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

Area of Science:

• Dynamical Systems and Control Theory
• Machine Learning and Artificial Intelligence
• Computational Modeling

Background:

• Neural networks are powerful data-driven models but require extensive data, leading to high collection costs.
• Accurate identification of stochastic dynamical systems is crucial for understanding complex phenomena.
• Existing sampling algorithms often require numerous data points and hyperparameter tuning.

Purpose of the Study:

• To develop a novel sampling algorithm to reduce data requirements for neural network-based system identification.
• To enhance the accuracy and efficiency of modeling stochastic dynamical systems.
• To introduce a few-shot identification (FSI) method for systems with limited data.

Main Methods:

• Proposed a residual-based multipeaks adaptive sampling (RMAS) algorithm, a novel approach to adaptive sampling.
• Integrated the RMAS algorithm with neural networks to create a few-shot identification (FSI) method.
• Applied the FSI method to identify a vegetation biomass change model and the Rayleigh-Van der Pol impact vibration model.

Main Results:

• The RMAS algorithm significantly reduces system identification error by 76% compared to classical methods with identical sample sizes.
• The proposed FSI method achieves high accuracy in predicting system behaviors, with prediction errors below 1.59×10-2.
• The RMAS algorithm demonstrates superior performance without requiring any hyperparameters.

Conclusions:

• The RMAS algorithm effectively reduces data collection costs and improves system identification accuracy for stochastic dynamical systems.
• The FSI method offers a robust and efficient solution for modeling complex systems with limited data.
• This work advances the application of neural networks in scientific modeling by addressing data scarcity challenges.