{"ID":22918784,"CreatedAt":"2026-09-17T01:02:08.507062015Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.17841","arxiv_id":"2609.17841","title":"Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method","abstract":"We develop a hybrid modeling framework for coupling pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alternating method. We consider the two-dimensional advection-diffusion equation in the advection-dominated, Peclet-number 10^6 regime. We first demonstrate that, unlike the corresponding physics-informed neural network (PINN), a monolithic NINN can be accurately trained on our model problem without domain decomposition. We then employ overlapping multiplicative Schwarz as a deployment mechanism for coupling a pre-trained, subdomain-local NINN with a neighboring FOM, with the NINN weights held fixed throughout the Schwarz iteration. We consider two training approaches for the subdomain-local NINNs: a top-down approach, in which boundary data are obtained from a coupled Schwarz solve on the full domain with a FOM on each subdomain (FOM-FOM Schwarz), and a bottom-up approach, in which boundary traces are generated synthetically on the NINN subdomain without requiring any full-domain solves. The resulting hybrid NINN-FOM solutions agree closely with the corresponding FOM-FOM Schwarz solutions, with the top-down and bottom-up training approaches yielding comparable accuracy.","short_abstract":"We develop a hybrid modeling framework for coupling pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alternating method. We consider the two-dimensional advection-diffusion equation in the advection-dominated, Peclet-number 10^6 regime. We first...","url_abs":"https://arxiv.org/abs/2609.17841","url_pdf":"https://arxiv.org/pdf/2609.17841v1","authors":"[\"George Chumbipuma\",\"Irina Tezaur\",\"Alejandro Diaz\",\"Beatrice Riviere\"]","published":"2026-09-15T21:01:30Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}