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arXiv Machine Learning By George Chumbipuma, Irina Tezaur, Alejandro Diaz, Beatrice Riviere

Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method

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The paper introduces a hybrid modeling framework that couples numerics-informed neural networks (NINNs) with classical full order models (FOMs) via the overlapping Schwarz alternating method. It demonstrates that a monolithic NINN can be accurately trained on a two-dimensional advection-diffusion problem in a high Peclet-number regime without domain decomposition, and then uses overlapping multiplicative Schwarz to couple a pre-trained, subdomain-local NINN with a neighboring FOM while keeping the NINN weights fixed during iteration. Two training strategies—top-down, using full-domain FOM-FOM Schwarz data, and bottom-up, generating synthetic boundary traces—both yield hybrid NINN-FOM solutions that closely match the corresponding FOM-FOM Schwarz results.

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