Title: “Statistical Downscaling via Optimal Transport and Conditional Diffusion Models”
Abstract: Statistical downscaling has been one of the primary tools for studying the effects of climate change at a regional scale under various climate models. In essence, statistical downscaling aims to create a mapping that transforms low-resolution snapshots from a (potentially biased) coarse-grained numerical simulation, which is cost-effective to compute, into high-resolution snapshots, such that the resulting high-resolution output is statistically consistent with snapshots from high-fidelity simulations (or real data).
In this talk we will introduce a two-stage probabilistic framework for statistical downscaling between unpaired data. The framework tackles the problem by composing two transformations: a debiasing step that is performed by an optimal transport map, and an upsampling step that is achieved by a probabilistic diffusion model with a posteriori conditional sampling. This approach characterizes a conditional distribution without the need for paired data, and faithfully recovers relevant physical statistics from biased samples.
We will demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties in numerical simulation of weather and climate. We will show that our method produces statistically correct high-resolution outputs from low-resolution inputs, by upsampling resolutions of 8x and 16x, while correctly matching the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives.