# 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).

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.

**: 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.**

*Award citation*