Computing transition pathways for the study of rare events using deep reinforcement learning

The transition pathway plays a central role in understanding the transition mechanism of dynamical systems. Identifying the transition pathway is usually a challenging task for complex and high-dimensional systems, for example, in the study of conformational changes for bio-molecules. In this work, we propose a deep reinforcement learning method for computing the transition pathway. The method employs a geometric approximation of the pathway by polygonal chains in the configuration space. The path-finding task is formulated as a cost minimization problem, where a cost function is adapted from the Freidlin-Wentzell action functional so that it is able to deal with rough potential-energy landscapes. Then the problem is solved by introducing an actor-critic algorithm, which incorporates the potential force of the system in the exploration policy and combines physical properties of the system in the neural networks for molecular systems. The proposed method in conjunction with reinforcement learning provides a way for exploring the transition region and computing the globally optimal transition pathway for systems with rough energy landscapes. We highlight the abilities of the method on three benchmark problems, including an extended Mueller system and a Lennard-Jones system of seven particles.