6 citations · 12 across the 11 of their papers we have counts for
14 papers · 1 filter
Mixed Consistent PINNs for Elliptic Obstacle Problems with Stability Analysis
Arbaz Khan, Kent-Andre Mardal, Shiv Mishra
We propose a consistent physics-informed neural networks (CPINNs) framework for elliptic obstacle problems formulated as variational inequalities. The method is based on a mixed lo…
A robust and time-parallel preconditioner for parabolic reconstruction problems using Isogeometric Analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
We consider a PDE-constrained optimization problem of tracking type with parabolic state equation. The solution to the problem is characterized by the Karush-Kuhn-Tucker (KKT) syst…
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,…
Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arriv…
Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure
Wietse M. Boon, Miroslav Kuchta, Kent-Andre Mardal +1
We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), an…