论文标题
一种数据驱动的方法，用于发现具有非高斯征费噪声的随机动力学系统
A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise
论文作者
论文摘要
随着有价值的观测，实验性和模拟复杂系统数据的快速增加，正在竭尽全力发现这些系统演变基础的管理法律。但是，现有技术仅限于从数据中提取管理法律，作为确定性微分方程或具有高斯噪声的随机微分方程。在目前的工作中，我们开发了一种新的数据驱动方法，以提取具有非高斯对称lévy噪声以及高斯噪声的随机动力学系统。首先，我们通过表达漂移系数，扩散系数和跳跃测量（即，异常扩散）来建立一个可行的理论框架，以在样本路径数据方面为基础随机动力学系统。然后，我们设计了一种数值算法来计算漂移，扩散系数和跳跃度量，从而用高斯和非高斯噪声提取了管理随机微分方程。最后，我们通过应用几个典型的一，二维和三维系统来证明方法的疗效和准确性。这种新方法将成为从观察或模拟复杂现象的嘈杂数据集发现控制动态定律的工具，例如由具有沉重和轻尾统计特征的随机波动触发的罕见事件。
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing techniques are limited to extract governing laws from data as either deterministic differential equations or stochastic differential equations with Gaussian noise. In the present work, we develop a new data-driven approach to extract stochastic dynamical systems with non-Gaussian symmetric Lévy noise, as well as Gaussian noise. First, we establish a feasible theoretical framework, by expressing the drift coefficient, diffusion coefficient and jump measure (i.e., anomalous diffusion) for the underlying stochastic dynamical system in terms of sample paths data. We then design a numerical algorithm to compute the drift, diffusion coefficient and jump measure, and thus extract a governing stochastic differential equation with Gaussian and non-Gaussian noise. Finally, we demonstrate the efficacy and accuracy of our approach by applying to several prototypical one-, two- and three-dimensional systems. This new approach will become a tool in discovering governing dynamical laws from noisy data sets, from observing or simulating complex phenomena, such as rare events triggered by random fluctuations with heavy as well as light tail statistical features.
