Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach
Numerical Analysis
2025-04-16 v2 Numerical Analysis
Abstract
The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficiently learn quantities of interest of solutions to a parametric PDE. The central component in our approach is an efficient neural-network-weighted Minimal-Residual formulation, which, after training, provides Galerkin-based approximations in standard discrete spaces that have accurate quantities of interest, regardless of the coarseness of the discrete space.
Keywords
Cite
@article{arxiv.2304.01722,
title = {Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach},
author = {Ignacio Brevis and Ignacio Muga and David Pardo and Oscar Rodriguez and Kristoffer G. van der Zee},
journal= {arXiv preprint arXiv:2304.01722},
year = {2025}
}