Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are presented to compute the most probable transition pathway. It is shown that the expected loss is bounded by the empirical loss. And the convergence result for the empirical loss is obtained. Then, a sampling method of rare events is presented to simulate the transition path by the Markovian bridge process. And we investigate the inverse problem to extract the stochastic differential equation from the most probable transition pathway data and the Markovian bridge process data, respectively. Finally, several numerical experiments are presented to verify the effectiveness of our methods.

翻译：元国家之间的过渡现象在复杂系统中由于吵闹的波动而起着重要作用。 在本文中,物理知情神经网络(PINNs)被介绍来计算最可能的过渡路径。 显示预期损失受经验损失的束缚。 并获得经验损失的趋同结果。 然后, 提出稀有事件的抽样方法, 以模拟Markovian桥的过渡路径。 我们研究反向问题, 从最可能的过渡路径数据和Markovian桥进程数据中提取随机差异方程。 最后, 提出了数项实验, 以验证我们方法的有效性 。