Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation

Zlatko Drmač; Benjamin Peherstorfer

doi:10.1007/978-3-030-95157-3_3

Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation

Zlatko Drmač, Benjamin Peherstorfer

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.

Original language	English (US)
Title of host publication	Realization and Model Reduction of Dynamical Systems
Subtitle of host publication	A Festschrift in Honor of the 70th Birthday of Thanos Antoulas
Publisher	Springer International Publishing
Pages	39-57
Number of pages	19
ISBN (Electronic)	9783030951573
ISBN (Print)	9783030951566
DOIs	https://doi.org/10.1007/978-3-030-95157-3_3
State	Published - Jan 1 2022

Keywords

Concentration inequalities
Dynamical systems
Model reduction
System identification

ASJC Scopus subject areas

General Engineering
General Mathematics

Access to Document

10.1007/978-3-030-95157-3_3

Cite this

Drmač, Z., & Peherstorfer, B. (2022). Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation. In Realization and Model Reduction of Dynamical Systems: A Festschrift in Honor of the 70th Birthday of Thanos Antoulas (pp. 39-57). Springer International Publishing. https://doi.org/10.1007/978-3-030-95157-3_3

Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation. / Drmač, Zlatko; Peherstorfer, Benjamin.
Realization and Model Reduction of Dynamical Systems: A Festschrift in Honor of the 70th Birthday of Thanos Antoulas. Springer International Publishing, 2022. p. 39-57.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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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.",

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PY - 2022/1/1

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N2 - 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.

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Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation

Abstract

Keywords

ASJC Scopus subject areas

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