Transition Path Theory from Biased Simulations

TL;DR

This paper develops an efficient computational scheme for Transition Path Theory (TPT) that leverages biased simulations and enhanced sampling techniques to analyze rare transition events in complex systems.

Contribution

It extends the Self-Consistent Path Sampling algorithm to compute the committor function and introduces algorithms for direct sampling of transition paths from non-equilibrium trajectories.

Findings

Extended SCPS algorithm for committor calculation

Efficient algorithms for transition path ensemble sampling

Applicable to complex systems with rare events

Abstract

Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q^+(x), which provides the ideal reaction coordinate. Furthermore, the reactive dynamics and kinetics are fully characterized in terms of two time-independent scalar and vector distributions. In this work, we develop a scheme which enables all these ingredients of TPT to be efficiently computed using the short non-equilibrium trajectories generated by means of a specific combination of enhanced path sampling techniques. In particular, first, we further extend the recently introduced Self-Consistent Path Sampling (SCPS) algorithm in order to compute the committor q^+(x). Next, we show how this result can be exploited in order to define efficient algorithms which enable us to directly sample the transition path ensemble.