Exploration of effective potential landscapes using coarse reverse integration.
We describe a reverse integration approach for the exploration of low-dimensional effective potential 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 saddle points, 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. The performance 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 the ring 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 a molecular 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 (in closed-form) quantities (local drift and diffusion coefficient estimates) required for reverse ring integration; this naturally leads to approximations of the effective landscape.
Frewen
Thomas A
TA
Department of Chemical Engineering, Princeton University, Engineering Quadrangle, Olden Street, Princeton, New Jersey 08544, USA. tfrewen@princeton.edu
Hummer
Gerhard
G
Kevrekidis
Ioannis G
IG
D000465:Algorithms; D004151:Dipeptides / Q000737:chemistry; D008968:Molecular Conformation; D056004:Molecular Dynamics Simulation; D013816:Thermodynamics; D014867:Water / Q000737:chemistry
D004151:Dipeptides; D014867:Water; C002956:alanylalanine