Applied Math Colloquium: Dr. Harbir Antil

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.