Hybrid Coupling With Operator Inference and the Overlapping Schwarz Alternating Method

ABSTRACT This paper presents a hybrid approach for coupling subdomain‐local, nonintrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain‐local, high‐fidelity full order models (FOMs) using the overlapping Schwarz alternating method (O‐SAM). The proposed methodology addresses significant challenges in multiscale modeling and simulation, particularly the long runtime and complex mesh generation requirements associated with traditional high‐fidelity simulations. By leveraging the flexibility of O‐SAM, we enable the seamless integration of disparate models, meshes, and time integration schemes, enhancing computational efficiency while maintaining high accuracy. Our approach is demonstrated through a series of numerical experiments on increasingly complex three‐dimensional solid dynamics problems, showcasing speedups of up to 106 times compared to conventional FOM–FOM couplings. This work paves the way for more efficient simulation workflows in engineering applications, with potential extensions to a wide range of partial differential equations.