Work

A Modified AAA Algorithm for Learning Stable Reduced-Order Models from Data

Year: 2025

Type: article

Abstract: In recent years, the Adaptive Antoulas-Anderson () algorithm has been applied extensively for generating Reduced Order Models (ROMs) of large scale Linear Time-Invariant systems starting from measurements of their transfer functions. When used for Model Order Reduction (MOR) of an asymptotically stable system, the ROMs generated applying are not guaranteed to preserve this fundamental property, thus rendering them impractical in many relevant applications. To overcome this issue, we propose a novel algebraic characterization for the stability of ROMs represented under the barycentric structure. We then translate such characterization into a set of convex semidefinite constraints that can be embedded into the optimization routine to explicitly maximize the model accuracy while ensuring its stability. Finally, we generalize the resulting modeling framework to allow for efficient stable MOR of Multi-Input-Multi-Output systems. An extensive set of numerical experiments provides practical evidence for the effectiveness of the proposed approach and compares its performance with those of available state-of-the-art methods.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-025-02825-0

Authors: Tommaso Bradde, Stefano Grivet-Talocia, Quirin Aumann, Ion Victor Gosea

Institutions: Politecnico di Torino, Max Planck Institute for Dynamics of Complex Technical Systems

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Politecnico di Torino