Two-level deep domain decomposition method

Two-level deep domain decomposition method

Victorita Dolean (1) , Serge Gratton (2, 3) , Alexander Heinlein (4, 5) , Valentin Mercier (6, 7, 3)

1 TU/e - Eindhoven University of Technology [Eindhoven]
2 IRIT-RMESS - Réseaux, Mobiles, Embarqués, Sans fil, Satellites
3 Toulouse INP - Institut National Polytechnique (Toulouse)
4 TU Delft - Delft University of Technology
5 DIAM - Delft Institute of Applied Mathematics
6 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
7 IRIT-APO - Algorithmes Parallèles et Optimisation

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). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning.

Mots clés: Deep leaning; PINNs; Domain decomposition

Domaines: Intelligence artificielle [cs.AI]; Modélisation et simulation

Victorita Dolean, Serge Gratton, Alexander Heinlein, Valentin Mercier. Two-level deep domain decomposition method. 2024. ⟨hal-04669699⟩