从频域数据直接构建二阶微分系统模型，兼顾速度与精度。
Second-order AAA algorithms for structured data-driven modeling
- 基于二阶结构的重心形式扩展自适应算法，保留物理结构。
- 三种变体分别侧重计算速度与建模精度，可灵活选择。
- 在三个数值实验中均优于传统无结构方法。
从真实世界数据构建精确计算模型的数据驱动建模已成为重要工具。然而，常忽略所研究物理现象背后的微分结构，导致学习到的模型难以物理解释。本文提出三种直接从频域数据构建具有二阶微分结构的动力系统数据驱动建模方法。基于二阶结构化的重心形式，将经典的自适应Antoulas-Anderson算法扩展至二阶系统场景。根据可用计算资源，提出侧重计算速度或建模精度的算法变体，并对预期精度与性能进行理论分析。三个数值实例表明，新方法在建模效果上显著优于经典无结构数据驱动方法。
原文摘要 · Abstract (English)
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.
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