COURSE PURPOSES

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 algorithms for the solution of a wide variety of IPs arising in several engineering fields, this implies a growing need for users that do not have a very high degree of 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 exercises will 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 ill-posedness and non-linearity;
  • Applicative examples including exercises regarding specific engineering applications.

Teachers

Prof. MASSA Andrea
DICAM @ University of Trento, Italy
UESTC, China
Tsinghua University, China

Prof. OLIVERI Giacomo
DICAM @ University of Trento, Italy

Prof. ROCCA Paolo
DICAM @ University of Trento, Italy
Xidian University, China

Dr. ANSELMI Nicola
DICAM @ University of Trento, Italy

Dr. POLI Lorenzo
DICAM @ University of Trento, Italy

Dr. SALUCCI Marco
DICAM @ University of Trento, Italy

Course in Synthesis

Teachers
6
Hours
32
Days
5
ECTS Credits
4

Course Coordinators

Prof. MASSA Andrea
DICAM @ University of Trento, Italy
UESTC, China
Tsinghua University, China

Prof. ROCCA Paolo
DICAM @ University of Trento, Italy
Xidian University, China

Contact Us

ELEDIA@UniTN – University of Trento
DICAM – Department of Civil, Environmental, and Mechanical Engineering
Via Mesiano 77, 38123 Trento – Italy

Phone: +39 0461 285227

Mail: summer-schools@eledia.org

Sponsors