Upcoming Event: SIAM Speaker Series

Operator learning meets inverse problems: Algorithms, analysis, and applications

Dr. Nicholas Nelsen, Klarman Fellow, Cornell University Incoming Assistant Professor, UT Austin

Abstract

Operator learning involves data-driven models that accept continuum forms of data as inputs or outputs. Such models are robust to refinement of numerical discretizations and are thus well-suited for solving problems in computational science and engineering. This talk reviews the operator learning framework and emphasizes the interplay between theoretical insights and algorithm development. The talk showcases recent efforts to bring operator learning ideas to the field of inverse problems. The presentation emphasizes probabilistic methods, such as transport maps or Bayesian inversion, that regularize the fundamental instability of such ill-posed problems. The talk will also highlight recent progress on operator learning in the space of probability measures, with applications in medical imaging and data assimilation.

Biography

Nick Nelsen is a Klarman Fellow in the Department of Mathematics at Cornell University and an incoming tenure-track assistant professor at The University of Texas at Austin starting Fall 2026. He works in the research areas of computational mathematics and scientific machine learning. Nelsen’s research develops artificial intelligence methods for high- and infinite-dimensional problems, establishes mathematical guarantees on the reliability and trustworthiness of these methods, and applies the methods in the physical, engineering, and data sciences. He received the SIAM Review SIGEST award in 2024 from the Society for Industrial and Applied Mathematics (SIAM) and a College of Arts & Sciences Distinguished Alumni and Rising Star award from Oklahoma State University (OSU) in 2025. His research is funded by the AMS, Simons Foundation, U.S. National Science Foundation (NSF), and SIAM. Previously, he was an NSF Mathematical Sciences Postdoctoral Research Fellow at MIT. Nelsen received his Ph.D. from Caltech in 2024, where he was supported by the Amazon AI4Science Fellows Program and an NSF Graduate Research Fellowship. His doctoral dissertation on the “statistical foundations of operator learning” was awarded the W. P. Carey & Co. Best Thesis Prize in Applied Mathematics and the Centennial Prize for the Best Thesis in MCE. He obtained his M.Sc. from Caltech in 2020 and his B.Sc., B.S.M.E., and B.S.A.E. degrees from OSU in 2018.