Title of the thesis: “On the variational approach to mollification in the theory of ill-posed problems and applications”
Walter Cedric Simo Tao Lee, AIMS-Cameroon alumnus of the 2015/2016 batch, has successfully earned a Ph.D. in Applied Mathematics at the Université de Toulouse III – Paul Sabatier in France.
Realized under the supervision and co-supervision of Pierre MARECHAL and Anne VANHEMS respectively, the main aim of his work was to study methods to solve ill-posed linear inverse problems.
During his defense on December 10, 2020, Simo Tao Lee pointed out that Inverse problems are a fast-growing area in Applied Mathematics which has gained great attention in the last decades due to its ubiquity in several fields of sciences and technology; yet, they most often result in unstable mathematical equations.
He further mentioned that inverse problems most often result in unstable mathematical equations or solutions that do not continuously depend on the data and as a matter of fact, very little perturbations on the data leads to arbitrary large errors on the solutions.
To solve this problem, he presented several regularization techniques with a focus on the class of techniques that try to recover smooth versions of the unknown solutions via the study and application of the variational formulation of mollification.
Simo Tao Lee was able to show that the variational approach can be extended to the regularization of ill-posed problems involving non-compact operators where he successfully applied the method to a statistics problem known as the nonparametric instrumental regression.
A relevance of his study is that it highlights a poorly known regularization method which yet has great potential and is able to provide comparatively better approximate solutions compared to well-known classical regularization techniques. Besides, his work designs a new regularization method which is promising in the regularization of exponentially ill-posed problems, especially for inverse heat conduction problems.
These great results have been submitted for peer review to highly qualified scientific journals.
Dr. Simo Tao Lee acknowledged the CIMI Ph.D. scholarship, the Institut de Mathématiques de Toulouse (IMT), and EDMITT for their contributions to the success of his work.
While envisaging a future academic position in Teaching and Research, he currently holds a temporary teaching and research associate position at the INSA (Institut Supérieure de Sciences Appliquées) and the Université de Toulouse in Toulouse, France.