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DY: Fachverband Dynamik und Statistische Physik

DY 33: Poster: Nonlinear Dynamics, Pattern Formation and Networks

DY 33.6: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster C

A novel cutoff criterion for spectral derivatives in the context of ordinary differential equation model estimation — •Oliver Strebel — Angelstr. 17, 75392 Deckenpfronn

After the advent of SINDy-methods [1] estimation of ordinary differential equation models involves typically the numerical calculation of derivatives for noisy data. This contribution presents a novel determination method concerning the cutoff parameter for spectral derivatives. The method is benchmarked against 60 differential equations and estimation methods of reference [2].

It is compared to numerical differentiation methods like finite differences, derivatives using the Friedrichs mollifier and weak differentiation using this mollifier. The hyperparameters of all these methods are optimized against the test set of these equations at a fixed noise level. Then the resilence against larger noise or fewer data points per time interval is examined. It turns out that the novel method is overall superior to the other methods.

[1] Steve L. Brunton, PNAS 113 (2016):

https://doi.org/10.1073/pnas.1517384113

[2] Oliver Strebel, Nonlinear Dynamics 111 (2023):

https://doi.org/10.1007/s11071-023-08242-y

Keywords: nonlinear dynamical system; model estimation; numerical differentiation; system identification; time series analysis