Uncertainty Quantification in Inverse Problems with CUQIpy

Welcome to the book on “Uncertainty Quantification in Inverse Problems with CUQIpy”. This book contains training material on how to use the CUQIpy library for uncertainty quantification in inverse problems. It also covers some of the theoretical background behind the methods implemented in CUQIpy.

⚠️ Disclaimer: The code in this book runs without a fixed random seed, so results will vary with each re-compilation and user run. While conclusions should remain consistent, specific values may differ due to the probabilistic nature of Bayesian sampling, which is fundamental when working with uncertainty quantification.

Table of contents¶

• Uncertainty Quantification in Inverse Problems with CUQIpy
• Chapter 1: Introduction to CUQIpy
  • Overview of CUQIpy
  • Running the mini-book code examples
  • Probably the simplest BIP in the world (the short story)
  • Probably the simplest BIP in the world (the long story)
• Chapter 2: Problem examples
  • Two forward models
  • Two target distributions
• Chapter 3: Basics of CUQIpy for solving BIPs
  • Introduction to distributions and basic sampling in CUQIpy
  • Forward models, data generation and forward UQ
  • Bayesian Inverse Problems
• Chapter 4: Advanced use cases of CUQIpy
  • Gibbs sampling
  • X-ray CT using CUQIpy and CUQIpy-CIL plugin
  • Solving PDE-based BIP using core CUQIpy
  • PDE-based BIP using CUQIpy and CUQIpy-FEniCS plugin
  • Hamiltonian Monte Carlo with CUQIpy-PyTorch
• Chapter 5: More on CUQIpy technical details
  • Geometry Objects: Representation, Parametrization, and Mapping
• Chapter 6: More theory on priors
  • Markov random fields in CUQIpy
  • Computing the entropy of a distribution, numerically
• Chapter 7: More theory on sampling
  • Sampling with CUQIpy: five little stories
• Chapter 8: More resources

Authors¶

• Amal Mohammed A Alghamdi

• Nicolai André Brogaard Riis

• Jakob Sauer Jørgensen

• Chao Zhang

• Felipe Uribe