Statistical Downscaling via Optimal Transport and Conditional Diffusion Models

"Statistical Downscaling via Optimal Transport and Conditional Diffusion Models", organizado por CITMAga. Será impartido por Leonardo Zepeda Núñez (Google Research [USA])

Data: xoves, 15 de febreiro

Hora: 17:00 h.

Duración: 45 min

Lugar: En liña (MS Teams)

Abstract:

Statistical downscaling has been one of the main tools to study the effect of climate change at a regional scale under different climate models. In a nutshell, statistical downscaling seeks a map to transform low-resolution data from a (possibly biased) coarse-grained numerical scheme (which is cheap to compute) to high-resolution data that is consistent with a high-fidelity one.

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 present in numerical simulations 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.