Speaker: Alex Townsend
Bio: Prof. Alex Townsend is the Goenka Family Tenure-Track Assistant Professor at Cornell University in the Mathematics Department. His research is in Applied Mathematics and focuses on spectral methods, low-rank techniques, fast transforms, and theoretical aspects of deep learning. Prior to Cornell, he was an Applied Math instructor at MIT (2014-2016) and a DPhil student at the University of Oxford (2010-2014). He was awarded an NSF CAREER in 2021, a SIGEST paper award in 2019, the SIAG/LA Early Career Prize in applicable linear algebra in 2018, and the Leslie Fox Prize in numerical analysis in 2015.
Title: Low-rank techniques for PDE solving and PDE learning
Abstract: Matrices and tensors in computational mathematics are so often well-approximated by low-rank objects. In the first part of the talk, we will use the ADI method, a classic partial differential equation (PDE) solver, to understand the prevalence of compressible matrices and tensors, and resolve a long-standing problem of finding an optimal complexity spectrally-accurate Poisson solver. In the second part of the talk, we will use low-rank techniques for PDE learning where one is given input-output training data from an unknown uniformly elliptic PDE and would like to recover the PDE operator. By exploiting the hierarchical low-rank structure of Green’s functions and randomized linear algebra, we will describe the first rigorous scheme for PDE learning with a provable “learning rate.”
Time: Apr 14, 2021 10:00 AM Seoul
Join Zoom Meeting
Contact: Seick Kim (firstname.lastname@example.org)