Preserving Correlations Between Trajectories for Efficient Path Sampling

TL;DR

This paper explores correlation-based schemes for importance sampling of long trajectories in complex systems, using a modern MCMC perspective to improve efficiency in path sampling of chaotic dynamics.

Contribution

It introduces a noise guidance strategy for trajectory proposals, enhancing sampling efficiency for long, chaotic trajectories by leveraging a non-equilibrium statistical mechanics framework.

Findings

Noise guidance can synchronize trajectories effectively.

Efficient path sampling achieved for very long trajectories.

Method applicable to chaotic dynamical systems.

Abstract

Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to dynamical pathways that are substantial, yet sufficiently modest to obtain reasonable acceptance rates. Satisfying this requirement becomes very challenging in the case of long trajectories, due to the characteristic divergences of chaotic dynamics. Here we examine schemes for addressing this problem, which engineer correlation between a trial trajectory and its reference path, for instance using artificial forces. Our analysis is facilitated by a modern perspective on Markov Chain Monte Carlo sampling, inspired by non-equilibrium statistical mechanics, which clarifies the types of sampling strategies that can scale to long trajectories. Viewed in this light, the most promising such strategy guides a trial trajectory by manipulating the sequence of random numbers that advance its stochastic time evolution, as done in a handful of existing methods. In cases where this "noise guidance" synchronizes trajectories effectively, as the Glauber dynamics of a two-dimensional Ising model, we show that efficient path sampling can be achieved even for very long trajectories.