# Data-driven balancing of linear dynamical systems

arXiv: https://arxiv.org/abs/2104.01006 · HTML: https://mlsanity.com/paper/2104.01006/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2021.

## Built on by (most cited first, 5 of 5)

- [On the sample complexity of stabilizing linear dynamical systems from data](https://mlsanity.com/paper/2203.00474/) (2022)
- [Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction](https://mlsanity.com/paper/2507.20463/) (2025)
- [Rank-Minimizing and Structured Model Inference](https://mlsanity.com/paper/2302.09521/) (2023)
- [Symmetric Hermite quadrature-based balanced truncation for learning linear dynamical systems from derivative data](https://mlsanity.com/paper/2606.00298/) (2026)
- [Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver](https://mlsanity.com/paper/2609.24021/) (2026)

## Abstract (arXiv)

We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without reference to any prescribed realization of the original model. Data are represented by sampled values of the transfer function {or the impulse response} corresponding to the original model. We discuss parallels that our approach bears with the Loewner framework, another popular data-driven model reduction method. We illustrate our approach numerically in both continuous-time and discrete-time cases.