# Active-learning-based non-intrusive Model Order Reduction

arXiv: https://arxiv.org/abs/2204.08523 · HTML: https://mlsanity.com/paper/2204.08523/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 8 Apr 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Digital Twin: Values, Challenges and Enablers](https://mlsanity.com/paper/1910.01719/) (2019)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [DR-RNN: A deep residual recurrent neural network for model reduction](https://mlsanity.com/paper/1709.00939/) (2017)
- [Long-time predictive modeling of nonlinear dynamical systems using neural networks](https://mlsanity.com/paper/1805.12547/) (2018)
- [Model Order Reduction based on Runge-Kutta Neural Network](https://mlsanity.com/paper/2103.13805/) (2021)
- [Recurrent Neural Networks (RNNs) with dimensionality reduction and break down in computational mechanics; application to multi-scale localization step](https://mlsanity.com/paper/2112.12842/) (2021)
- [Empirical Differential Gramians for Nonlinear Model Reduction](https://mlsanity.com/paper/1902.09836/) (2019)

## Built on by (most cited first, 2 of 2)

- [Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems](https://mlsanity.com/paper/2306.06174/) (2023)
- [Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference](https://mlsanity.com/paper/2601.00038/) (2025)

## Abstract (arXiv)

The Model Order Reduction (MOR) technique can provide compact numerical models for fast simulation. Different from the intrusive MOR methods, the non-intrusive MOR does not require access to the Full Order Models (FOMs), especially system matrices. Since the non-intrusive MOR methods strongly rely on the snapshots of the FOMs, constructing good snapshot sets becomes crucial. In this work, we propose a new active learning approach with two novelties. A novel idea with our approach is the use of single-time step snapshots from the system states taken from an estimation of the reduced-state space. These states are selected using a greedy strategy supported by an error estimator based Gaussian Process Regression (GPR). Additionally, we introduce a use case-independent validation strategy based on Probably Approximately Correct (PAC) learning. In this work, we use Artificial Neural Networks (ANNs) to identify the Reduced Order Model (ROM), however the method could be similarly applied to other ROM identification methods. The performance of the whole workflow is tested by a 2-D thermal conduction and a 3-D vacuum furnace model. With little required user interaction and a training strategy independent to a specific use case, the proposed method offers a huge potential for industrial usage to create so-called executable Digital Twins (DTs).