Uncertainty Quantification: introduction and examples,
Prof Pierre Gremaud
It is simplistic, but useful, to think of Uncertainty Quantification (UQ) as a way to provide error bars on numerical results from modeling and simulation. The goal of this workshop is to give researchers involved in numerical simulation a set of tools allowing for the quantification of confidence in their results. The presentation will be at an introductory level and will not attempt to be comprehensive.
In the first part of the workshop, we will introduce key concepts such verification and validation of numerical experiments, aleatory versus epistemic uncertainties and various notions of numerical sensitivity. The second part will discuss the necessary computational framework. We will cover the following three key steps:
- data assimilation, i.e., the characterization of uncertainties in the inputs,
- uncertainty propagation, i.e., performing simulations which account for the identified uncertainties,
- certification: quantification of the confidence in the results.
Uncertainty propagation involves a number of choices. We will look at both probabilistic vs non-probabilistic frameworks and intrusive vs non-intrusive methods. We will also introduce various families of reduced order methods, i.e., surrogate models from polynomial chaos to methods from non-parametric statistics.
Most of the concepts and methods will be introduced from scratch and illustrated by examples.
Prof Pierre Gremaud comes to us from North Carolina State University, his research interests include numerical PDEs, mathematical modeling, material and medical science applications, granular materials.
You are warmly invited to attend this workshop. Please email email@example.com to register your interest.