# Structured vector fitting framework for mechanical systems

arXiv: https://arxiv.org/abs/2110.09220 · HTML: https://mlsanity.com/paper/2110.09220/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2021.

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

- [Rank-Minimizing and Structured Model Inference](https://mlsanity.com/paper/2302.09521/) (2023)
- [Second-order AAA algorithms for structured data-driven modeling](https://mlsanity.com/paper/2506.02241/) (2025)

## Abstract (arXiv)

In this paper, we develop a structure-preserving formulation of the data-driven vector fitting algorithm for the case of modally damped mechanical systems. Using the structured pole-residue form of the transfer function of modally damped second-order systems, we propose two possible structured extensions of the barycentric formula of system transfer functions. Integrating these new forms within the classical vector fitting algorithm leads to the formulation of two new algorithms that allow the computation of modally damped mechanical systems from data in a least squares fashion. Thus, the learned model is guaranteed to have the desired structure. We test the proposed algorithms on two benchmark models.