Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation
This work addresses robustness to noise in model learning for dynamical systems, which is incremental as it analyzes an existing method rather than introducing a new one.
The paper tackled the problem of learning low-dimensional dynamical-system models from noisy frequency-response data using Loewner rational interpolation, showing that the error due to Gaussian noise grows at most linearly with the standard deviation under certain conditions, as demonstrated numerically on benchmarks.
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.