用进化算法从数据中挖掘含非高斯噪声的随机动力系统方程
An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas
- 结合遗传编程与稀疏回归，基于非局部Kramers-Moyal公式构建搜索框架
- 可准确识别含莱维噪声的复杂随机系统，验证模型涵盖多种典型动力学行为
- 适合从事随机建模、物理系统逆问题研究的研究者使用
从包含（高斯）布朗运动和（非高斯）莱维噪声的样本路径数据中发现显式随机动力系统的控制方程极具挑战，原因在于可能存在的复杂函数形式及莱维运动的固有复杂性。本文提出一种进化符号稀疏回归（ESSR）方法，基于非局部Kramers-Moyal公式、遗传编程与稀疏回归，从数据中提取非高斯随机动力系统。具体而言，遗传编程生成多样候选函数，稀疏回归学习其系数，而非局部Kramers-Moyal公式则作为遗传编程的适应度度量和稀疏回归的损失函数基础。该方法在多个示范模型上展示了其有效性与能力，表明其是解析非高斯随机动力学的强大工具，具有广泛的应用前景。
原文摘要 · Abstract (English)
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.
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