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arXiv · 2304.01722

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

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

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Ignacio Brevis, Ignacio Muga, David Pardo, Oscar Rodriguez, Kristoffer G. van der Zee. 2023-04-04. Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach. https://doi.org/10.1016/j.camwa.2024.04.006

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