The IV AMMCS International Conference

Waterloo, Ontario, Canada | August 20-25, 2017

AMMCS Prize-Winning Lecture: Kolmogorov-Wiener Prize for Young Researchers

Sparse polynomial approximation of high-dimensional functions

Ben Adcock (Simon Fraser University)

Many problems in scientific computing require the approximation of smooth, high-dimensional functions from limited amounts of data. For instance, a common problem in uncertainty quantification involves identifying the parameter dependence of the output of a computational model. Complex physical systems require computational models with many parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse of dimensionality essentially prohibits collecting or processing enough data to reconstruct the unknown function using classical approximation techniques.
   In this talk, I will give an overview of the approximation of smooth, high-dimensional functions by sparse polynomial expansions. I will focus on the recent application of techniques from compressed sensing to this problem, and demonstrate how such approaches theoretically overcome the curse of dimensionality. If time, I will also discuss a number of extensions, including dealing with corrupted and/or unstructured data, the effect of model error and incorporating additional information such as gradient data. I will also highlight several challenges and open problems.
   This is joint work with Casie Bao, Simone Brugiapaglia and Yi Sui (SFU).
At the IV AMMCS International Conference, Dr. Benjamin Adcock of Simon Fraser University is presenting his lecture as a winner of the AMMCS Kolmogorov-Wiener Prize for Young Researchers. The award was granted at the previous AMMCS meeting, organized jointly with the Canadian Applied and Industrial Mathematics Society. More details can be found here. Ben Adcock is an assistant professor at Simon Fraser University. Born in England, he studied mathematics at the University of Cambridge, receiving his BA in 2005, his MMath in 2006, and his PhD in 2011. He held NSERC and PIMS postdoctoral fellowships at Simon Fraser University from 2010 to 2012, and was an assistant professor in the Department of Mathematics at Purdue University from 2012 to 2014, before returning to Canada in August of that year. He was the recipient of a Leslie Fox Prize in Numerical Analysis in 2011 and an Alfred P. Sloan Research Fellowship in 2015. His research interests include applied and computational harmonic analysis, numerical analysis and approximation theory.

Award citation: Benjamin Adcock received his PhD from the University of Cambridge in 2010. After his graduation, he received NSERC and PIMS Postdoctoral Fellowships and was carrying his research at Simon Fraser University. In 2012 he joined Purdue University as an Assistant Professor. Since August 2014 he is on the faculty of mathematics at Simon Fraser University. Dr. Adcock’s research interests include applied and computational harmonic analysis, sampling theory, compressed sensing, as well as approximation theory and numerical analysis. He made original significant contributions to sampling theory and compressed sensing which have potential applications in the areas ranging from medical imaging to geophysical signal processing. At the time of the award, he has published twenty journal publications, most of which are in the top tier journals of his field. Dr. Adcock’s work bridges the gap between theory and practice by developing and applying highly innovative mathematical tools.