Two-level deep domain decomposition method

2024/08/22 by Dolean, Victorita, Gratton, Serge, Heinlein, Alexander +1
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2408.12198

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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