MECH 597 Uncertainty Quantification - Spring 2016

Course Information

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 uncertain 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.

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Instructors:

Prof. Guang Lin

Office: MATH 410, 150 N. University Street, West Lafayette, IN, 47907

Email: guanglin@purdue.edu

Homepage: https://www.math.purdue.edu/~lin491/

Prof. Ilias Bilionis

Email: ibilion@purdue.edu

Homepage: http://www.predictivesciencelab.org/people.html

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Textbook: We will mainly use lecture notes and some books as reading material.

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Lecture Notes in Jupyter Notebook Format:

https://github.com/PredictiveScienceLab/uq-course

Lecture notes in PDF Format:

Jan 12-14	Lecture 1	Lecture 2
Jan 19-21	Lecture 3	Lecture 4
Jan 26-28	Lecture 5	Lecture 6
Feb 2-5	Lecture 7	Lecture 8
Feb 9-12	Lecture 13	Lecture 14
Feb 16-18	Lecture 16	Lecture 17
Feb 23-25	Lecture 19	Lecture 20
Mar 2-4	Lecture 22	Lecture 23
Mar 9-11	Lecture 25	Lecture 26
Mar 23-25	Lecture 28	Lecture 29
Mar 30-Apr 1	Lecture 31	Lecture 32
Apr 6-8	Lecture 34	Lecture 35

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Lectures Time and Location

The class meets every Tuesday and Thursday 1:30pm-2:45pm at ME 3021.

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Syllabus

Syllabus

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Homework:

Homework should be readable and stapled. Illegible scribbling will receive no credit from the grader. For Python projects, you should hand in the printout of your Python session, including the source code and the generated graphs. You are encouraged to discuss with your classmates. However, your write-up must be independent. Homework assignments of high similarity will receive no credit.

Homework 1 (PDF, ipynb) 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.

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Grading Policy:

10% Participation

60% Homework

30% Final Project

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Final projects

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Installation of Required Software for Viewing the Notebookes

Find and download the right version of Anaconda for Python 2.7 from Continuum Analytics. This package contains most of the software we are going to need.

OS Specific Instructions

Microsoft Windows

We need C, C++, Fortran compilers, as well as the Python sources. Start a command line (look for cmd) and type:

conda install mingw libpython

Finally, you need git. As you install it, make sure you select that you want to use it from the Windows command prompt.

Apple OS X

Download and install Xcode
Agree to the license of Xcode by opening a terminal and typing:

sudo xcrun cc

Install your favorite version of the GNU compiler suite. You can do this with Homebrew (after you install it of course), by typing in the terminal:

brew install gcc

Alternatively, you may use the MacPorts.

Linux

Nothing special is required.

Installation of Required Python Packages

Independently of the operating system, use the command line to install the following Python packages:

Seaborn, for beatiful graphics:

conda install seaborn

GPy for Gaussian process regression:

conda install GPy

PyMC for MCMC sampling:

conda install pymc

py-design for generating designs for computer codes:

pip install py-design

py-orthpol for generating orthogonal polynomials with respect to arbitrary probability measures:

pip install py-orthpol

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Running the notebooks

Open the command line.
cd to your favorite folder.
Then, type:

git clone https://github.com/PredictiveScienceLab/uq-course.git

This will download the contents of this repository in a folder called uq-course.
Enter the uq-course folder:

cd uq-course

Start the jupyter notebook by typing the command:

jupyter notebook

Use the browser to navigate the course, experiment with code etc.
If the course contented is updated, type the following command (while being inside uq-course) to get the latest version:

git pull origin master

Keep in mind, that if you have made local changes to the repository, you may have to commit them before moving on.