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Machine learning framework for computing the most probable paths of stochastic dynamical systems
Physical Review E ( IF 2.4 ) Pub Date : 2021-01-21 , DOI: 10.1103/physreve.103.012124
Yang Li , Jinqiao Duan , Xianbin Liu

The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understanding the mechanism of transition behaviors. The shooting method is a common technique for this purpose to solve the Euler-Lagrange equation for the associated action functional, while losing its efficacy in high-dimensional systems. In the present work, we develop a machine learning framework to compute the most probable paths in the sense of Onsager-Machlup action functional theory. Specifically, we reformulate the boundary value problem of a Hamiltonian system and design a neural network to remedy the shortcomings of the shooting method. The successful applications of our algorithms to several prototypical examples demonstrate its efficacy and accuracy for stochastic systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise. This approach is effective in exploring the internal mechanisms of rare events triggered by random fluctuations in various scientific fields.

中文翻译:

机器学习框架,用于计算随机动力学系统的最可能路径

噪声引起的亚稳态之间的过渡现象的出现在广泛的非线性系统中起着根本性的作用。最可能的路径的计算是了解过渡行为机理的关键问题。射击方法是为此目的常用的技术,用于解决相关联的动作函数的欧拉-拉格朗日方程,同时在高维系统中失去其功效。在当前的工作中,我们开发了一种机器学习框架来计算Onsager-Machlup动作功能理论意义上的最可能路径。具体来说,我们重新制定了哈密顿系统的边值问题,并设计了神经网络来弥补射击方法的缺点。我们的算法在几个典型示例中的成功应用证明了其对于具有(高斯)布朗噪声和(非高斯)Lévy噪声的随机系统的有效性和准确性。这种方法有效地探索了由各个科学领域中的随机波动触发的罕见事件的内部机制。
更新日期:2021-01-21
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