Deep Tempering for Sampling Complex Energy Landscapes. Theory and Application to RNA riboswitches.

Sampling complex energy landscapes has always been a central problem in statistical mechanics. More recently, inverse statistical mechanics provided a framework to infer that complex landscape directly from data. In this thesis, these two objectives are addressed with Restricted Boltzmann Machines (RBMs), an energy based machine learning model which defined by a bilayer network. This kind of architecture has been used in many inference problems but it is proven to suffer from poor mixing times just as bad as simple Monte Carlo algorithms. Here we explore Deep Tempering, which like simulated annealing introduces copies of the original system, but in this case, instead of having systems at different temperatures, we have hierarchically coarse-grained versions of the original landscape. This sequential coarse-graining is achieved by stacking RBMs in such a way that the dimensionality of the problem is gradually reduced. Along with a theoretical work, contrasted with simulations on toy datasets, with apply the method on a dataset of RNA SAM-riboswitches, a segment of bacterial RNA that is able to switch between two structural conformations depending on the concentration of S-Adenosyl methionine (SAM).