Speaker: Daniel Sanz-Alonso (University of Chicago)

Abstract: Operator learning is an emerging paradigm at the 
intersection of scientific computing and machine learning. 
Its central objective is to learn operators between infinitedimensional function spaces from data. 
Although operator learning has found broad applications 
across science and engineering, its theoretical 
foundations remain underdeveloped. 

In this talk, I will present recent progress on the statistical 
and computational limits of operator learning, focusing on 
several fundamental operator classes: 
bounded linear operators between Sobolev spaces, 
pseudo-differential operators central to the analysis of 
partial differential equations (PDEs) and mathematical 
physics, and Fourier integral operators associated with 
hyperbolic systems and wave propagation. Across these 
settings, a common multiscale framework yields minimaxoptimal statistical rates together with computationally 
efficient estimators. These results contribute to a unified 
theory of operator learning at the interface of analysis and 
PDEs, computational mathematics, statistics, and data 
science.

Biography: Prof. Sanz-Alonso is an Associate Professor in the Department of 
Statistics at the University of Chicago, and a member of the 
Committee on Computational and Applied Mathematics. Previously, 
he was a postdoc in the Division of Applied Mathematics and a 
member of the Data Science Initiative at Brown University. He was 
awarded the José Luis Rubio de Francia prize to the best Spanish 
mathematician under 32 by the Spanish Royal Society of Mathematics, 
and received an NSF CAREER award in 2023. Since 2025, he has been 
an Associate Editor of the SIAM/ASA Journal on Uncertainty 
Quantification and Stochastics and Partial Differential Equations: 
Analysis and Computations.