Inverse Theory II: Applications

Abstract

This second part of the course on Inverse Theory provides an introduction to the numerical solution of (non-)linear inverse problems including uncertainty quantification. Specific examples are drawn from different areas of geophysics and image processing. Students solve various model problems using Jupyter notebooks (in Julia), and familiarize themselves with relevant open-source libraries.

Objective

This course provides numerical tools and recipes to solve (non)-linear inverse problems arising in nearly all fields of science and engineering. After successful completion of the class, the students will have a thorough understanding of suitable solution algorithms, common challenges and possible mitigations to infer parameters that govern large-scale physical systems from sparse data measurements. Prerequisites for this course are (i) 651-4096-00L Inverse Theory: Basics, (ii) basic programming skills.

Content

The class discusses several important concepts to solve (non)-linear inverse problems and demonstrates how to apply them to real-world data applications. All sessions are split into a lecture part in the first half, followed by tutorials using Jupyter notebooks in the second. The range of covered topics include: 1. Regularization filters and image deblurring 2. Link between regularization, deterministic and probabilistic approaches for the solution of linear inverse problems. 3. Optimization for nonlinear inverse problems (line-search methods). 4. Adjoint methods and time reversal, computing gradients for large-scale inverse problems. 5. Full-waveform inversion. 6. Machine learning basics (artificial neural networks) and links to inverse problems. 6. Uncertainty quantification and (Hamiltonian) Monte Carlo method

Resources