# Uncertainty Quantification and Propagation

## Lecture notes

MODULE 0: INTRODUCTION AND REVIEW OF PROBABILITY THEORY

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

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

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

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

MODULE 1: UNCERTAINTY PROPAGATION: SAMPLING METHOD

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

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

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

MODULE 2: UNCERTAINTY PROPAGATION: PERTURBATION AND SURROGATE BASED APPROACH

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

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

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

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

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

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

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

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

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

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

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

[L20]Markov Chain Monte Carlo - Part 2 [lecture video][lecture notes][lecture notes annotated]

[L21]Bayesian Model Selection and Sequential Monte Carlo [lecture video][lecture notes][lecture notes annotated]

[L22]Sequential Monte Carlo and Model-form uncertainty [lecture video][lecture notes]

MODULE 4: CONCLUSION

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

## Syllabus

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.

## References

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

## Projects

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

## Course info

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