论文标题
用于计算随机动力系统最可能路径的机器学习框架
A Machine Learning Framework for Computing the Most Probable Paths of Stochastic Dynamical Systems
论文作者
论文摘要
噪声引起的亚稳态状态之间的过渡现象的出现在广泛的非线性系统中起着基本作用。最可能的路径的计算是了解过渡行为机制的关键问题。拍摄方法是为此目的的一种常见技术，可以解决相关的动作功能的Euler-Lagrange方程，同时在高维系统中失去疗效。在目前的工作中，我们开发了一个机器学习框架，以计算Onsager-Machlup动作功能理论的意义上的最可能的路径。具体而言，我们重新制定了哈密顿系统的边界价值问题，并设计了一个神经网络来纠正拍摄方法的缺点。我们的算法在几个原型示例中的成功应用表明了其对具有（高斯）布朗噪声和（非高斯）lévy噪声的随机系统的功效和准确性。这种新颖的方法有效地探索了由各个科学领域的随机波动触发的罕见事件的内部机制。
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 understand the mechanism of transition behaviors. 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 Hamiltonian system and design a neural network to remedy the shortcomings of 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 novel approach is effective in exploring the internal mechanisms of rare events triggered by random fluctuations in various scientific fields.
