This work focuses on the design of experiments of multi-fidelity computer experiments. We consider the autoregressive Gaussian process model proposed by Kennedy and O'Hagan (2000) and the optimal nested design that maximizes the prediction accuracy subject to a budget constraint. An approximate solution is identified through the idea of multi-level approximation and recent error bounds of Gaussian process regression. The proposed (approximately) optimal designs admit a simple analytical form. We prove that, to achieve the same prediction accuracy, the proposed optimal multi-fidelity design requires much lower computational cost than any single-fidelity design in the asymptotic sense. Numerical studies confirm this theoretical assertion.

翻译：本文聚焦于多保真度计算机实验的设计优化问题。我们采用Kennedy与O'Hagan（2000）提出的自回归高斯过程模型，研究在预算约束下最大化预测精度的最优嵌套设计。通过多层逼近思想与高斯过程回归的最新误差界理论，我们确定了近似最优解。所提出的（近似）最优设计具有简洁的解析形式。我们证明：在渐近意义下，为达到同等预测精度，所提出的最优多保真度设计比任何单保真度设计所需的计算成本显著更低。数值实验验证了这一理论结论。