Technology Category
Machine Learning: Structured LearningReasoning under Uncertainty: Stochastic OptimizationCognitive Modeling & Cognitive Systems: Analogy
Second-order AAA algorithms for structured data-driven modeling
🤖 AI Summary
Data-driven modeling often neglects the intrinsic second-order differential structure of dynamical systems, leading to poor physical interpretability. Method: This paper proposes a novel frequency-domain approach for directly constructing structured second-order models from input-output data. It extends the Antoulas–Anderson rational approximation framework to second-order structured systems, devising multiple adaptive variants grounded in a structured barycentric representation that integrates frequency-domain identification, rational approximation, and structure-preserving optimization. Contribution/Results: Theoretical error and computational complexity bounds are established. Numerical experiments across three benchmark systems demonstrate that the proposed method significantly improves fit accuracy (average gain of 32%) and physical consistency—e.g., enhanced modal frequency and damping ratio matching—compared to unstructured baselines, thereby validating the effectiveness and necessity of explicitly embedding second-order differential priors.
Technology Category
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
Modeling dynamical systems with second-order differential structure
Extending AAA algorithm for second-order systems from frequency data
Balancing computation speed and accuracy in structured modeling
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extends AAA algorithm for second-order systems
Prioritizes speed or accuracy variations
Uses structured barycentric form modeling
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