Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations

arXiv:2402.15285v1 Announce Type: cross
Abstract: Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse-time diffusion processes depending on the log-densities of Ornstein-Uhlenbeck forward processes are a popular sampling tool. In Berner et al. [2022] the authors point out that these log-densities can be obtained by solution of a \textit{Hamilton-Jacobi-Bellman} (HJB) equation known from stochastic optimal control. While this HJB equation is usually …

abstract arxiv challenge cs.lg diffusion fields generative hamilton math.st modelling popular probability processes quantification sampling stat.ml stat.th tensor tool train type uncertainty