MTH 655 - Sec 010

(Cross-listed with MTH659 for those who have previously taken a different MTH655)

Numerical Analysis:
Uncertainty Quantification

MWF 9:00-9:50 AM
MFD112
Winter 2023


Outline

Last modified: Mon Nov 28 15:42:56 PST 2022

  1. Introduction
    • Background on Predictive Science (Smith Chapter 1: Introduction)
      • Verification/Validation
      • Errors/Uncertainties
    • Mathematical Modeling
      • Prototypical Models (Smith Section 3.1)
      • Abstract Modeling Framework (Smith Section 3.3)
    • Probability Basic Concepts (Smith Chapter 4; Xiu Chapter 2)
      • Probability Distributions
      • Stochastic Processes
      • Random vs Stochastic Differential Equations (Smith 4.7)
  2. Representation of Random Inputs
    • Karhunen-Loeve Expansion (Smith Chapter 5; Xiu Chapter 4)
    • PCA
    • SVD
  3. Uncertainty Propagation
    • Sampling, Perturbation, Spectral
    • Generalized Polynomial Chaos (Xiu Chapter 3)
    • Stochastic Galerkin
      • Stochastic Finite Element Method
      • Error Analysis
    • Stochastic Collocation
      • Projection vs Interpolation
      • Sparse Grid Collocation
      • Error Analysis
  4. Stochastic Differential Equations (Higham)
    • Brownian Motion
    • Stochastic Integrals
    • Euler-Maruyama Method
    • Strong vs Weak Convergence
    • Milstein Method
    • Theta Methods