I am a professor of mathematics at Simon Fraser University. Please see my bio page for more information about me. You may also want to take a look at my Google Scholar profile and my LinkedIn page.
Research areas
numerical analysis, scientific computing, mathematics of machine learning, approximation theory, mathematics of data science, applied and computational harmonic analysis
Research summary
My group investigates mathematical and computational aspects of approximating complex, high- or infinite-dimensional objects from limited data in scientific computing applications. We focus primarily on machine learning methods such as deep neural networks, deep neural operators and deep learning. Objects of interest include solutions to PDEs and parametric PDEs, operators between function spaces arising as input-output maps of complex physical systems, and images arising as solutions to inverse problems. These objects ubiquitous in applications such as medical, scientific and industrial imaging, climate and weather modelling, computational fluid dynamics, materials design and beyond. Our interests include fundamental questions, such as what is the minimum amount of data necessary for recovery, the development of active learning techniques for improved data acquisition, and the design of practical algorithms that achieve near-optimal generalization bounds.
Publications
I am the author of Compressive Imaging: Structure, Sampling, Learning (CUP, 2021) with Anders C. Hansen and Sparse Polynomial Approximation of High-Dimensional Functions (SIAM, 2022) with Simone Brugiapaglia and Clayton G. Webster.
Please see my Google Scholar profile for a full list of my publications.
Prospective students and postdocs
My group has opportunities for talented undergraduate, graduate and postdoctoral researchers. Please read my Opportunities page for more information.