Fixed-budget optimal designs for multi-fidelity computer experiments

TL;DR

This paper develops a method for designing multi-fidelity computer experiments that optimally balance prediction accuracy and computational cost under budget constraints, using Gaussian process models.

Contribution

It introduces an approximately optimal nested design for multi-fidelity experiments with a simple analytical form, improving efficiency over single-fidelity designs.

Findings

Optimal multi-fidelity designs require significantly lower computational cost.

The proposed designs achieve comparable prediction accuracy to single-fidelity methods.

Numerical studies validate the theoretical efficiency gains.

Abstract

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.