Optimization and Reduced Order Models for Digital Twins

Abstract: This talk begins by discussing the role of partial differential equation-constrained optimization in the development of digital twins.  In particular, applications to identify weaknesses in structures and aneurysms are considered.  Next, we analyze a data-driven optimization problem constrained by Darcy’s law to design a permeability that achieves uniform flow properties despite having nonuniform geometries.  We establish the well-posedness of the problem, as well as differentiability, which enables the use of rapidly converging, derivative-based optimization methods.

The second part of the talk will focus on an inexact adaptive and provably convergent semi-smooth Newton method for general-purpose optimization problems.  In particular, dynamic optimization problems, which are known to be highly expensive are the focus.  A memory-efficient reduced-order modeling approach based on randomized matrix sketching is introduced.

Speaker’s Bio: Harbir Antil is the Director of the Center for Mathematics and Artificial Intelligence and a Professor of Mathematics at George Mason University.  His areas of interest include optimization, calculus of variations, partial differential equations, numerical analysis, and scientific machine learning.   He received his Ph.D. from the University of Houston and spent time as a postdoc at Rice University and the University of Maryland, College Park.    

His research is supported by the National Science Foundation, Air Force Office of Scientific Research, Defense Advanced Research Projects Agency, Defense Threat Reduction Agency, Department of Energy, and the Department of Navy.  He is a member of the Intelligence Science and Technology Experts Group at the National Academy of Sciences.  He is also the President of SIAM Washington DC - Baltimore Section. He is on the editorial board of journals such as SIAM Reviews, SIAM J. of Sci. Comp., Journal of Optimization Theory and Applications, and he is the Editor-in-Chief of Advances in Continuous and Discrete Models.