Exploration of effective potential landscapes using coarsereverse integration

摘要

We describe a reverse integration approach for the exploration of low-dimensional effectivepotential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient navigation on the landscape terrain: Escape from local effective potential wells, detection of saddlepoints, and identification of significant transition paths between wells. We consider several distinct ring evolution modes: Backward stepping in time, solution arc length, and effective potential. Theperformance of these approaches is illustrated for a deterministic problem where the energy landscape is known explicitly. Reverse ring integration is then applied to noisy problems where thering integration routine serves as an outer wrapper around a forward-in-time inner simulator. Two versions of such inner simulators are considered: A Gillespie-type stochastic simulator and amolecular dynamics simulator. In these "equation-free" computational illustrations, estimation techniques are applied to the results of short bursts of inner simulation to obtain the unavailable (inclosed-form) quantities (local drift and diffusion coefficient estimates) required for reverse ring integration; this naturally leads to approximations of the effective landscape.