Following the Committor Flow: A Data-Driven Discovery of Transition Pathways.

The discovery of transition pathways to unravel distinct reaction mechanisms and, in general, rare events that occur in molecular systems is still a challenge. Recent advances have focused on analyzing the transition-path ensemble using the committor probability, widely regarded as the most informative one-dimensional reaction coordinate. Consistency between transition pathways and the committor function is essential for accurate mechanistic insight. In this work, we propose an iterative framework to infer the committor and, subsequently, to identify the most relevant transition pathways. Starting from an initial guess for the transition path, we generate biased sampling, from which we train a neural network to approximate the committor probability. From this learned committor, we extract dominant transition channels as discretized strings lying on isocommittor surfaces. These pathways are then used to enhance sampling and iteratively refine both the committor and transition paths until convergence. The resulting committor enables accurate estimation of the reaction rate constant. We demonstrate the effectiveness of our approach on benchmark systems, including a two-dimensional model potential, peptide conformational transitions, a Diels-Alder reaction, and the reversible folding of the Trp-cage.