Uncertainty Quantification and Propagation

MODULE 0: INTRODUCTION AND REVIEW OF PROBABILITY THEORY 

[L1 - L3] Introduction to UQ, review of probability and statistics (P1) [lecture video][lecture notes annotated]

[L4] Review of probability and statistics - Part 2 [lecture notes annotated]

[L5] Review of probability and statistics - Part 3 [lecture notes annotated]

[L6] Review of probability and statistics - Part 4 [lecture notes annotated]

MODULE 1: UNCERTAINTY PROPAGATION: SAMPLING METHOD 

[L7] Uncertainty propagation: Sampling method - Part 1 [lecture notes annotated]

[L8] Uncertainty propagation: Sampling method - Part 2 [lecture notes annotated]

[L9] Uncertainty propagation: Sampling method - Part 3 [lecture notes annotated]

MODULE 2: UNCERTAINTY PROPAGATION: PERTURBATION AND SURROGATE BASED APPROACH

[L10] Uncertainty Propagation: Perturbation Methods - Part 1 [lecture notes annotated]

[L11] Uncertainty Propagation: Perturbation Methods - Part 2 [lecture notes annotated]

[L12] Uncertainty Propagation: Surrogate-based approach - Part 1 (PCE) [lecture notes annotated]

[L13] Uncertainty Propagation: Surrogate-based approach - Part 2 (BLR) [lecture notes annotated]

[L14] Uncertainty Propagation: Surrogate-based approach - Part 3 (BLR) [lecture notes annotated]

[L15] Uncertainty Propagation: Surrogate-based approach - Part 4 (GP) [lecture notes annotated]

[L16] Uncertainty Propagation: Surrogate-based approach - Part 5 (GP) [lecture notes annotated]

MODULE 3: UNCERTAINTY QUANTIFICATION/INVERSE PROBLEM, MODEL SELECTION, AND MODEL FORM UNCERTAINTY

[L17] Inverse Problems/Model Calibration: Classic Approaches [lecture notes]

[L18] Inverse Problems/Model Calibration: Bayesian Approaches [lecture notes]

[L19] Markov Chain Monte Carlo - Part 1 [lecture notes annotated]

[L20]Bayesian Model Selection and Sequential Monte Carlo [lecture notes annotated]

[L21]Sequential Monte Carlo and Model-form uncertainty  [lecture notes]

MODULE 4: CONCLUSION

[L23] Sensitivity Analysis, open problems, and way ahead

• Need for UQ in computational mechanics, types of uncertainty and errors. 

• Review of fundamentals of probability

• Random processes and statistics, representation of random inputs

• Sampling method for uncertainty propagation

• Perturbation method for uncertainty propagation

• Surrogate-based approach for uncertainty propagation

• Solving inverse problems, uncertainty quantification in inverse problems

• Model form uncertainty, Bayesian model selection, and Model form uncertainty quantification in dynamical systems

• Sensitivity analysis.

Lecture notes and references will be provided on the course web site. The following books are recommended:

• Smith, R. C. (2013). Uncertainty quantification: theory, implementation, and applications (Vol. 12). SIAM.

• Sullivan, T. J. (2015). Introduction to uncertainty quantification (Vol. 63). Springer.

• Rasmussen, Carl Edward. Gaussian processes in machine learning, In Summer school on machine learning, pp. 63-71. Springer, Berlin, Heidelberg, 2003

• Homework 1: Review of probability and statistics [homework]

• Homework 2:Propagating uncertainty using sampling and Perturbation methods [homework]

• Homework 3: PCE and Bayesian Linear Regression [homework]

• Homework 4: Gaussian Proccess [homework]

• Homework 5: Quantifying model-form uncertainty [homework]

• Each student will have to complete a term project as part of this course

Credit: 3 Units (3-0-0)

Timing: To be decided

Venue: To be decided

Instructor: Dr. Souvik Chakraborty 

Teaching Assistants: Tapas Tripura

Course Objective: The objective of this course is to introduce the fundamentals of uncertainty quantification techniques and their application in computational mechanics. On completion of this course, a student would have adequate knowledge on different UQ techniques and their applications in science and engineering. The course is particularly designed for PG, Ph.D., and senior UG students.

Intended audience: Senior UG, PG, and Ph.D. students