Introduction to Uncertainty Quantification

This version of the course is being taught at Purdue University during Spring 2016. The code for the course is ME 59700. The instructors are Prof. Ilias Bilionis and Prof. Guang Lin. The class meets every Tuesday and Thursday 1:30pm-2:45pm at ME 3021.

The goal of this course is to introduce the fundamentals of uncertainty quantification to advanced undergraduates or graduate engineering and science students with research interests in the field of predictive modeling. 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 parameters of physical models using experimental data.
• Combine multiple sources of information to enhance the predictive capabilities of models.
• Pose and solve design optimization problems under uncertainty involving expensive computer simulations.

Student Evaluation

• 10% Participation
• 60% Homework
• 30% Final Project

Lectures

• Lecture 1 - Introduction to Uncertainty Quantification on 01/12/2016.

• Lecture 2 - Probability Theory on 01/14/2016.

• Lecture 3 - Probability Distributions on 01/19/2016.

• Lecture 4 - Uncertainty Propagation using Sampling Methods: Monte Carlo on 01/21/2016.

• Lecture 5 - Uncertainty Propagation using Sampling Methods: Latin-hypercube designs on 01/26/2016.

• Lecture 6 - Uncertainty Propagation using Polynomial Chaos I on 01/28/2016.

• Lecture 7 - Uncertainty Propagation using Polynomial Chaos II on 02/02/2016.

• Lecture 8 - Maximum Likelihood, Bayesian Parameter Estimation, Bayesian Linear Regression on 02/04/2016.

• Lecture 9 - Priors of Function Spaces: Gaussian Processes on 02/09/2016.

• Lecture 10 - Gaussian Process Regression on 02/11/2016.

• Lecture 11 - Representation of Prior Uncertainty - The Maximum Entropy Principle on 02/16/2016.

• Lecture 12 - Dimensionality Reduction: Principal Component Analysis on 02/18/2016.

• Lecture 13 - Dimensionality Reduction of Random Fields: The Karhunen-Loeve Expansion on 02/23/2016.

• Lecture 14 on 02/25/2016.

• Lecture 15 on 03/01/2016.

• Lecture 16 on 03/03/2016.

• Lecture 17 on 03/08/2016.

• Lecture 18 on 03/10/2016.

• Lecture 19 on 03/22/2016.

• Lecture 20 on 03/24/2016.

• Lecture 21 on 03/29/2016.

• Lecture 22 on 03/31/2016.

• Lecture 23 on 04/05/2016.

• Lecture 24 on 04/07/2016.

• Lecture 25 on 04/12/2016.

• Lecture 26 on 04/14/2016.

• Lecture 27 on 04/19/2016.

• Lecture 28 on 04/21/2016.

• Lecture 29 on 04/26/2016.

• Lecture 30 on 04/28/2016.

Homework Sets

• Homework 1 due on 01/26/2016.

• Homework 2 due on 02/09/2016.

• Homework 3 due on 02/23/2016.

• Homework 4 due on 03/08/2016.

• Homework 5 due on 03/29/2016.

• Homework 6 due on 04/12/2016.

Installation of Required Software for Viewing the Notebookes

Microsoft Windows

Apples OS X

Linux

• Anaconda from Continuum Analytics, is absolutely essential to group the installation of many packages.

• A working latex distribution. We suggest MacTex for OS X users, and MikTex for Windows users.

• Jupyter Notebook Extensions is required to properly display latex in the document (bibliography and equation numbers).

• Essential UQ software developed by the Predictive Science Laboratory:

  • py-orthpol for generating orthogonal polynomials with respect to arbitrary probability measures. Requires FORTRAN compiler.

  • py-design for generating designs for computer codes. Requires FORTRAN compiler.

• RISE is required only if you want to view the presentation as slides.