An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas

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@Article{Li:2025:cnsns,

• author = "Yang Li2 and Shengyuan Xu and Jinqiao Duan",
• title = "An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas",
• journal = "Communications in Nonlinear Science and Numerical Simulation",
• year = "2025",
• volume = "145",
• pages = "108751",
• keywords = "genetic algorithms, genetic programming, Nonlocal Kramers-Moyal formulas, Stochastic dynamical systems, Evolutionary symbolic sparse regression method, Levy motion",
• ISSN = "1007-5704",
• URL = "https://www.sciencedirect.com/science/article/pii/S1007570425001625",
• DOI = "doi:10.1016/j.cnsns.2025.108751",
• abstract = "Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) Levy noise from data is challenging due to the possible intricate functional forms and the inherent complexity of Levy motion. This research endeavors to develop an evolutionary symbolic 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. Specifically, genetic programming is employed to generate a diverse array of candidate functions, sparse regression is used to learn 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 demonstrated through its application to several illustrative models. This approach stands out as a powerful tool for deciphering non-Gaussian stochastic dynamics from available datasets, suggesting a wide range of applications across various fields",

}

Genetic Programming entries for Yang Li2 Shengyuan Xu Jinqiao Duan

Citations