Nested Maximum Entropy Designs for Computer Experiments

Abstract

Presently, computer experiments with multiple levels of accuracy are widely applied in science and engineering. This paper introduces a class of nested maximum entropy designs for such computer experiments. A multi-layer DETMAX algorithm is proposed to construct nested maximum entropy designs. Based on nested maximum entropy designs, we also propose an integer-programming procedure to specify the sample sizes in multi-fidelity computer experiments. Simulated annealing techniques are used to tackle complex optimization problems in the proposed methods. Illustrative examples show that the proposed nested entropy designs can yield better prediction results than nested Latin hypercube designs in the literature and that the proposed sample-size determination method is effective.