Sampling from Boltzmann densities with physics informed low-rank formats
This addresses a computational bottleneck in statistical physics and machine learning for researchers, though it appears incremental as it builds on existing annealing and Sequential Monte Carlo methods.
The paper tackles the problem of efficiently sampling from unnormalized Boltzmann densities by solving the continuity equation using a low-rank tensor train format, achieving improved efficiency in numerical examples.
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.