cbe67701-uncertainty-quantification

Index of Python Libraries used in this Repository

autograd

• 6.3.8.1 Example: Over-damped oscillator
• 6.3.9.1 Example: Preditor-prey dynamics of the Hare/Lynx system
• 6.3.9.2 Example: Managing COVID-19 on a College Campus

csv

• 7.2.2.1 Set up diffusion reaction equation

gc

• 6.4.3.3 Solver comparisons

ghalton

• 7.2 Latin Hypercube Sampling

gpflow

• 10.1.2 Import Libraries

GPy

• 10.2.3.1 Take the GPR model as the surrogate

io

• 3.2 Principal Component Analysis

itertools

• 8.3.2.2 Example for Figure 8.6

math

• 4.1 Local sensitivity analysis and difference approximation
• 4.2.3 4.3.1 Simple ADR Example
• 6.1.3 Codes
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 10.2.3 Implementation
• 11.2 Markov Chain Monte Carlo Examples
• 11.3 The Kennedy-O’Hagan Predictive Model

matplotlib

• 1.1 Our First Notebook
• 2.1.5 Python Code
• 2.2 Rejection Sampling, Skewness, and Kurtosis
• 3.1 Copulas
• 3.2 Principal Component Analysis
• 4.1 Local sensitivity analysis and difference approximation
• 4.2.3 4.3.1 Simple ADR Example
• 5.1 Ridge Regression
• 5.2 Lasso Regression
• 5.3 Elastic Net Regression
• 6.1.3 Codes
• 6.2 A Simple Example of Adjoint Sensitivity Analysis
• 6.3.4.2 Solution
• 6.3.7.2 Example: One compartment model
• 6.3.8.1 Example: Over-damped oscillator
• 6.3.9.1 Example: Preditor-prey dynamics of the Hare/Lynx system
• 6.3.9.2 Example: Managing COVID-19 on a College Campus
• 6.4.3.1 Simple test problems
• 6.4.4 PDE constrained test problem
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 8.2.1 Reproduce Figure 8.6:
• 8.3 Advanced First-Order Second-Moment Methods
• 9.1 Hermite Expansion for Normally Distributed Parameters
• 9.2.3 Importing libraries
• 10.1.2 Import Libraries
• 10.2.3 Implementation
• 10.3.3 Import libraries
• 11.1.1 Example: Multivariate distribution
• 11.2 Markov Chain Monte Carlo Examples
• 11.3 The Kennedy-O’Hagan Predictive Model
• 12.1 Predictions under epistemic uncertainty with p-boxes
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean

numpy

• 1.1 Our First Notebook
• 2.1.5 Python Code
• 2.2 Rejection Sampling, Skewness, and Kurtosis
• 3.1 Copulas
• 3.2 Principal Component Analysis
• 4.1 Local sensitivity analysis and difference approximation
• 4.2.3 4.3.1 Simple ADR Example
• 5.1 Ridge Regression
• 5.2 Lasso Regression
• 5.3 Elastic Net Regression
• 6.1.3 Codes
• 6.2 A Simple Example of Adjoint Sensitivity Analysis
• 6.3.3.2 Solution
• 6.3.4.2 Solution
• 6.3.7.2 Example: One compartment model
• 6.4.3.1 Simple test problems
• 6.4.4 PDE constrained test problem
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 8.2.1 Reproduce Figure 8.6:
• 8.3 Advanced First-Order Second-Moment Methods
• 9.1 Hermite Expansion for Normally Distributed Parameters
• 9.2.3 Importing libraries
• 10.1.2 Import Libraries
• 10.2.3 Implementation
• 10.3.3 Import libraries
• 11.1.1 Example: Multivariate distribution
• 11.2 Markov Chain Monte Carlo Examples
• 11.3 The Kennedy-O’Hagan Predictive Model
• 12.1 Predictions under epistemic uncertainty with p-boxes
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean

os

• 1.1.3 Installing Packages in Colab
• 1.1.5.1 Download the data into Colab
• 3.2 Principal Component Analysis
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 8.3 Advanced First-Order Second-Moment Methods
• 9.2 Uniform Random Variables: Legendre Polynomials
• 12.1 Predictions under epistemic uncertainty with p-boxes

pandas

• 1.1 Our First Notebook
• 3.1 Copulas
• 3.2 Principal Component Analysis
• 9.2.3 Importing libraries
• 10.1.2 Import Libraries
• 10.3.3 Import libraries
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean

random

• 3.1 Copulas
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean

requests

• 1.1.5.1 Download the data into Colab
• 3.2 Principal Component Analysis
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 8.3 Advanced First-Order Second-Moment Methods
• 9.2 Uniform Random Variables: Legendre Polynomials

scipy

• 2.2 Rejection Sampling, Skewness, and Kurtosis
• 4.1 Local sensitivity analysis and difference approximation
• 4.1 Local sensitivity analysis and difference approximation
• 4.1 Local sensitivity analysis and difference approximation
• 4.2.3 4.3.1 Simple ADR Example
• 4.2.3 4.3.1 Simple ADR Example
• 4.2.3 4.3.1 Simple ADR Example
• 6.1.3 Codes
• 6.1.3 Codes
• 6.1.3 Codes
• 6.4.3.1 Simple test problems
• 6.4.3.1 Simple test problems
• 6.4.4 PDE constrained test problem
• 6.4.4 PDE constrained test problem
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 7.2 Latin Hypercube Sampling
• 7.2 Latin Hypercube Sampling
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 11.2 Markov Chain Monte Carlo Examples
• 12.2.2 Example 1: KS Test on Distributions of the Same Mean

seaborn

• 9.1 Hermite Expansion for Normally Distributed Parameters
• 9.2.3 Importing libraries
• 10.3.3 Import libraries

shutil

• 1.1.3 Installing Packages in Colab
• 12.1 Predictions under epistemic uncertainty with p-boxes

similaritymeasures

• 12.1 Predictions under epistemic uncertainty with p-boxes

sobol_seq

• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling

sympy

• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling

sys

• 1.1.3 Installing Packages in Colab
• 12.1 Predictions under epistemic uncertainty with p-boxes

tabulate

• 6.1.3.5 Compare sensitivities to parameters resulted from finite differences and the adjoint methodology: $\rho$, $\omega$,$\kappa_l$,$\kappa_h$,$q$ respectively
• 7.2.2.1 Set up diffusion reaction equation

tensorflow

• 10.1.2 Import Libraries

time

• 6.4.3.3 Solver comparisons

unyt

• 10.1.2 Import Libraries

urllib

• 1.1.5.1 Download the data into Colab
• 3.2 Principal Component Analysis
• 7.1 Latin Hypercube and Quasi-Monte Carlo Sampling
• 7.2 Latin Hypercube Sampling
• 8.1.3 First-Order Second-Moment (FOSM) Exmaple-Exmaple)
• 8.3 Advanced First-Order Second-Moment Methods
• 9.2 Uniform Random Variables: Legendre Polynomials

warnings

• 6.4.3.3 Solver comparisons