Generative multi-scale modeling via spatial autoregressive transport maps

Abstract: We propose a scalable Bayesian emulator that learns the joint, potentially non-Gaussian distribution of nonstationary spatial fields across multiple resolutions from a small number of training samples. The model decomposes a field into a coarse-to-fine sequence of scales and uses autoregressive transport maps to link them, which acts as a structured dimension reduction for high-dimensional fields. We apply the method to downscaling of climate model output to regional resolution with full posterior uncertainty quantification, outperforming existing approaches; the same construction transfers to emulation of expensive simulators and to compact representations of large ensembles.