Dr. Anthony Gruber - Active Manifolds: A Geometric Approach to Dimension Reduction for Sensitivity Analysis

Oak Ridge, TN

August 1, 2018

Dr. Anthony Gruber
Dr. Anthony Gruber

Wednesday, August 1, 2018, 3:00pm-4:00pm
Location:  4100, Room J302

Abstract:  We consider an approach to analyzing functions with a problematically high number of input parameters, specifically to address limitations present in the Active Subspaces (AS) method of Constantine. Our method, Active Manifolds (AM), relies on exploiting the geometry of the function to provide a useful low-dimensional analogue. We discuss the mathematical justification for AM, and some results from the application of our algorithm. We have shown that AM reduces approximation error by an order of magnitude compared to AS on initial test functions. Additionally, we compare AS to AM in analyzing parameter sensitivity of two different real-world functional models: magnetohydrodynamic power generation, and the reproduction rate of Ebola. Our results give more detailed information than AS about what parameters have the most effect on these quantities, and where sensitivity changes within the parameter space.

Biography:  Anthony is a PhD candidate at Texas Tech University in Lubbock studying mathematics.  More specifically, he is using techniques from variational calculus and differential geometry to study critical points of the generalized Willmore energy functional, known as Willmore surfaces.  His research interests include geometry, dynamical systems, analytic and algebraic topology, and how to apply knowledge from these fields to data scientific problems. Anthony is completing an NSF Math Science Graduate Internship at ORNL.