Mini-Course: Computational methods in applied inverse problems - Class 01

Mini-Course: Uri Ascher (British Columbia, Canada)
Title: Computational methods in applied inverse problems

Abstract
Below is a brief description of my planned short course at IMPA, given as part of the Thematic Program on Parameter Identification in Mathematical Models. It consists of four lectures, at most 90 minutes each, planned for October 17, 19, 24 and 26, 2017.
In the past two decades there have been many developments in computational methods for applied inverse problems. These include PDE constrained optimization, sparsity-enhancing methods, level set methods, probabilistic methods, randomized algorithms, machine learning techniques (e.g., deep learning) and more. Optimization techniques play a prominent role, as do PDE discretization methods and fast solution techniques. I will attemp to shed some light on several of the challenges and solution techniques in these computational areas, using my own research to demonstrate and highlight issues. This document is meant to describe a tentative rather than final plan. The lectures will be adjusted according to audience level of interest and needs as well as the instructor’s limitations.

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