Mittag-Leffler correlated noise (M-L noise) plays a crucial role in the dynamics of complex systems, yet the scientific community has lacked tools for its direct generation. Addressing this gap, our work introduces GenML, a Python library specifically designed for generating M-L noise. We detail the architecture and functionalities of GenML and its underlying algorithmic approach, which enables the precise simulation of M-L noise. The effectiveness of GenML is validated through quantitative analyses of autocorrelation functions and diffusion behaviors, showcasing its capability to accurately replicate theoretical noise properties. Our contribution with GenML enables the effective application of M-L noise data in numerical simulation and data-driven methods for describing complex systems, moving beyond mere theoretical modeling.

翻译：米塔格-莱弗勒相关噪声（M-L噪声）在复杂系统动力学中起着关键作用，然而科学界长期以来缺乏直接生成该噪声的工具。针对这一空白，我们提出了GenML——一个专为生成M-L噪声而设计的Python库。本文详细阐述了GenML的架构、功能及其底层算法方法，该方法能够实现对M-L噪声的精确模拟。通过对自相关函数和扩散行为的定量分析，我们验证了GenML的有效性，展示了其准确复现理论噪声特性的能力。我们贡献的GenML使得M-L噪声数据能够有效应用于复杂系统的数值模拟与数据驱动方法，从而超越单纯的理论建模范畴。