Finding efficient trade-offs in multi-fidelity response surface modelling

Abstract

In optimization approaches to engineering applications, time-consuming simulations are often utilized that can be configured to deliver solutions for various fidelity (accuracy) levels. It is common practice to train hierarchical surrogate models on objective functions in order to speed up the optimization process. These operate under the assumption that there is a correlation between the different fidelities that can be exploited to gain information cheaply. However, limited guidelines are available to help divide the available computational budget between multiple fidelities in practice. This article evaluates a range of different choices for a two-fidelity setup that provide helpful intuitions about this trade-off. An heuristic method is presented based on subsampling from an initial Design of Experiments to find a suitable division of the computational budget between the fidelity levels. This enables the setting up of multi-fidelity optimizations that utilize the available computational budget efficiently, independently of the multi-fidelity model used.