Finding Efficient Trade-offs in Multi-Fidelity Response Surface Modeling

TL;DR

This paper investigates how to efficiently allocate computational resources between different fidelity levels in surrogate modeling for optimization, proposing a heuristic to improve multi-fidelity optimization setup.

Contribution

It introduces a heuristic method based on subsampling from initial experiments to optimize budget division in multi-fidelity surrogate models.

Findings

Heuristic improves budget allocation in multi-fidelity models.

Trade-offs between high- and low-fidelity evaluations are characterized.

Method is adaptable to various multi-fidelity modeling approaches.

Abstract

In the context of optimization approaches to engineering applications, time-consuming simulations are often utilized which can be configured to deliver solutions for various levels of accuracy, commonly referred to as different fidelity levels. It is common practice to train hierarchical surrogate models on the objective functions in order to speed-up the optimization process. These operate under the assumption that there is a correlation between the high- and low-fidelity versions of the problem that can be exploited to cheaply gain information. In the practical scenario where the computational budget has to be allocated between multiple fidelities, limited guidelines are available to help make that division. In this paper we evaluate a range of different choices for a two-fidelity setup that provide helpful intuitions about the trade-off between evaluating in high- or low-fidelity. We present a heuristic method based on subsampling from an initial Design of Experiments (DoE) to find a suitable division of the computational budget between the fidelity levels. This enables the setup of multi-fidelity optimizations which utilize the available computational budget efficiently, independent of the multi-fidelity model used.