Hybrid coupling with operator inference and the overlapping Schwarz alternating method

2025/11/20 by Irina Tezaur, Tezaur, Irina, Eric Parish +10 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Matrix Theory and Algorithms #Model Reduction and Neural Networks #cs.AI #cs.NA #math-ph #math.MP #math.NA

paper · pdf · doi:10.48550/arxiv.2511.20687

openalex publication_date 2025/11/20 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

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.

Citations

• Domain Decomposition for Data-Driven Reduced Modeling of Large-Scale Systems
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Anderson Acceleration for Fixed-Point Iterations
• Galerkin proper orthogonal decomposition methods for parabolic problems

Cited by

• ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching

Related

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• Transmission Conditions for the Non-Overlapping Schwarz Coupling of Full Order and Operator Inference Models
• The Schwarz alternating method for the seamless coupling of nonlinear reduced order models and full order models
• A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations