Upcoming Event: Oden Institute Seminar

Multilevel Function Approximation

Mike Giles, Professor, Mathematical Institute, University of Oxford

Abstract

Building on established techniques for classical and sparse grid interpolation, this seminar will discuss the approximation of parametric functions of the form ƒ(θ) where θ is multi-dimensional and each function evaluation corresponds to either a functional of the solution of a PDE, with parametric dependence on θ, or the expected value of a functional of the solution of an SDE, again with a parametric dependence on θ. In both cases, exact sampling of ƒ(θ) is not possible, and greater accuracy comes at a higher computational cost. 

The key idea to improve the computational cost for a given accuracy is a multilevel representation of the function ƒ(θ) with coarse levels using very accurate approximations of ƒ(θ) at a very limited number of points, whereas fine levels use inaccurate approximations at a large number of points. 

Biography

In my early career, I worked at MIT and in the Oxford University Computing Laboratory on computational fluid dynamics applied to the analysis and design of gas turbines, but in around 2008 I moved into computational finance and research on Monte Carlo methods for a variety of applications.

My research focus is on improving the accuracy, efficiency and analysis of Monte Carlo methods. A particular highlight has been the development and numerical analysis of multilevel Monte Carlo methods; this has been the basis of much of my research in the past 15 years and has stimulated a lot of research elsewhere.

I am also interested in various aspects of scientific computing, including high performance parallel computing, and I have worked extensively on the exploitation of many-core GPUs for a variety of applications.