Hybrid coupling with operator inference and the overlapping Schwarz alternating method

2025-11-20

AI Summary

In multi-scale, multi-physics simulations, high-fidelity models suffer from prohibitive computational cost and complex mesh generation. To address this, we propose a subdomain-local coupling framework that synergistically integrates the overlapping Schwarz alternating method (O-SAM) with non-intrusive operator inference (OpInf)-based reduced-order models (ROMs). The framework requires no modification to existing high-fidelity solvers, enables seamless integration of heterogeneous models, non-conforming meshes, and disparate time steps, and is inherently parallelizable. Its key innovation lies in the first-ever embedding of OpInf within an overlapping domain decomposition architecture, enabling efficient and stable coupling between ROMs and full-order models at the subdomain level. Numerical experiments on a 3D solid dynamics benchmark demonstrate up to 106× speedup over conventional full-order coupling while maintaining high accuracy, thereby validating the method’s efficiency, fidelity, and scalability.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Application Domains: Humanities & Computational Social Science

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Coupling reduced and full order models across subdomains
• Reducing runtime and mesh complexity in multiscale simulations
• Integrating disparate models with different meshes and schemes

Innovation

• Hybrid coupling of reduced and full order models
• Using overlapping Schwarz alternating method integration
• Achieves significant speedup in multiscale simulations