Nicolas Boullé is an Assistant Professor in Applied Mathematics at Imperial College London. He obtained a PhD in numerical analysis at the University of Oxford in 2022. His research focuses on the intersection between numerical analysis and deep learning, with a specific emphasis on learning physical models from data, particularly in the context of partial differential equations learning. He was awarded a Leslie Fox Prize in 2021 and a SIAM Best Paper Prize in Linear Algebra in 2024 for his work on operator learning.
Speaker
Talk Title
An Overview of Operator Learning
Talk Summary
Operator Learning is an emerging field at the intersection of machine learning, physics and mathematics, that aims to discover properties of unknown physical systems from experimental data. Popular techniques exploit the approximation power of deep learning to learn solution operators, which map source terms to solutions of the underlying PDE. Solution operators can then produce surrogate data for data-intensive machine learning approaches such as learning reduced order models for design optimization in engineering and PDE recovery. In this talk, we will provide a brief overview of the growing field of operator learning and see how numerical linear algebra algorithms, such as the randomized singular value decomposition, can be exploited to gain theoretical and mechanistic understanding of operator learning architectures.
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