Modelling with gradient information

Abstract

Response surface models (RSMs) can be used to model expensive simulations or real measurements [1]. An RSM is constructed by simulating solutions at systematic points in a design space and fitting a model to them. The RSM is then employed in subsequent calculations (for instance in optimization) effectively replacing the original expensive simulator, which leads to considerable savings in time and money. A novel technique is presented here which uses the gradient of a function as well as the function itself to construct the RSM. Such an approach is possible because, for many types of simulations, gradient information is simple and cheap to obtain. The design of an electromagnetic speaker assembly is used to illustrate the new approach. The finite element method (FEM), on which the simulation is based, can provide gradient information at little extra cost and hence the benefits of using gradient information are considerable, being especially marked in higher-dimensional spaces.