  Understanding the transition events between metastable states in complex
systems is an important subject in the fields of computational physics,
chemistry and biology. The transition pathway plays an important role in
characterizing the mechanism underlying the transition, for example, in the
study of conformational changes of bio-molecules. In fact, computing the
transition pathway is a challenging task for complex and high-dimensional
systems. In this work, we formulate the path-finding task as a cost
minimization problem over a particular path space. The cost function is adapted
from the Freidlin-Wentzell action functional so that it is able to deal with
rough potential landscapes. The path-finding problem is then solved using a
actor-critic method based on the deep deterministic policy gradient algorithm
(DDPG). The method incorporates the potential force of the system in the policy
for generating episodes and combines physical properties of the system with the
learning process for molecular systems. The exploitation and exploration nature
of reinforcement learning enables the method to efficiently sample the
transition events and compute the globally optimal transition pathway. We
illustrate the effectiveness of the proposed method using three benchmark
systems including an extended Mueller system and the Lennard-Jones system of
seven particles.
