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A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling

Authors

An,  Xiao-Kai

Du,  Lin

Jiang,  Feng

Zhang,  Yu-Jia

Deng,  Zi-Chen

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

An, X.-K., Du, L., Jiang, F., Zhang, Y.-J., Deng, Z.-C., Kurths, J. (2024): A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling. - Chaos, 34, 7, 073118.
https://doi.org/10.1063/5.0209779


Cite as: https://publications.pik-potsdam.de/pubman/item/item_30728
Abstract
Neural networks are popular data-driven modeling tools that come with high data collection costs. This paper proposes a residual-based multipeaks adaptive sampling (RMAS) algorithm, which can reduce the demand for a large number of samples in the identification of stochastic dynamical systems. Compared to classical residual-based sampling algorithms, the RMAS algorithm achieves higher system identification accuracy without relying on any hyperparameters. Subsequently, combining the RMAS algorithm and neural network, a few-shot identification (FSI) method for stochastic dynamical systems is proposed, which is applied to the identification of a vegetation biomass change model and the Rayleigh–Van der Pol impact vibration model. We show that the RMAS algorithm modifies residual-based sampling algorithms and, in particular, reduces the system identification error by 76% with the same sample sizes. Moreover, the surrogate model accurately predicts the first escape probability density function and the P bifurcation behavior in the systems, with the error of less than 1.59 x 10-2⁠. Finally, the robustness of the FSI method is validated.