47 citations · 190 across the 24 of their papers we have counts for
Showing 2023Show all
2 papers · 1 filter
math.NA2023
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…
math.NA2023★ 5 cited
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,…