cbe67701-uncertainty-quantification

This seminar course explores modern topics in computation, data analytics, and modeling relevant for engineering and the chemical sciences. Ph.D. students in engineering, science, and mathematics are the intended audience. Each meeting, 1 or more enrolled students will (co-)lead the discussion on chapters in the semester text. The goal of these discussions is not to lecture on the material, but instead present a working example that highlights a core concept or method from each chapter.

For Summer 2020, we are studying Uncertainty Quantification and Predictive Computational Science by Prof. Ryan McClarren.

Table of Contents

Data Index

Figure Index

Python Module Index

Chapter 1.0 Introduction to Uncertainty Quantification and Predictive Sciences

• 1.1 Our First Notebook

Chapter 2.0 Probability-and-Statistics-Preliminaries

• 2.1 Multivariate Distributions: Example from Texbook
• 2.2 Rejection Sampling, Skewness, and Kurtosis

Chapter 3.0 Input Parameter Distributions

• 3.1 Copulas
• 3.2 Principal Component Analysis

Chapter 4.0 Local Sensitivity Analysis Based on Derivative Approximations

• 4.1 Local sensitivity analysis and difference approximation
• 4.2 Advection-Diffusion-Reaction (ADR) Example

Chapter 5.0 Regression Approximations to Estimate Sensitivities

• 5.1 Ridge Regression
• 5.2 Lasso Regression
• 5.3 Elastic Net Regression

Chapter 6.0 Adjoint-Based Local Sensitivity Analysis

• 6.1 Nonlinear Diffusion-Reaction Equation
• 6.2 A Simple Example of Adjoint Sensitivity Analysis
• 6.3 Sensitivity Analysis with Adjoint Operators
• 6.4 Adjoint Sensitivity Notes on Numerical Computation

Chapter 7.0 Sampling-Based Uncertainty Quantification: Monte Carlo and Beyond

• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 7.3 Meaningful Title Goes Here

Chapter 8.0 Reliability Methods for Estimating the Probability of Failure

• 8.1 First-Order Second-Moment (FOSM) Method Example
• 8.2 Advanced First-Order Seccond-Momemt Methods (AFSOM)
• 8.3 Advanced First-Order Second-Moment Methods

Chapter 9.0 Stochastic Projection and Collocation

• 9.1 Hermite Expansion for Normally Distributed Parameters
• 9.2 Uniform Random Variables: Legendre Polynomials

Chapter 10.0 Gaussian Process Emulators and Surrogate Models

• 10.1 Using GPflow package for Gaussian Process Regression
• 10.2 A simple example of Bayesian quadrature
• 10.3 Using scikit-learn for Gaussian Process Regression

Chapter 11.0 Predictive Models Informed by Simulation, Measurement, and Surrogates

• 11.1 Gibbs Sampling to Approximate Bayes’ Integral
• 11.2 Markov Chain Monte Carlo Examples
• 11.3 The Kennedy-O’Hagan Predictive Model

Chapter 12.0 Epistemic Uncertainties: Dealing with a Lack of Knowledge

• 12.1 Predictions under epistemic uncertainty with p-boxes
• 12.2 Epistemic Uncertainty Quantification