# Domain decomposition for data-driven reduced modeling of large-scale systems

arXiv: https://arxiv.org/abs/2311.00883 · HTML: https://mlsanity.com/paper/2311.00883/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2023.

## Built on by (most cited first, 6 of 6)

- [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)
- [Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine](https://mlsanity.com/paper/2407.09994/) (2024)
- [Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction](https://mlsanity.com/paper/2507.20463/) (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)

## Abstract (arXiv)

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale datasets typically requires significant memory and computing resources which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training dataset. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating detonation rocket engine simulation scenario with over 75 million degrees of freedom and a sparse training dataset. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to 13 % and up to 5% for other key quantities, such as temperature, and fuel and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well.