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，然而科学界一直缺乏直接生成该噪声的工具。为填补这一空白，本研究推出了专为生成M-L噪声设计的Python库GenML。我们详细阐述了GenML的架构功能及其底层算法原理，该算法能够实现对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，验证了GenML的有效性，证明其能准确复现理论噪声特性。GenML的贡献在于使M-L噪声数据能够有效应用于描述复杂系统的数值模拟和数据驱动方法，从而超越了单纯的理论建模范畴。