Inverse Uncertainty Quantification with PyApprox
Tim Wildey
Sandia National Laboratories
Optimization and UQ
We often seek to develop a mutually beneficial relationship between experimentation and simulation, where the data from the experiments informs the computational models and the computational models are used to guide the optimal acquisition of new data. In this presentation, we will discuss some basic concepts to enable moving beyond forward simulation to build data-informed physics-based models. First, we discuss inverse problems from the Bayesian perspective and how one might go about approximating or generating samples from the posterior distribution. Then, we note that the collection of experimental data can be costly and time consuming. Thus, we may only be able to afford to perform a limited number of experiments, so we must choose the experiments that are likely to produce informative data. Moreover, the optimality of the experiment must be chosen with respect to the ultimate objective. We demonstrate that the optimal experimental design often depends on whether our objective is to characterize the uncertainty in model input parameters or in the prediction of quantities of interest that cannot be observed directly. The presentation will include descriptions of the basic concepts, live demonstrations using PyApprox, and opportunities for the audience to gain hands-on experience in both Bayesian inference and experimental design. We conclude the presentation with a brief description of current research directions identified in a recent report from the Department of Energy, Office of Science.