Application of Higher Order Derivatives to Parameterization

Abstract

Research on automatic differentiation is mainly motivated by gradient computation and optimization. However, in the optimal design area, it is quite difficult to use optimization tools. Some constraints (e.g., aesthetics constraints, manufacturing constraints) are quite difficult to describe by mathematical expressions. In practice, the optimal design process is a dialog between the designer and the analysis software (structural analysis, electromagnetism, computational fluid dynamics, etc.). One analysis may take a while. Hence, parameterization tools such as design of experiments (D.O.E.) and neural networks are used. The aim of those tools is to build surrogate models. We present a parameterization method based on higher order derivatives computation obtained by automatic differentiation.