An inverse problem in science is the process of calculating from a set of observation data the causal factors (model parameters) that have produced them. It is called an inverse problem because it starts with the results and then calculates the causes. This is the inverse of a forward problem, which starts with the causes and then calculates the results. Inverse problems arise in many areas of science including mathematics, engineering, medicine, physics, and geophysics. In the last twenty years the active research carried out in the field of inverse problems has made it become an active area of modern applied mathematics and one of the most interdisciplinary fields of science.
Inverse problems are typically ill posed, as opposed to the well-posed problems more typical in the corresponding forward problems. Of the three conditions for a well-posed problem suggested by J. Hadamard (existence, uniqueness, stability of the solution), the condition of stability is most often violated. While inverse problems are often formulated in infinite dimensional spaces, in practice they have to be recast in discrete form when we numerically solve them. For ill-conditioned inverse problems, regularization should be used by introducing mild assumptions on the solution or other a priori information.
This program consists of one workshop, one tutorial, and one conference on the latest developments in inverse problems, which intends to bring together scientific researchers working in the field of theories and numerics of inverse problems to discuss recent developments and new challenges in this fascinating field.