Review of multi-fidelity models

TL;DR

This review surveys surrogate-based multi-fidelity models (MFMs), outlining how high- and low-fidelity models are integrated to balance accuracy and computational cost across optimization and uncertainty quantification tasks. It clarifies the architectural distinction between multi-fidelity surrogate models (MFSMs) and multi-fidelity hierarchical models (MFHMs), detailing four correction paradigms (additive, multiplicative, comprehensive, space mapping) and the split between deterministic and non-deterministic methods. The paper emphasizes reproducibility, benchmarking, open-source dissemination, and educational toy problems, while summarizing current trends such as physics-informed learning, neural operators, and transfer learning. It concludes with guidance on reporting cost-accuracy trade-offs, highlights interpretability challenges, and outlines future research directions for more integrated, scalable, and transparent MFMs in diverse engineering domains.

Abstract

Multi-fidelity models provide a framework for integrating computational models of varying complexity, allowing for accurate predictions while optimizing computational resources. These models are especially beneficial when acquiring high-accuracy data is costly or computationally intensive. This review offers a comprehensive analysis of multi-fidelity models, focusing on their applications in scientific and engineering fields, particularly in optimization and uncertainty quantification. It classifies publications on multi-fidelity modeling according to several criteria, including application area, surrogate model selection, types of fidelity, combination methods and year of publication. The study investigates techniques for combining different fidelity levels, with an emphasis on multi-fidelity surrogate models. This work discusses reproducibility, open-sourcing methodologies and benchmarking procedures to promote transparency. The manuscript also includes educational toy problems to enhance understanding. Additionally, this paper outlines best practices for presenting multi-fidelity-related savings in a standardized, succinct and yet thorough manner. The review concludes by examining current trends in multi-fidelity modeling, including emerging techniques, recent advancements, and promising research directions.

Figures (20)

• Figure 1: Connection between high-fidelity and low-fidelity models is commonly attributed to one or more of the following factors: dimensionality reduction, grid coarsening, linearization, partial convergence, reduced geometry complexity, and simplified physics.
• Figure 2: Within the frame of multi-fidelity modeling, surrogate models are commonly used to integrate information from different fidelities. When constructing a surrogate model that combines fidelities explicitly, such as co-Kriging, the resulting approach is referred to as a multi-fidelity surrogate model. In contrast, multi-fidelity hierarchical models combine fidelities without requiring to build an explicit multi-fidelity surrogate model architecture. Methods such as importance sampling fall under the multi-fidelity hierarchical category.
• Figure 3: Proportions of different attributes found in the reviewed multi-fidelity literature fernandez2019issues.
• Figure 4: Main differences between fidelities found in the literature.
• Figure 5: Prevalence of multi-fidelity surrogate models over multi-fidelity hierarchical models in surveyed literature up to 2016. Recent trends suggest a growing shift towards hierarchical models due to advancements in computing and algorithms.