Upcoming Event: Oden Institute Seminar

Quasi-Monte Carlo, lattices, kernel methods, DNNs, and how to connect them

Frances Y. Kuo & Dirk Nuyens, UNSW, Sydney, Australia & KU Leuven, Belgium

Abstract

Lattice rules are our favorite family of quasi-Monte Carlo (QMC) methods. They are proven to be effective for high dimensional integration and multivariate function approximation in a number of settings. They are extremely easy to implement thanks to their very simple formulation - all we require is a "good" integer vector of length matching the dimensionality of the problem. We know how to construct such good vectors tailored to applications in different areas, e.g., in PDEs with random coefficients for uncertainty quantification, both for computing expected values (integrals) of quantities of interet as well as in obtaining surrogates of the PDE solution using lattice-based kernal interpolants. This talk will showcase our recent works on the application of lattice rules, including how they can be used in the framework of Deep Neural Networks (DNNs). 

Biography

Frances Y. Kuo completed a BCMS(Hons) in 1999 and a PhD in 2002 at the University of Waikato in New Zealand, and subsequently joined the School of Mathematics and Statistics at the University of New South Wales in 2003. Started as a Research Fellow, Frances obtained a UNSW Vice-Chancellor's Research Fellowship in 2004-2006, an ARC QEII Fellowship in 2007-2011, and was appointed a Senior Lecturer in 2012. She is an ARC Future Fellow since 2013, Associate Professor since 2015, and Professor since 2019. Frances was the recipient of the inaugural Information-based Complexity Young Researcher Award in 2003, and the ANZIAM J.H. Michell Medal in 2011, and the Information-based Complexity Prize in 2014. She works in the theory and applications of high dimensional integration and approximation, especially quasi-Monte Carlo methods, multilevel and multivariate decomposition techniques. Her recent interests are in their application to partial differential equations with random coefficients and uncertainty quantification.

Dirk Nuyens graduated from the Computer Science program at the KU Leuven in 2002 and obtained a PhD in numerical analysis and applied mathematics at the KU Leuven in 2007, on the topic of lattice rules (a quasi-Monte Carlo method) for high-dimensional integration. He was a postdoc at the University of New South Wales (Sydney, Australia) in 2008-2009 and became an assistant professor at the KU Leuven in 2013. His research focusses on the construction of good point sets for high-dimensional integrals, expectations and approximation problems.