## Hierarchical Uncoupling-Coupling of Metastable Conformations

Please always quote using this URN: urn:nbn:de:0297-zib-6296
• Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.

Author: Alexander Fischer, Christof Schütte, Peter Deuflhard, Frank Cordes ZIB-Report $n$-pentane molecule; almost invariant sets; bridge sampling; hierarchical annealing; hybrid Monte Carlo; metastability; ratio of normalizing co 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J22 Computational methods in Markov chains [See also 65C40] 65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods 65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C40 Computational Markov chains 82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80] 2001/02/23 ZIB-Report (01-03) Appeared in: Computational Methods for Macromolecules: Challenges and Applications. Proc. of the 3rd Int. Workshop on Methods for Macromolecular Modeling, New York, Oct. 12-14, 2000. T. Schlick, Gan, H. H. (eds.) Springer 2002. LNCSE 24, pp. 235-259