A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling
Xiao-Kai An, Lin Du, Feng Jiang, Yujia Zhang, Zichen Deng, Jürgen Kurths
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 1.59×10-2. Finally, the robustness of the FSI method is validated.