Abstract / Description of output
We investigate the theoretical foundations of the simulated tempering (ST) method and use our findings to design an efficient accelerated sampling algorithm. Employing a large deviation argument first used for replica exchange molecular dynamics (Plattner et al 2011 J. Chem. Phys. 135 134111), we demonstrate that the most efficient approach to simulated tempering is to vary the temperature infinitely rapidly. In this limit, we can replace the equations of motion for the temperature and physical variables by averaged equations for the latter alone, with the forces rescaled according to a positiondependent function defined in terms of temperature weights. The averaged equations are similar to those used in Gao's integratedovertemperature method, except that we show that it is better to use a continuous rather than a discrete set of temperatures. We give a theoretical argument for the choice of the temperature weights as the reciprocal partition function, thereby relating simulated tempering to Wang–Landau sampling. Finally, we describe a selfconsistent algorithm for simultaneously sampling the canonical ensemble and learning the weights during simulation. This infinite switch simulated tempering (ISST) algorithm is tested on three examples of increasing complexity: a system of harmonic oscillators; a continuous variant of the Curie–Weiss model, where ISST is shown to perform better than standard ST and to accurately capture the secondorder phase transition observed in this model; and alanine12 in vacuum, where ISST also compares favorably with standard ST in its ability to calculate the free energy profiles of the root mean square deviation (RMSD) and radius of gyration of the molecule in the 300–500 K temperature range.
Original language  English 

Article number  013207 
Number of pages  32 
Journal  Journal of Statistical Mechanics: Theory and Experiment 
Volume  2019 
Issue number  1 
DOIs  
Publication status  Published  16 Jan 2019 
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Benedict Leimkuhler
 School of Mathematics  Chair of Applied Mathematics
Person: Academic: Research Active