Prof. Tan-Bui Thanh, Ph.D. – On Unifying Randomized Methods for Inverse Problems

Leader of Pho-Ices Group & 
Department of Aerospace Engineering and Engineering Mechanics
The University of Texas in Austin

Abstract:

Two hundreds years ago James Clerk Maxwell stated: „…Therefore the true logic for this world is the calculus of Probabilities…“ The question is not if we agree with this statement—as there will not be a unique subjective answer— but how this statement, 200 years later, could precisely reflect the language of people, the language of sciences, and the language of computation.  We adapt Frank Lad’s arguments on why probability is the language of people and the language of science. We then show that we have adapted the language of probability via randomization, to our advantages, to simplify and to speed up scientific computations to advance the progress of sciences. In particular, we shall present a unified randomized framework that not only recovers many existing randomized inverse methods but also discovers new ones. Constructive derivations, rigorous analyses, and applications will be presented.