# Hybrid coupling with operator inference and the overlapping Schwarz alternating method

arXiv: https://arxiv.org/abs/2511.20687 · HTML: https://mlsanity.com/paper/2511.20687/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 67 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [D3M: A deep domain decomposition method for partial differential equations](https://mlsanity.com/paper/1909.12236/) (2019)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
- [Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reduction](https://mlsanity.com/paper/2204.02462/) (2022)
- [Reduced operator inference for nonlinear partial differential equations](https://mlsanity.com/paper/2102.00083/) (2021)
- [Defining Foundation Models for Computational Science: A Call for Clarity and Rigor](https://mlsanity.com/paper/2505.22904/) (2025)
- [Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning](https://mlsanity.com/paper/2407.15887/) (2024)
- [Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method](https://mlsanity.com/paper/2311.00224/) (2023)
- [Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling](https://mlsanity.com/paper/2504.11383/) (2025)
- [Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decomposition](https://mlsanity.com/paper/2401.10245/) (2023)
- [Domain decomposition for data-driven reduced modeling of large-scale systems](https://mlsanity.com/paper/2311.00883/) (2023)
- [Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method](https://mlsanity.com/paper/2409.01433/) (2024)
- [Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Method](https://mlsanity.com/paper/2311.05643/) (2023)
- [Kernel manifolds: nonlinear-augmentation dimensionality reduction using reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2509.00224/) (2025)
- [Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2506.10224/) (2025)

## Built on by (most cited first, 4 of 4)

- [NN-OpInf: an operator inference approach using structure-preserving composable neural networks](https://mlsanity.com/paper/2603.08488/) (2026)
- [ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching](https://mlsanity.com/paper/2512.19643/) (2025)
- [Adaptive hybrid coupling with operator inference, the overlapping Schwarz alternating method and reinforcement learning](https://mlsanity.com/paper/2609.17837/) (2026)
- [Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method](https://mlsanity.com/paper/2609.17841/) (2026)

## Abstract (arXiv)

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.