Hierarchic Flows to Estimate and Sample High-dimensional Probabilities

arXiv:2405.03468v1 Announce Type: cross
Abstract: Finding low-dimensional interpretable models of complex physical fields such as turbulence remains an open question, 80 years after the pioneer work of Kolmogorov. Estimating high-dimensional probability distributions from data samples suffers from an optimization and an approximation curse of dimensionality. It may be avoided by following a hierarchic probability flow from coarse to fine scales. This inverse renormalization group is defined by conditional probabilities across scales, renormalized in a wavelet basis. For a $\varphi^4$ scalar …

abstract approximation arxiv cs.lg data dimensionality fields low optimization physics.flu-dyn probability question sample samples stat.ml turbulence type work