Applied Math Colloquium: Dr. Harbir Antil
George Mason University
Title: Fractional Operators: Analysis, Control, and Applications in Deep Learning
Abstract: Fractional calculus and its application to anomalous diffusion has
recently received a tremendous amount of attention. In
complex/heterogeneous material mediums, the long-range correlations or
hereditary material properties are presumed to be the cause of such
anomalous behavior. Owing to the revival of fractional calculus, these
effects are now conveniently modeled by fractional-order differential
operators and the governing equations are reformulated accordingly.
Similarly, the potential of fractional operators has been harnessed in
various scientific domains like geophysical electromagnetics, imaging
science, deep learning, etc.
In this talk, fractional operators will be introduced and both linear and
nonlinear, fractional-order differential equations will be discussed. New
notions of optimal control and optimization under uncertainty will be
presented. A special emphasis will be given on enriching Deep Neural
Networks using fractional operators. Several applications from geophysics,
imaging science, and deep learning will be presented.