Date: 18 February 2013
Time: 10.00 am - 12 noon
Venue: Charles Babbage Room (Fusionopolis, level 17, Connexis South)
Speaker: Prof. Dr. Uwe Naumann, Aachen University
About the Seminar:
“How sensitive are the values of the outputs of my computer program with respect to changes in the values of the inputs? How sensitive are these first-order sensitivities with respect to changes in the values of the inputs? How sensitive are the second-order sensitivities with respect to changes in the values of the inputs? ”
Computational scientists, engineers, and economists as well as quantitative analysts tend to ask these questions on a regular basis. They write computer programs in order to simulate diverse real-world phenomena. The underlying mathematical models often depend on a possibly large number of (typically unknown or uncertain) parameters. Values for the corresponding inputs of the numerical simulation programs can, for example, be the result of (typically error-prone) observations and measurements. If very small perturbations in these uncertain values yield large changes in the values of the outputs, then the feasibility of the entire simulation becomes questionable. Nobody should make decisions based on such highly uncertain data.
Quantitative information about the extent of this uncertainty is crucial. First- and higher-order sensitivities of outputs of numerical simulation programs with respect to their inputs (also first and higher derivatives) form the basis for various approximations of uncertainty. They are also crucial ingredients of a large number of numerical algorithms ranging from the solution of (systems of) nonlinear equations to optimization under constraints given as (systems of) partial differential equations. This talk describes a set of techniques for modifying the semantics of numerical simulation programs such that the desired first and higher derivatives can be computed accurately and efficiently. Computer programs implement algorithms. Consequently, the subject is known as Algorithmic (also Automatic) Differentiation (AD).
No of Participants: 21