Recent Advances in Emergent and Probabilistic Numerical Algorithms

Vanja Dukic. Dept Applied Mathematics, University of Colorado

There have been exciting developments at the intersection between Statistics and Applied Mathematics over the years. One of these areas is "probabilistic numerics", which considers traditional numerical analysis algorithms in a probabilistic framework. The goal is the study of algorithms which simultaneously solve for the traditional deterministic answer as well as provide a rigorous quantification of the uncertainty associated with the variations in inputs and/or data. While this methodology is related to conventional uncertainty quantification, there is a distinction in that it is the algorithm itself which is the focus of study. In this talk, I will provide a brief overview of this nascent field as well as some of the recent developments including probabilistic numerical algorithms to solve differential equations.

Joint work with: David Bortz, Andrew Christlieb, and Anna Gilbert