Generative multi-fidelity modeling and downscaling via spatial autoregressive transport maps

Spatial fields are often available at multiple fidelities or resolutions, where high-fidelity data is typically more costly to obtain than low-fidelity data. Statistical surrogates or emulators can predict high-fidelity fields from cheap low-fidelity output. We propose a highly scalable Bayesian approach that can learn the joint non-Gaussian distribution and nonlinear dependence structure of nonstationary spatial fields at multiple fidelities from a small number of training samples. Our method is based on fidelity-aware autoregressive GPs with suitably chosen regularization-inducing priors. Exploiting conjugacy, the integrated likelihood is available in closed form, enabling efficient hyperparameter optimization via stochastic gradient descent. After training, the method also characterizes in closed form the distribution of higher-fidelity fields given lower-fidelity data. In our numerical comparisons, we show that our approach substantially outperforms existing methods and that it can be used to characterize and simulate high-fidelity fine-scale climate behavior based on output from coarse (low-fidelity) global circulation models.