Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning
Francesca Bartolucci - Delft Institute of Applied Mathematics (TU Delft)
Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined on paper, neural operators require discretization in the transition to computer implementations. This step can compromise their integrity, often causing them to deviate from the underlying operators. This research offers a fresh take on neural operators with a Representation equivalent Neural Operators (ReNO) framework designed to address these issues. At its core is the concept of operator aliasing, which measures inconsistency between neural operators and their discrete representations. More generally, this framework not only sheds light on existing challenges but, given its constructive and broad nature, also potentially offers tools for developing new neural operators. This is a joint work with Rima Alaifari, Emmanuel de Bézenac, Siddhartha Mishra, Roberto Molinaro and Bogdan Raonić.
Francesca Bartolucci is an assistant professor in the Analysis research group at the Delft Institute of Applied Mathematics, TU Delft. Before joining TU Delft, she was a postdoc at the Department of Mathematics at ETH Zürich in the research group of Prof. Rima Alaifari. She obtained her PhD degree from the University of Genoa under the supervision of Prof. Filippo De Mari and Prof. Ernesto De Vito. Her research interests include applied harmonic analysis, group representation theory, phase retrieval and the mathematical foundations of machine learning.
Monday February 19th, 4.00pm
Room 508 @ DIBRIS/DIMA, Via Dodecaneso 35, Genoa