Pacific Institute for the Mathematical Sciences - PIMS

Sparse polynomial approximation of high-dimensional functions

Many problems in scientific computing require the approximation of smooth, high-dimensional functions from limited amounts of data. For instance, a typical problem in uncertainty quantification involves identifying the parameter dependence of the output of a computational model. Complex physical systems involve models with multiple 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 sufficient data to approximate the unknown function using classical techniques.

In this talk, I will give an overview of the approximation of smooth, high-dimensional functions using sparse polynomial expansions. I will focus on the application of techniques from compressed sensing to this problem, and discuss the extent to which such approaches overcome the curse of dimensionality. If time, I will also discuss several 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).

Location: ESB 4133