The NUEN 647 course introduces the fundamentals of uncertainty quantification to graduate nuclear engineering students with research interests in the field of predictive modeling and uncertainty quantification. Upon completion of this course, the students should be able to:

- Represent mathematically the uncertainty in the parameters of physical models.
- Propagate parametric uncertainty through physical models to quantify the induced uncertainty on quantities of interest.
- Calibrate the uncertain parameters of physical models using experimental data.
- Combine multiple sources of information to enhance the predictive capabilities of models.
- Pose and solve complex nuclear engineering problems under uncertainty.

**Background:**

The ability to predict the behavior or response of a system depends on the interplay between the mathematical model and the data used as its input. Often, this data is usually subject to uncertainty, as are model parameters. Furthermore, the model itself may also be an approximate representation of reality. In many applications, it is

essential that predictions based on models and data consider these uncertainties. The topic of uncertainty quantification (UQ) includes mathematical and statistical methods that address the modeling, assessment, and propagation of uncertainties. The field of UQ draws upon many foundational ideas and techniques in mathematics and statistics (e.g., approximation theory, error estimation, statistical inference, stochastic modeling, and Monte Carlo methods) and applies these to discipline-specific models and problems.

**Objectives:**

The objective of this course is to present an introduction to the basic tools of uncertainty quantification, with the goal of helping students address UQ questions in their application areas of interest. Lectures will provide basic introductions to probability and stochastic processes, data analysis, estimation and inference, sensitivity

analysis, uncertainty propagation, sampling methods, Bayesian computation, experimental design, and model

validation.

Typical topics discussed during the course include:

- Aleatoric vs epistemic uncertainties
- Review of probability theory and Random Variables
- Regression techniques; generalized linear models
- Sampling techniques
- Perturbation approaches and adjoint-based sensitivity
- Polynomial Chaos
- Gaussian Processes
- Proper Orthogonal Decomposition (POD) methods