Two-level deep domain decomposition method
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Abstract (arXiv)
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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References · 7
- 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
- 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
- 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 284
- 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
- 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
- 2019D3M: A deep domain decomposition method for partial differential equationscited by 44
- 2023A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networkscited by 7
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