Perspectives on Automatic Differentiation: Past, Present, and Future?

Automatic (or algorithmic) differentiation (AD) is discussed from the standpoint of transformation of algorithms for evaluation of functions into algorithms for evaluation of their derivatives. Such dinite numerical algorithms are commonly formulated as computer programs or subroutines, hence the use of the term “automatic.” Transformations to evaluate derivatives are thus based on the wellknown formulas for derivatives of arithmetic operations and various differentiable intrinsic functions which constitute the basic steps of the algorithm. The chain rule of elementary calculus then guarantees the validity of the process. The chain rule can be applied in various ways to obtain what are called the “forward” and “reverse” modes of automatic differentiation. These modes are described in the context of the early stages of the development of AD, and a brief comparison is given. Following this brief survey, a view of present tasks and future prospects focuses on the need for further education, communication of results, and expansion of areas of application of AD. In addition, some final remarks are made concerning extension of the method of algorithm transformation to problems other than derivative evaluation.