Upcoming Event: Oden Institute & College of Natural Sciences

Operator Learning for Scientific Computing

Margaret Trautner, Postdoctoral Researcher, California Institute of Technology

Abstract

Operator learning uses data to approximate maps between infinite-dimensional function spaces. As such, operator learning provides a natural framework for using machine learning in applications with partial differential equations (PDEs), which form a critical component of scientific models. While operator learning architectures have successfully modeled a variety of physical phenomena in practice, the theoretical foundations underpinning these successes remain in early stages of development. 

This talk showcases some results in this area, including methods for multiscale constitutive PDEs and learning solutions to an elliptic PDE in the presence of discontinuities and corner interfaces. Following this, the talk introduces, at a high level, some results on theory for operator learning more generally. This work builds understanding of operator learning from several perspectives and contributes both theoretical advancements and practical methodologies that improve the applicability of operator learning models to scientific problems. 

Biography

Margaret Trautner is a postdoctoral researcher at the California Institute of Technology in the Department of Computing and Mathematical Sciences. She obtained her Ph.D. at Caltech in 2025 and her B.S. in Mathematics from MIT in 2020. Her doctoral work was supported by a Department of Energy Computational Sciences Graduate Fellowship. Dr. Trautner's research develops rigorous foundations for scientific machine learning by combining mathematical analysis with computational methods.