# Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems

arXiv: https://arxiv.org/abs/2303.12576 · HTML: https://mlsanity.com/paper/2303.12576/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2023.

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

- [Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes](https://mlsanity.com/paper/2310.07485/) (2023)
- [Second-order AAA algorithms for structured data-driven modeling](https://mlsanity.com/paper/2506.02241/) (2025)

## Abstract (arXiv)

An essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling dynamical systems with second-order time derivatives using their frequency domain input-output data. By imposing a set of interpolation conditions, the systems' transfer functions are rewritten in different barycentric forms using different parametrizations. Loewner-like algorithms are developed for the explicit computation of second-order systems from data based on the developed barycentric forms. Numerical experiments show the performance of these new structured data driven modeling methods compared to other interpolation-based data-driven modeling techniques from the literature.