Roles of Uncertainty Quantification in Materials Science

Tuesday, July 28, 2015 - 1:30pm - 5:00pm
DLR Room 131
Ralph Smith (North Carolina State University)
In this lecture, we will provide an overview of concepts pertaining to uncertainty quantification (UQ) in the context of materials science. We will begin by motivating pertinent issues in the context of macroscopic models for piezoelectric, magnetic and shape memory alloys and X-ray absorption to determine the local structure of crystalline materials. We will demonstrate that the basic UQ goal is quantify uncertainties inherent to parameters, initial and boundary conditions, measured data, and models themselves to make predictions with reduced and quantified uncertainties. We will then discuss global sensitivity techniques for parameter selection, Bayesian model calibration, sampling and spectral methods for uncertainty propagation, and issues pertaining to surrogate model construction. The goal is to provide attendees with a basic understanding of issues associated with uncertainty quantification as well as open questions.

The development and use of efficient and robust computational algorithms comprises a central component of uncertainty quantification. During the associated lab, we will use MATLAB code for a recently developed Delayed Rejection Adaptive Metropolis (DRAM) algorithm to construct posterior parameter densities and prediction intervals for a simple nonlinear model. This will provide attendees with initial experience regarding the implementation of Bayesian model calibration and uncertainty propagation algorithms.