# Data-driven balanced truncation for second-order systems with generalized proportional damping

arXiv: https://arxiv.org/abs/2506.10118 · HTML: https://mlsanity.com/paper/2506.10118/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Symmetric Hermite quadrature-based balanced truncation for learning linear dynamical systems from derivative data](https://mlsanity.com/paper/2606.00298/) (2026)

## Abstract (arXiv)

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop a new approach for the structured data-driven surrogate modeling of linear dynamical systems described by second-order time derivatives via balanced truncation model-order reduction. The proposed method is a data-driven reformulation of position-velocity balanced truncation for second-order systems and generalizes the quadrature-based balanced truncation for unstructured first-order systems to the second-order case. The computed surrogates encode a generalized proportional damping structure, and we propose a computational procedure for inferring the damping coefficients from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method.