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This paper develops a hybrid framework that couples pre-trained numerics-informed neural networks with classical full order models using the overlapping Schwarz alternating method to solve advection-diffusion equations efficiently, with results comparable to full-domain solutions.
The paper introduces a reinforcement learning-based approach for adaptively selecting full and reduced order models in hybrid domain decomposition simulations, using deep Q-networks to balance accuracy and cost in transient problems.
This paper introduces LatentDDM, a method that pretrains neural operators on small subdomains and composes them to improve accuracy and reduce adaptation cost for physical simulations in varying domains.
Proposes a hierarchical attention mechanism using overlapping Schwarz domain decomposition to replace dense global low-rank attention with a two-level additive structure of local and coarse blocks, showing faster training and better accuracy with fewer parameters.