# Second-order AAA algorithms for structured data-driven modeling

arXiv: https://arxiv.org/abs/2506.02241 · HTML: https://mlsanity.com/paper/2506.02241/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [Data-driven Structured Realization](https://mlsanity.com/paper/1611.02072/) (2016)
- [Quadrature-Based Vector Fitting: Implications For H2 System Approximation](https://mlsanity.com/paper/1403.4655/) (2014)
- [The p-AAA algorithm for data driven modeling of parametric dynamical systems](https://mlsanity.com/paper/2003.06536/) (2020)
- [Structured vector fitting framework for mechanical systems](https://mlsanity.com/paper/2110.09220/) (2021)
- [Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems](https://mlsanity.com/paper/2303.12576/) (2023)
- [A modified AAA algorithm for learning stable reduced-order models from data](https://mlsanity.com/paper/2312.16978/) (2023)
- [Data-Driven Identification of Rayleigh-Damped Second-Order Systems](https://mlsanity.com/paper/1910.00838/) (2019)
- [Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms](https://mlsanity.com/paper/2002.12226/) (2020)
- [Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods](https://mlsanity.com/paper/2201.06518/) (2022)
- [Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction](https://mlsanity.com/paper/2305.10806/) (2023)

## Abstract (arXiv)

The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical phenomena are often neglected making the reinterpretation of the learned models in a physically meaningful sense very challenging. In this work, we present three data-driven modeling approaches for the construction of dynamical systems with second-order differential structure directly from frequency domain data. Based on the second-order structured barycentric form, we extend the well-known Adaptive Antoulas-Anderson algorithm to the case of second-order systems. Depending on the available computational resources, we propose variations of the proposed method that prioritize either higher computation speed or greater modeling accuracy, and we present a theoretical analysis for the expected accuracy and performance of the proposed methods. Three numerical examples demonstrate the effectiveness of our new structured approaches in comparison to classical unstructured data-driven modeling.