# Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method

arXiv: https://arxiv.org/abs/2409.01433 · HTML: https://mlsanity.com/paper/2409.01433/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 2 Sep 2024.

## Builds on (most cited first, 9 of 9)

- [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)
- [Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference](https://mlsanity.com/paper/2110.07653/) (2021)
- [Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference](https://mlsanity.com/paper/1908.11233/) (2019)
- [Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference](https://mlsanity.com/paper/2107.02597/) (2021)
- [Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method](https://mlsanity.com/paper/2311.00224/) (2023)
- [Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Method](https://mlsanity.com/paper/2311.05643/) (2023)
- [A Novel Partitioned Approach for Reduced Order Model -- Finite Element Model (ROM-FEM) and ROM-ROM Coupling](https://mlsanity.com/paper/2206.04736/) (2022)
- [An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations](https://mlsanity.com/paper/2211.14528/) (2022)

## Built on by (most cited first, 5 of 5)

- [The role of interface boundary conditions and sampling strategies for Schwarz-based coupling of projection-based reduced order models](https://mlsanity.com/paper/2410.04668/) (2024)
- [Hybrid coupling with operator inference and the overlapping Schwarz alternating method](https://mlsanity.com/paper/2511.20687/) (2025)
- [Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems](https://mlsanity.com/paper/2601.12161/) (2026)
- [NN-OpInf: an operator inference approach using structure-preserving composable neural networks](https://mlsanity.com/paper/2603.08488/) (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 and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs), following a domain decomposition of the spatial geometry on which a given partial differential equation (PDE) is posed. Joining subdomain-local models is accomplished using the overlapping Schwarz alternating method, a minimally-intrusive multiscale coupling technique that works by transforming a monolithic problem into a sequence of subdomain-local problems, which communicate through transmission boundary conditions imposed on the subdomain interfaces. After formulating the overlapping Schwarz alternating method for OpInf ROMs, termed OpInf-Schwarz, we evaluate the method's accuracy and efficiency on several test cases involving the heat equation in two spatial dimensions. We demonstrate that the method is capable of coupling together arbitrary combinations of OpInf ROMs and FOMs, and that speed-ups over a monolithic FOM are possible when performing OpInf ROM coupling.