提取受非高斯列维噪声扰动随机动力系统的最大似然转移路径的数据驱动方法

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中文摘要：机器学习和数据科学技术的飞速发展，很大程度上满足了许多领域通过数据预测比较实际或复杂的动力系统的需求。列维噪声是一个比高斯白噪声更普适和复杂的涨落模型，它被广泛应用于许多非高斯情形来模拟爆炸或跳跃行为。在本文中，我们设计了一个系统的数据驱动方法来识别受高斯白噪声和非高斯列维噪声扰动的系统的最大似然转移路径。其中涉及的主要理论和数值概念包括经典动力系统理论中的非局部Kramers-Moyal公式、非局部Fokker-Planck方程以及一个通过交叉验证解决稀疏回归问题的机器学习框架。接下来我们给出两个例子从细节方面展现了该方法的可操作性，并且对最大似然转移路径做了简要的分岔分析。该方法将作为相关理论研究对应的数值方法以及数值角度的验证，并为该高斯扩散过程的推广复杂系统的其他诸如平均离出时间或离出概率等动力学指征的数值识别工作提供一些洞见。

外文标题：Data-driven approach for extracting the most probable exit trajectory of stochastic dynamical systems with non-Gaussian Lévy noise

外文摘要：The burgeoning data-driven techniques endow large potential to predict fairly practical or complex dynamical systems in various fields through massive data.Lévy noise,a more universal and intricate fluctuation model comparing with Gaussian white noise,is widely employed in many non-Gaussian cases to mimic bursting or hopping.In this manuscript,we present a systematic data-driven method to identify the most probable exit trajectory of a system that is perturbed both by Gaussian white noise and non-Gaussian Lévy noise.The main theoretical and numerical conceptions involve a set of extended Kramers-Moyal formulas and the Kolmogorov forward equation in classic dynamical systems theory as well as a supervise learning theory to solve the fitting problems by using the Cross Validation.We then give two examples to show the feasibility in detail,and do a brief bi-furcation analysis for the most probable exit trajectory.The above approach will serve as a numerical correspondence to as well as verification for the relative theoretical research,and provide a referential resolution to the numerical identification of more transition indicators of this complex system,which is more general than the Gaussian diffusion process.

外文关键词：

Rare random transitionsThe most probable exit pathNon-local Kramers-Moyal formulasNon-local Kolmogorov for-ward equationNon-Gaussian noise pertubation

作者：

陆凌弘志、李扬、刘先斌

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作者单位：

State Key Laboratory of Mechanics and Control for Mechanical Structures,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China

关键词：

Rare random transitions The most probable exit path Non-local Kramers-Moyal formulas Non-local Kolmogorov for-ward equation Non-Gaussian noise pertubation

基金：

国家自然科学基金江苏省高等学校优势学科建设工程项目

项目编号：

12172167

出版年：

2024

DOI：

10.1007/s10409-023-23094-x

力学学报(英文版)

CSTPCD

影响因子：0.363

ISSN：0567-7718

年,卷(期)：2024.40(1)

参考文献量40