# Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference

arXiv: https://arxiv.org/abs/1908.11233 · HTML: https://mlsanity.com/paper/1908.11233/

## Key facts

- Cited by 20 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 29 Aug 2019.

## Built on by (most cited first, 20 of 20)

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- [Active operator inference for learning low-dimensional dynamical-system models from noisy data](https://mlsanity.com/paper/2107.09256/) (2021)
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- [Learning Latent Space Dynamics with Model-Form Uncertainties: A Stochastic Reduced-Order Modeling Approach](https://mlsanity.com/paper/2409.00220/) (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)
- [Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference](https://mlsanity.com/paper/2402.17698/) (2024)
- [An adaptive data sampling strategy for stabilizing dynamical systems via controller inference](https://mlsanity.com/paper/2506.01816/) (2025)

## Abstract (arXiv)

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model reduction techniques that require full knowledge of governing equations and operators of the high-dimensional systems. Thus, the learned models are guaranteed to inherit the well-studied properties of reduced models from traditional model reduction. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. The numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.