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The paper presents a reinforcement‑learning framework that dynamically selects between full‑order models (FOMs) and reduced‑order models (ROMs) in hybrid domain decomposition simulations using the overlapping Schwarz alternating method (O‑SAM). Offline‑trained Deep Q‑networks choose subdomain‑local FOMs or pre‑trained Operator Inference ROMs based on a reward that balances accuracy, computational cost, and model‑switching frequency, and the learned policies are deployed on unseen problem instances without needing a reference FOM solution. Experiments on a 1D advection‑diffusion problem and a 3D elastic wave propagation benchmark show that the RL‑guided policies adaptively allocate high‑fidelity resolution as features propagate, outperforming static FOM/ROM assignments and demonstrating the feasibility of predictive online fidelity adaptation in Schwarz‑based hybrid simulations.
arXiv:2609.07814v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of s...
arXiv:2607. 11094v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy.
arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
arXiv:2609.14841v1 Announce Type: new Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...