Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) L\'evy noise from data is chanllenging due to possible intricate functional forms and the inherent complexity of L\'evy motion. This present research endeavors to develop an evolutionary symbol sparse regression (ESSR) approach to extract non-Gaussian stochastic dynamical systems from sample path data, based on nonlocal Kramers-Moyal formulas, genetic programming, and sparse regression. More specifically, the genetic programming is employed to generate a diverse array of candidate functions, the sparse regression technique aims at learning the coefficients associated with these candidates, and the nonlocal Kramers-Moyal formulas serve as the foundation for constructing the fitness measure in genetic programming and the loss function in sparse regression. The efficacy and capabilities of this approach are showcased through its application to several illustrative models. This approach stands out as a potent instrument for deciphering non-Gaussian stochastic dynamics from available datasets, indicating a wide range of applications across different fields.

本研究针对从数据中发现非高斯随机动态系统的复杂性问题，提出了一种演化符号稀疏回归（ESSR）方法。该方法结合非局部克拉默-莫雅尔公式、遗传编程和稀疏回归，通过生成候选函数和学习关联系数，有效地揭示了非高斯随机动力学的结构，展示了其在多领域广泛应用的潜力。

基于非局部克拉默-莫雅尔公式的非高斯随机动态系统发现的演化方法