Two-level deep domain decomposition method - Algorithmes Parallèles et Optimisation
Preprints, Working Papers, ... Year : 2024

Two-level deep domain decomposition method

Two-level deep domain decomposition method

Abstract

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.
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Dates and versions

hal-04669699 , version 1 (09-08-2024)

Identifiers

  • HAL Id : hal-04669699 , version 1

Cite

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