5 citations · 7 across the 6 of their papers we have counts for
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A priori error analysis of the proximal Galerkin method
Brendan Keith, Rami Masri, Marius Zeinhofer
The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preservin…
Variational Formulations of the Strong Formulation -- Forward and Inverse Modeling using Isogeometric Analysis and Physics-Informed Networks
Kent-Andre Mardal, Jarle Sogn, Marius Zeinhofer
The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equ…
A Unified Framework for the Error Analysis of Physics-Informed Neural Networks
Marius Zeinhofer, Rami Masri, Kent-André Mardal
We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity,…
Learning Mesh Motion Techniques with Application to Fluid-Structure Interaction
Johannes Haubner, Ottar Hellan, Marius Zeinhofer +1
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion…