics-based Rao-Blackwellization
Gian-Luca Geuken, Jörn Mosler, Patrick Kurzeja
The concept of Rao-Blackwellization is employed to improve predictions of artificial neural networks by physical information. The error norm and the proof of improvement are transf…