An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas
This addresses the challenge of modeling complex non-Gaussian stochastic dynamics from data, with potential applications across various fields, though it appears incremental as it builds on existing techniques like genetic programming and sparse regression.
The researchers tackled the problem of discovering explicit governing equations for stochastic dynamical systems with both Gaussian and non-Gaussian noise from data, by developing an evolutionary symbol sparse regression approach that successfully extracted such systems from sample path data, as demonstrated on several illustrative models.
Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise from data is chanllenging due to possible intricate functional forms and the inherent complexity of Lévy 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.