Second Argonne theory institute on differentiation of computational approximations of functions.

Abstract

A Theory Institute on ''Differentiation of Computational Approximations to Functions'' was held at Argonne National Laboratory on May 18--20, 1998. The institute was organized by Christian Bischof and Paul Hovland of the Mathematics and Computer Science Division at Argonne National Laboratory. The Theory Institute brought together 38 researchers from the US, Great Britain, France, and Germany. Mathematicians, computer scientists, physicists, and engineers from diverse disciplines discussed advances in automatic differentiation (AD) theory and software and described benefits from applying AD methods in application areas. These areas include fluid mechanics, structural engineering, optimization, meteorology, and computational mathematics for the solution of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). This meeting was the fourth workshop dedicated to automatic differentiation. Earlier meetings were the 1991 SIAM conference in Breckenridge, Colorado; the first Argonne Theory Institute on computational differentiation in 1993; and the 1996 SIAM conference in Santa Fe, New Mexico. AD methods can be used whenever gradient information or higher-order derivative information must be computed. The problem is defined by a computer program (without gradient information) that is able to compute numerical values of some output variables for a given set of input variables. As a result of applying AD methods to this computer program, a new computer program is generated automatically to compute the derivatives of the output variables with respect to the input variables. This at first glance, astonishing fact can be easily understood by viewing the program from a compiler angle. A complicated computational sequence is split into a sequence of simple operations. Then, to compute the gradients, the chain rule of differentiation is applied successively to this sequence completely automatically. The resultant gradients are accurate up to roundoff errors (which are always present in numerical evaluations).