Mathematical Physics and Harmonic Analysis Seminar

Date: September 17, 2021

Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Daniele Mortari, TAMU

Title: The Theory of Functional Connections

Abstract: This lecture summarizes what the Theory of Functional Connections (TFC) is and presents the most important applications to date. The TFC performs linear functional interpolation. This allows to derive analytical expressions with embedded constraints, expressions describing all possible functions satisfying a set of constraints. These expressions are derived for a wide class of constraints, including points and derivatives constraints, relative constraints, linear combination of constraints, component constraints, and integral constraints. An immediate impact of TFC is on constrained optimization problems as the whole search space is reduced to just the space of solutions fully satisfying the constraints. This way a large set of constrained optimization problems can be transformed in unconstrained problems, allowing more simple, fast, reliable, and accurate methods to solve them. For instance, TFC allows to obtain fast and machine-error accurate solutions of linear and nonlinear ordinary differential equations. TFC has been extended to n-dimensions (Multivariate TFC). This allows to derive numerical methods to solve partial and stochastic differential equations. This lecture also provides some other TFC applications as, for instance, to homotopy continuation, calculus of variation, nonlinear programming, and optimal control (energy-efficient optimal landing on large bodies). Location: Meeting id: 980 8118 3032 Passcode: mpf21 Join Zoom Meeting https://tamu.zoom.us/j/98081183032?pwd=WitENWJqWjRyWVQvU3RQZDd4Mm9sUT09