Sampling from Boltzmann densities with physics informed low-rank formats

Abstract: Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.