Recent Advances in Probabilistic Scientific Machine Learning through Generative Diffusion Models

The advent of generative AI has turbocharged the development of a myriad of commercial applications while slowly permeating scientific computing. In this talk, we discussed how recasting the formulation of old and new problems within a probabilistic approach opens the door to leveraging and tailoring state-of-the-art generative AI tools. As such, we review recent advancements in Probabilistic SciML—including computational fluid dynamics, inverse problems, and particularly climate sciences, with an emphasis on statistical downscaling.

Statistical downscaling is a crucial tool for analyzing the regional effects of climate change under different climate models: it seeks to transform low-resolution data from a (potentially biased) coarse-grained numerical scheme (which is computationally inexpensive) into high-resolution data consistent with high-fidelity models. We recast this problem in a two-stage probabilistic framework using unpaired data by combining two transformations: a debiasing step performed by an optimal transport map, followed by an upsampling step achieved through a probabilistic conditional diffusion model. Our approach characterizes conditional distributions without requiring paired data and faithfully recovers relevant physical statistics, even from biased samples.

We will show that our method generates statistically correct high-resolution outputs from low-resolution ones for well-known climate models and weather data. We show that the framework can upsample resolutions by ~500x while accurately matching the statistics of physical quantities, including extreme compounded events—even when the low-frequency content of the inputs and outputs differs. This is a crucial yet challenging requirement that existing state-of-the-art methods usually struggle with.

Bio
https://people.math.wisc.edu/~zepedanunez/

Zepeda-Núñez earned his Ph.D. in Mathematics from MIT and held postdoctoral and faculty positions at Lawrence Berkeley National Laboratory and UC Irvine. He is dedicated to increasing diversity in STEM and serve as a faculty mentor for the MΔth Alliance, supporting underrepresented students in mathematics. His research focuses on developing machine learning and numerical methods with applications to weather and climate, quantum chemistry, wave propagation, and inverse problems. Current projects involve generative AI, optimal transport, and data-driven approaches to dynamics and statistical downscaling.