Inverse problems (IPs) have been traditionally considered as mathematically challenging because they are intrinsically ill-posed.There are many practical IPs in a variety of engineering disciplines requiring suitable mathematical tools for their robust/stable solution, by recovering the well-posedness typical of forward/direct problems through suitable regularization and information-acquisition/exploitation techniques. Since industry requires fast and simple algorithmsfor the solution of awide variety of IPs arising inseveral engineering fields, this implies a growing need for usersthat do not have a very high degreeof mathematical education.
The course will review fundamentals and main issues of IPs, then focusing on classical/state-of-the-art and recently introduced inverse solution procedures and algorithms. Applicative examples including exerciseswill corroborate the theoretical concepts.
Course Topics
- Introduction and basics: motivations (methodological, applicative), synthesis and design problems in engineering as IPs;
- Formulation of IPs and numerical techniques for dealing with their resolution;
- Ill-posedness and non-linearity: on the role of information in IPs;
- Ill-posedness and the need for regularization;
- Non-linearity: physical meaning, degree of non linearity, the role of a-priori/available information;
- Solution of IPs as minimization/maximization of a cost-function/functional;
- Multi-resolution and information-acquisition strategies as an effective recipe to counteract illposedness and non-linearity;
- Applicative examples including exercises regarding specific engineering applications.
Date
From: 28 August 2023
To: 1 September 2023
Location
Onsite (Trento) and Online