Instructors:

Dimitris Giovanis, Assistant Research Professor, Johns Hopkins University

Michael D. Shields, Associate Professor, Johns Hopkins University

Description:

This three-day course introduces the fundamental concepts of uncertainty quantification (UQ) and propagation in complex multiscale engineering systems. Each day is broken into two sessions. In the first session UQ methodology is presented. This is followed by Python modeling exercises using the UQpy software in the second session. At the end of this course, it is the goal that attendees will have a foundation in the principles of UQ and will begin developing the practical skills to apply these principles to problems in their application areas of interest.

More specifically, attendees will learn how to:

• Identify source of uncertainties in models and data

• Represent uncertainties in model inputs and outputs and experimental data sources

• Select and apply methods to propagate uncertainties in computational models with an eye on computational efficiency.

• Apply Bayesian techniques for inferring uncertainty from various data sources.

Pre-Workshop Activities

• Participants should have an undergraduate-level knowledge of probability and statistics. Probability theory will not be presented in general, only specific components that are necessary will be presented but will require some prerequisite knowledge.

• Participants should have Python installed on their system and have at least a beginning knowledge of how to code in Python

• Participants will be given instructions for installing the open source software UQpy and any other necessary software on their system.

• If the participant has a simple code that they would like to use for UQ, they are encouraged to have an example available.

Day 1: Intro & Uncertainty Propagation using Monte Carlo Methods

Session 1.1 – Theory

1. Introduction: Types of uncertainty (epistemic, aleatoric, decision)

2. Probability theory. Random variables and Probability Distributions. Law of large numbers. Central Limit theorem.

3. Sampling methods: Monte Carlo method & variance reduction (i.e. IS, LHS, STS)

4. Markov Chain Monte Carlo – Theory & Algorithms

Session 1.2 – Activities

1. UQpy: Installation

2. Linking to a computational model: The RunModel module

3. Monte Carlo using the SampleMethods module

4. Running Markov Chain Monte Carlo algorithms with the MCMC class

Day 2: Uncertainty Propagation using Numerical Methods & Surrogate Models

Session 2.1 – Theory

1. Gaussian process (GP) regression / Kriging surrogates

2. Adaptive Kriging methods (AK-MCS, EGO, etc.)

3. Polynomial chaos expansions

Session 2.2 – Activities

1. Building/Training a GP surrogate model from data

2. Use the GP surrogate to perform UQ.

Day 3: Inverse UQ & Model Selection Using Bayesian Methods

Session 3.1 – Theory

1. Bayesian Rule

2. Bayesian parameter estimation

3. Maximum likelihood estimation

4. Bayesian and Information Theoretic model selection

Session 3.2 - Activities

1. Using MCMC to sample from a posterior

2. Parameter estimation from data (MLE and Bayesian)

3. Model selection from data