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.
An Always-Accepting Algorithm for Transition Path Sampling
Institute of Physics, University of Augsburg（奥格斯堡大学物理研究所）；Faculty of Physics, University of Vienna（维也纳大学物理学院）；Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam（阿姆斯特丹大学范特霍夫分子科学研究所）；Research Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna（维也纳大学加速光反应发现研究平台）
