Past Event: Oden Institute Seminar

The Theory of Functional Connections: Current Status

Daniele Mortari, Professor, Texas A&M

Abstract

This lecture summarizes what the Theory of Functional Connections (TFC) is and presents some of its applications in optimization problems. The TFC performs analytical functional interpolation. The theory allows to derive functionals representing all possible functions satisfying a set of n constraints. These constraints can be points, derivatives, integrals, limits, components, and any linear combination of them. These functionals reduce the whole functions space (where to search the solution) to just the subspace that fully satisfy the constraints. This way a large set of constrained optimization problems are transformed into unconstrained problems, allowing more simple, fast, robust, and accurate methods to solve them. For instance, TFC allows to obtain fast and machine-error accurate solutions of linear and nonlinear differential equations via least-squares. TFC has been extended to multivariate domains, to shear-type and mixed derivatives, and to fractional derivative/integral constraints. Baby steps on the extension to generic domains has been done via bijective domain mapping.

Biography

Daniele Mortari is Professor of Aerospace Engineering at Texas A&M University, working in the field of attitude and position estimation, satellite constellation design, sensor data processing, and various topic in linear algebra and numerical algorithms. He has taught at the School of Aerospace Engineering of the University of Rome, and at Electronic Engineering of the University of Perugia. He received his doctorate degree in Nuclear Engineering from the University of Rome. He has been widely recognized for his work, including receiving best papers Award from US conference and from journal Mathematics, three NASA Awards, the 2007 IEEE Judith A. Resnik Award, and the 2016 AAS Dirk Brouwer Award. He has published more than 120 journal articles, 250 conference papers, and delivered more than 110 invited seminars. He is a Member of the International Academy of Astronautics, he is IEEE, AAIA, and AAS Fellow, AIAA Associate Fellow, Honorary Member of IEEE-AESS Space System Technical Panel, and former IEEE Distinguish Speaker. He is the Editor-in-Chief of the Functional Interpolation section of the Journal Mathematics.