CMX Lunch Seminar

Operator learning without the adjoint

Nicolas Boullé, Assistant Professor, Applied Mathematics, Imperial College London,

Speaker's Bio:
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 and was a postdoc at the University of Cambridge from 2022-2024. 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 .

There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest that one can accurately recover an operator while only using data generated by the forward action of the operator without access to the adjoint. However, naively, it seems essential to sample the action of the adjoint for learning time-dependent PDEs. In this talk, we will first explore connections with low-rank matrix recovery problems in numerical linear algebra. Then, we will show that one can approximate a family of non-self-adjoint infinite-dimensional compact operators via projection onto a Fourier basis without querying the adjoint.

Event Sponsors:

Computing and Mathematical Sciences (CMS) - More events from this Sponsor

For more information, please contact Jolene Brink by phone at (626)395-2813 or by email at jbrink@caltech.edu or visit CMX Website.

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