Title: Simulated Tempering Method in the Infinite Switch Limit with Adaptive Weight Learning,
Abstract: We investigate the theoretical foundations of the simulated tempering method
and use our findings to design efficient algorithms. Employing a large
deviation argument first used for replica exchange molecular dynamics [Plattner
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 algorithm is tested on a system of harmonic oscillators as
well as a continuous variant of the Curie-Weiss model, where it is shown to
perform well and to accurately capture the second-order phase transition
observed in this model.