Exploration of effective potential landscapes using coarse reverse integration

Thomas A. Frewen, Gerhard Hummer, Ioannis G. Kevrekidis

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13 Scopus citations


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.

Original languageEnglish (US)
Article number134104
JournalJournal of Chemical Physics
Issue number13
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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