Snapshot-driven Rational Interpolation of Parametric Systems

TL;DR

This paper introduces a snapshot-driven method for parametric modeling of systems, using interpolation techniques to construct a global model that accounts for parameter variations, supported by numerical examples.

Contribution

It presents a novel approach combining Loewner interpolation and linear fractional transformations for efficient global parametric system modeling.

Findings

Effective interpolation of parameter snapshots using Loewner framework

Derivation of rank bounds for minimal system realization

Numerical examples demonstrating method accuracy and efficiency

Abstract

Parametric data-driven modeling is relevant for many applications in which the model depends on parameters that can potentially vary in both space and time. In this paper, we present a method to obtain a global parametric model based on snapshots of the parameter space. The parameter snapshots are interpolated using the classical univariate Loewner framework and the global bivariate transfer function is extracted using a linear fractional transformation (LFT). Rank bounds for the minimal order of the global realization are also derived. The results are supported by various numerical examples.