The simulated tempering method in the infinite switch limit with adaptive weight learning

Abstract

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 [Nuria et al. J. Chem. Phys. 135:134111 (2011)], 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 position-dependent function defined in terms of temperature weights. The averaged equations are similar to those used in Gao's integrated-over-temperature 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 self-consistent 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 second-order phase transition observed in this model; and Alanine-12 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 300-500K tempearture range.

The SAMPL6 SAMPLing challenge: assessing the reliability and efficiency of binding free energy calculations

“…Alternatively, other statistics such as acceptance rate and mean first-passage time have been reported [39][40][41], but these statistics are methodspecific, and not necessarily indicative of the error of the free energy estimate. Another common strategy to assess the efficiency of a method is the visual inspection of the decay of some error metric [42,43], but this qualitative analysis is not scalable nor statistically quantifiable when the number of methods and systems considered increases. Finally, there is a large body of theoretical work focusing on the efficiency of estimators and protocols in free energy calculations [24,37,40,42,44,45], but in many cases, they are difficult to apply to practical scenarios.…”

Local and global perspectives on diffusion maps in the analysis of molecular systems

“…The system is highly metastable: a standard simulation at 300 K requires at least 5 μs to converge [53]. Therefore, the trajectory studied here was obtained using the infinite-swap simulated tempering (ISST) [54] method with temperatures in the range from 300 K to 500 K (nominal stepsize 2 fs and nominal simulation length 2 μs). This method is incorporated into the MIST [55] library which is coupled to the GROMACS and Amber96 forcefields.…”

The SAMPL6 SAMPLing challenge: Assessing the reliability and efficiency of binding free energy calculations

“…Another common strategy to assess the efficiency of a method is the visual inspection of the decay of some error metric [39,40], but this qualitative analysis is not scalable nor statistically quantifiable when the number of methods and systems considered increases, and it becomes ambiguous if the relative performance of two methods is system-dependent. Finally, there is a large body of theoretical work focusing on the efficiency of estimators and protocols in free energy calculations [21,34,37,39,41,42], but in many cases, they are difficult to apply to practical scenarios.…”