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This research advances computational efficiency in multiscale simulations by hybridizing non-intrusive Operator Inference reduced order models with high-fidelity full order models via the overlapping Schwarz alternating method. The approach achieves significant speedups—up to 10^6x—in solving complex three-dimensional solid dynamics problems while maintaining accuracy across disparate meshes and time integration schemes. While primarily a numerical analysis breakthrough, it represents a critical step toward scalable AI-accelerated workflows for engineering PDEs where traditional high-fidelity simulations are computationally prohibitive.
Hybrid coupling with operator inference and the overlapping Schwarz alternating method
arXiv:2511.20687v4 Announce Type: replace-cross Abstract: This paper presents a novel hybrid approach for coupling subdomain-local non-intrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain-local high-fidelity full order models (FOMs) with 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 complex three-dimensional (3D) solid dynamics problems, showcasing speedups of up to 106x 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.
Abstract:This paper presents a novel hybrid approach for coupling subdomain-local non-intrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain-local high-fidelity full order models (FOMs) with 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 complex three-dimensional (3D) solid dynamics problems, showcasing speedups of up to 106x 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.
Numerical Analysis (math.NA); Artificial Intelligence (cs.AI); Mathematical Physics (math-ph)
arXiv:2511.20687 [math.NA]
(or arXiv:2511.20687v4 [math.NA] for this version)
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