Bi-Parametric Operator Preconditioning and Extensions

In this talk, Paul Escapil-Inchauspé will present results related to the framework of operator preconditioning for efficient Galerkin schemes, focusing on recent advances in the preconditioning of bi-parametric operators.  

He will showcase the theoretical developments that have enabled the construction of highly compressed preconditioners, particularly in the context of electromagnetic and acoustic scattering problems. These advances have led to provably stable convergence limits for iterative solvers.  

Additionally, he will explore the natural connection between operator preconditioning and the operator learning paradigm, outlining future directions towards the implementation of data-driven solvers.

Dr. Paul Escapil-Inchauspé is a researcher at Inria Chile. He holds an engineering degree from École Centrale de Nantes (France), as well as a bachelor's and master's degree in Mathematical and Industrial Engineering, and a Ph.D. in Civil Engineering from the Pontificia Universidad Católica de Chile. From 2021 to 2023, he completed a postdoctoral fellowship at Universidad Adolfo Ibáñez and then worked as a Data Science Engineer and Researcher at the Data Observatory from 2022 to 2024. His research interests include iterative solvers, uncertainty quantification, physics-informed neural networks, and boundary element methods.