Two-level deep domain decomposition method
This provides a more scalable approach for solving complex partial differential equations with machine learning, but it is incremental as it builds on existing domain decomposition and PINN methods.
The study tackled solving boundary value problems using physics-informed neural networks by introducing a two-level deep domain decomposition method with a coarse-level network, resulting in improved scalability and convergence rates, such as maintaining efficient convergence regardless of subdomain count in tests on a Poisson equation.
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.