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

In: Realization and Model Reduction of Dynamical Systems

Author

Listed:
  • Zlatko Drmač

    (University of Zagreb, Faculty of Science, Department of Mathematics)

  • Benjamin Peherstorfer

    (New York University, Courant Institute of Mathematical Sciences)

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.

Suggested Citation

  • Zlatko Drmač & Benjamin Peherstorfer, 2022. "Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation," Springer Books, in: Christopher Beattie & Peter Benner & Mark Embree & Serkan Gugercin & Sanda Lefteriu (ed.), Realization and Model Reduction of Dynamical Systems, pages 39-57, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95157-3_3
    DOI: 10.1007/978-3-030-95157-3_3
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