EU Regional School - McClarren Seminar
Prof. Dr. McClarren - Polynomial Chaos Expansions for Uncertainty Quantification
Texas A&M University
In computational science and engineering one often deals with computer simulations where inputs to the calculation are uncertain. A natural question to ask is how uncertain the output of a simulation is given uncertainties in the inputs. In this lecture I will give cover the application of orthogonal expansions in probability space (also known as polynomial chaos expansions) to determine the distribution of quantities of interest from a numerical simulation. I will detail how to apply these methods to a variety of input uncertainty distributions, and give concrete examples for simple functions as well as non-trivial applications. The examples will also be an opportunity to point out to students the pitfalls and common mistakes that can be made applying these techniques. Finally, I will cover more advanced ideas such as sparse quadrature and regularized regression techniques to estimate expansion coefficients.