A novel approach for dimensionality reduction of high-dimensional stochastic dynamical systems using symbolic regression

Abstract

This paper introduces an innovative data-driven approach for dimensionality reduction in stochastic dynamical systems. The method combines stochastic averaging theory with symbolic regression. First, this approach generates simulation data from the high-dimensional stochastic dynamical system that needs to be reduced. Then, a loss function is designed based on stochastic averaging theory, and symbolic regression is used to obtain a parameterized one-dimensional equation from the simulation data. Finally, the effectiveness of the approach proposed in this paper is demonstrated through validation on Hamiltonian systems with 5, 10, and 20 degrees of freedom (DOF) subjected to noisy excitation. The primary advantage of this method is that it ultimately provides a closed form rather than a black-box process. Furthermore, it overcomes the numerical integration challenges that stochastic averaging methods often face when dealing with high-dimensional systems, therefore it performs effectively with high-dimensional stochastic dynamical systems.