# Learning stable reduced-order models for hybrid twins

arXiv: https://arxiv.org/abs/2106.03464 · HTML: https://mlsanity.com/paper/2106.03464/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 1 of 1)

- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)

## Built on by (most cited first, 3 of 3)

- [Function+Data Flow: A Framework to Specify Machine Learning Pipelines for Digital Twinning](https://mlsanity.com/paper/2406.19670/) (2024)
- [Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Framework](https://mlsanity.com/paper/2512.15767/) (2025)
- [Building real-time digital twin instances with Function+Data Flow: user evaluation and extension for iterative pipelines](https://mlsanity.com/paper/2608.18480/) (2026)

## Abstract (arXiv)

The concept of Hybrid Twin (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model-order reduction framework-to obtain real-time feedback rates-and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast and accurate corrections in the Hybrid Twin framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several sub-variants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.