# Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decomposition

arXiv: https://arxiv.org/abs/2401.10245 · HTML: https://mlsanity.com/paper/2401.10245/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2023.

## Built on by (most cited first, 7 of 7)

- [Defining Foundation Models for Computational Science: A Call for Clarity and Rigor](https://mlsanity.com/paper/2505.22904/) (2025)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [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)
- [mLaSDI: Multi-stage latent space dynamics identification](https://mlsanity.com/paper/2506.09207/) (2025)
- [Sequential decoder training for improved latent space dynamics identification](https://mlsanity.com/paper/2510.03535/) (2025)
- [Latent Space Element Method](https://mlsanity.com/paper/2601.01741/) (2026)

## Abstract (arXiv)

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the E-pilot, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15 - 40 times faster with only ~ 1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.