Second-order AAA algorithms for structured data-driven modeling
This work addresses the challenge of making learned models physically interpretable for researchers in computational modeling, though it appears incremental as it extends an existing algorithm.
The authors tackled the problem of data-driven modeling of dynamical systems where physical differential structures are often neglected, by proposing three approaches for constructing second-order systems directly from frequency domain data, demonstrating effectiveness in numerical examples compared to classical unstructured methods.
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.