Operator learning without the adjoint

主讲人：Nicolas Boullé， Assistant Professor at Imperial College London

时间：2026年3月4日10：30

地点：徐汇校区三号楼332室

举办单位：数理学院

主讲人介绍：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 research fellow at the University of Cambridge from 2022 to 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. 

内容介绍：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.