Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach

Brevis, Ignacio; Muga, Ignacio; Pardo, David; Rodriguez, Oscar; van der Zee, Kristoffer G.

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.

Citation

Brevis, I., Muga, I., Pardo, D., Rodriguez, O., & van der Zee, K. G. (2024). Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach. Computers and Mathematics with Applications, 164, 139-149. https://doi.org/10.1016/j.camwa.2024.04.006

• Journal Article Type: Article
• Acceptance Date: Apr 11, 2024
• Online Publication Date: Apr 26, 2024
• Publication Date: Jun 15, 2024
• Deposit Date: Apr 18, 2024
• Publicly Available Date: Apr 27, 2025
• Journal: Computers and Mathematics with Applications
• Print ISSN: 0898-1221
• Electronic ISSN: 1873-7668
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 164
• Pages: 139-149
• DOI: https://doi.org/10.1016/j.camwa.2024.04.006
• Public URL: https://nottingham-repository.worktribe.com/output/33833640
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0898122124001640?via%3Dihub