Two-level deep domain decomposition method

TL;DR

This paper introduces a two-level Deep Domain Decomposition Method using physics-informed neural networks, enhancing scalability and convergence for solving boundary value problems more efficiently than single-level approaches.

Contribution

The paper proposes a novel two-level deep domain decomposition method with a coarse network, significantly improving scalability and convergence in PINN-based PDE solutions.

Findings

Outperforms single-level methods in convergence speed

Maintains efficiency across multiple subdomains

Effective for solving Poisson equations with boundary conditions

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.