Score-Based Methods for Applied Mathematics

by Ludovico Theo Giorgini (Stockholm University, Nordita)

Thursday 15 Jan 2026, 16:00 → 18:00 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

Modern generative AI relies on a simple but powerful mathematical object: the score function, defined as the gradient of the log-probability density. Knowledge of the score function allows sampling from a target probability distribution without estimating normalization constants, which are often intractable in high dimensions, and efficient algorithms have been developed in computer science to learn the score directly from data. In this talk, I will show how score-based methods can address fundamental questions in applied mathematics. Specifically, I will present three applications: (i) predicting the statistical response of far-from-equilibrium chaotic systems to perturbations using the Generalized Fluctuation–Dissipation Theorem, (ii) calibrating stochastic model parameters efficiently from steady-state data alone, and (iii) constructing parsimonious reduced-order models that faithfully reproduce both the steady-state distribution and temporal correlations of complex systems. These methods are demonstrated on a range of examples, from turbulent fluid flows to reaction–diffusion equations and climate-relevant slow–fast system

 

zoom link : https://stockholmuniversity.zoom.us/j/622224375