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Response surface models (RSMs) have found widespread use to reduce the overall computational cost of turbomachinery blading design optimization. Recent developments have seen the successful use of gradient information alongside sampled response values in building accurate response surfaces. This paper describes the use of gradients to enhance the performance of the RSM provided by a multi-layer perceptron. Gradient information is included in the perceptron by modifying the error function such that the perceptron is trained to fit the gradients as well as the response values. As a consequence, the back-propagation scheme that assists the training is also changed. The paper formulates the gradient-enhanced multi-layer perceptron using algebraic notation, with an emphasis on the ease of use and efficiency of computer code implementation. To illustrate the benefit of using gradient information, the enhanced neural network model is used in a multi-objective transonic fan blade optimization exercise of engineering relevance. Copyright © 2008 John Wiley & Sons, Ltd.

Original publication




Journal article


International Journal for Numerical Methods in Fluids

Publication Date





591 - 605