Adaptive Sampling with Varying Sampling Cost for Design Space Exploration

Abstract

Surrogate models have been developed to infer the response of engineering systems based on scattered tests/simulations. An effective sampling scheme enables surrogates to have a desirable accuracy while balancing the sampling budget. Most sampling methods implicitly assume that all samples have the same cost to produce. In some applications, however, the cost to obtain samples may substantially vary in the input variable space because some configurations are more expensive to test or simulate than others. As an initial effort to incorporate with varying sampling cost, this paper explores an adaptive sampling strategy in which the sampling cost varies (AS-C). The proposed scheme adopts the Gaussian process for design space exploration, which is based on space filling. Two surrogates are constructed: one for the target function (quantity of interest) and the other for the sampling cost. Then a value metric is defined to estimate the uncertainty reduction per cost. A new sample is added per iteration at the point with the maximum value metric. The proposed AS-C is evaluated using 1D and 2D analytical functions. Four different cost functions and 100 sets of initial samples are produced for evaluation. For a fixed sampling budget, the AS-C adds more samples in an inexpensive region and thus provides a better accuracy than the standard adaptive sampling strategy (AS). As a case study, the AS-C is applied to the design space exploration of behavioral emulation (BE). BE is a coarse-grained simulation method, which predicts the runtime of a given simulation using high-performance computing. Because the cost/runtime of BE varies by the orders of magnitude, the AS-C adds many more samples in the inexpensive region and greatly outperforms the AS for a given sampling budget.