Gabriel Earle: Change of Measure and the Simulation of Transition Paths

The simulation of transition paths, i.e. rare trajectories of some dynamics which cross low-probability regions between higher-probability ones, presents an important and challenging topic in the field of dynamical systems. Simulating such paths accurately often allows us to understand crucial phenomena well, such as chemical reactions or state changes. Here, I present a method for measuring the accuracy of the approximation to the transition dynamics by means of computing the change of measure to the exact dynamics. This makes it possible to compare the accuracy of different models and use the Kullback-Leibler divergence directly as an objective function, which was previously not computable for the transition path process. I will outline how these new formulas can aid the training of efficient models for simulating transitions.