Preserving Correlations Between Trajectories for Efficient Path Sampling

摘要

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