Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation

TL;DR

This paper analyzes the robustness of Loewner rational interpolation for learning low-dimensional dynamical-system models from noisy frequency-response data, showing that noise impact grows linearly with noise level under certain conditions.

Contribution

It provides a theoretical analysis of noise robustness in Loewner interpolation and proposes strategies to enhance its stability against measurement noise.

Findings

Noise error grows linearly with standard deviation

Linear transformations improve robustness

Numerical results confirm theoretical predictions

Abstract

Loewner rational interpolation provides a versatile tool to learn low-dimensional dynamical-system models from frequency-response measurements. This work investigates the robustness of the Loewner approach to noise. The key finding is that if the measurements are polluted with Gaussian noise, then the error due to noise grows at most linearly with the standard deviation with high probability under certain conditions. The analysis gives insights into making the Loewner approach robust against noise via linear transformations and judicious selections of measurements. Numerical results demonstrate the linear growth of the error on benchmark examples.