Applied Mathematics Colloquium with Leonardo Zepeda-Núñez, Google
Special day and time: Monday, October 23, 2023, 11:00 AM-12:00 PM, 210 Mudd, APAM Conference Room
Speaker: Leonardo Zepeda-Núñez, Google
Title: Statistical Downscaling via Optimal Transport and Conditional Diffusion Models
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.
Bio: Dr. Zepeda-Núñez is a senior research scientist at Google Research and an assistant professor (on leave) in the Department of Mathematics at the University of Wisconsin-Madison, where he belongs to the Applied and Computational Mathematics group. He is also an affiliate of the Institute for Foundations of Data Science (IFDS) at the Wisconsin Institute for Discovery (WID). Prior to UW-Madison, he was a postdoctoral fellow at the Lawrence Berkeley National Laboratory in the Mathematics group led by James Sethian, working primarily with Lin Lin., and was a visiting assistant professor at the Department of Mathematics at the University of California, Irvine, working with Hongkai Zhao. He graduated in June 2015 from MIT with a Ph.D. in Mathematics under the direction of Laurent Demanet. He is a former student of École Polytechnique and University Pierre et Marie Curie Paris VI. He is particularly interested in Machine Learning, Numerical Analysis, Scientific Computing, Wave Propagation and Inverse Problems.
This talk will be offered in a hybrid format. If you wish to participate remotely, please send an email to firstname.lastname@example.org.