5 citations · 7 across the 6 of their papers we have counts for
6 papers
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…
Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics
Anas Jnini, Flavio Vella, Marius Zeinhofer
We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, thi…
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,…
The modelling error in multi-dimensional time-dependent solute transport models
Rami Masri, Marius Zeinhofer, Miroslav Kuchta +1
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsat…
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…