no code implementations • 22 Aug 2024 • Victorita Dolean, Serge Gratton, Alexander Heinlein, Valentin Mercier
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs).
no code implementations • 23 May 2023 • Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L. Toint
Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems.
no code implementations • 7 Dec 2021 • Valentin Mercier, Serge Gratton, Pierre Boudier
We present an extension of this method that relies on the use of a coarse space correction, similarly to what is done in traditional DDM solvers.
no code implementations • 29 Sep 2021 • Elisa Riccietti, Valentin Mercier, Serge Gratton, Pierre Boudier
In this paper we introduce multilevel physics informed neural networks (MPINNs).
