In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more accurate calculation of mean exit time via computing large deviation prefactors with the research efforts of machine learning. More specifically, we design a neural network framework to compute quasipotential, most probable paths and prefactors based on the orthogonal decomposition of vector field. We corroborate the higher effectiveness and accuracy of our algorithm with a practical example. Numerical experiments demonstrate its powerful function in exploring internal mechanism of rare events triggered by weak random fluctuations.

翻译：本文提出大偏差理论，用于刻画弱噪声极限下随机动力系统中稀有事件的指数估计。我们旨在通过机器学习方法计算大偏差前因子，考虑次主导阶近似以实现平均逃逸时间的更精确计算。具体而言，我们基于向量场正交分解，设计了一个神经网络框架来计算拟势、最概然路径及前因子。通过实际案例验证了算法的高效性与准确性。数值实验表明，该算法在探索由弱随机涨落触发的稀有事件内在机制方面具有强大功能。