Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization - Perspective Paper

Aug 5, 2026

Multi-fidelity machine learning addresses system analysis and design optimization when multiple computational models represent the same physical system. The work contrasts high-fidelity models, which are accurate but computationally expensive, with low-fidelity models, which are efficient but less accurate. It surveys emerging ML-based multi-fidelity methods, emphasizing uncertainty quantification via multi-fidelity graph neural networks and multi-fidelity polynomial chaos expansion. For optimization, it focuses on multi-fidelity Bayesian optimization under a unified multi-fidelity prior, especially for objectives expressed as integrals or weighted sums.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Introduction

Multi-fidelity models: high vs low fidelity

Motivation for multi-fidelity balance

Multi-fidelity surrogates and uncertainty quantification

Problem setup and uncertainty propagation

Monte Carlo estimation

Multi-fidelity optimization

Multi-fidelity Bayesian optimization

Conclusion

arXiv :2410 .23482v1 [ cs .LG] 30 Oct 2024 MULTI-FIDELITY MACHINE LEARNING FOR UNCERTAINTY QUANTIFICATION AND OPTIMIZATION Ruda Zhang∗ University of Houston [rudaz@uh. edu](rudaz@uh. edu) Negin Alemazkoor University of Virginia [na7fp@virginia. edu](na7fp@virginia. edu) ABSTRACT In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classi􀀂ed as high-􀀂delity models, which provide highly accurate predictions but require signi􀀂cant computational resources, and low-􀀂delity models, which are computationally ef􀀂cient but less accurate. Multi-􀀂delity methods integrate high-and low-􀀂delity models to balance computational cost and predictive accuracy. This perspective paper provides an in-depth overview of the emerging 􀀂eld of machine learning-based multi-􀀂delity methods, with a particular emphasis on uncertainty quanti􀀂cation and optimization. For uncertainty quanti􀀂cation, a particular focus is on multi-􀀂delity graph neural networks, compared with multi-􀀂delity polynomial chaos expansion. For optimization, our emphasis is on multi-􀀂delity Bayesian optimization, offering a uni􀀂ed perspective on multi-􀀂delity priorsand proposing an application strategy when the objective function is an integral ora weighted sum. We highlight the current state of the art, identify critical gaps in the literature, and outline key research opportunities in this evolving 􀀂eld.1 Keywords multi-􀀂delity modeling · uncertainty quanti􀀂cation · Bayesian optimization 1 Introduction When studying a physical system, analysts often have access to multiple computational models. These models are typically classi􀀂ed as either high-􀀂delity or low-􀀂delity, depending on their predictive accuracy. High-􀀂delity models (HFMs) offer precise predictions of the system’s behavior, meeting speci􀀂c accuracy metrics, but they are computationally demanding. This computational demand is driven by the need for 􀀂ne mesh resolutions and small time steps to ensure both numerical stability and accuracy. On the other hand, low-􀀂delity models (LFMs) tradeoff some accuracy for greater computational ef􀀂ciency. These models are often derived through 􀀃 Corresponding author. 1This is the accepted version of the following article: Zhang, R. & Alemazkoor, N. Multi-􀀂delity Machine Learning for Uncertainty Quanti􀀂cation and Optimization. Journal of Machine Learning for Modeling and Computing, Vol. 5, No. 4, pp. 77–94, (2024), [https://doi.org/10.1615/JMachLearnModelComput.2024055786](https://doi.org/10.1615/JMachLearnModelComput.2024055786. This version is made)[. This version is made](https://doi.org/10.1615/JMachLearnModelComput.2024055786. This version is made) available under the terms of the Green Open Access Agreement. Multi-􀀂delity ML for UQ & Optimization techniques like mesh coarsening, simpli􀀂ed physics, or reduced-order modeling, resulting in less computationally expensive simulations. While relying exclusively on LFMs can reduce computational time, it risks producing myopic results due to their inherent lower accuracy. Conversely, replying solely on HFMs for analysis, especially in high dimensional spaces, can be computationally prohibitive. This limitation may hinder timely decision-making, which is critical for optimal system operation and management. Multi-􀀂delity (MF) methods aim to strike a balance between LFMs and HFMs, combining computational ef􀀂ciency with predictive accuracy to enhance decision-making in complex systems. The literature on MF methods is extensive, encompassing numerous strategies for integrating LFMs and HFMs across diverse scienti􀀂c and engineering applications. Peherstorfer et al. [39] offers a comprehensive survey of MF methods in uncertainty quanti􀀂cation (UQ), inference, and optimization. Since then, there has been a signi􀀂cant shift in the literature towards integrating machine learning (ML) with MF methods. In this w

FAQs

What problem do multi-fidelity methods solve in system optimization?

They balance computational cost and predictive accuracy by integrating low-fidelity models with high-fidelity models, enabling better decisions than using only one fidelity source.

How does the document approach uncertainty quantification (UQ)?

It focuses on uncertainty propagation from random inputs to outputs and highlights multi-fidelity graph neural networks as well as multi-fidelity polynomial chaos expansion methods.

How is optimization performed under the multi-fidelity framework?

The document emphasizes multi-fidelity Bayesian optimization and presents a unified perspective on multi-fidelity priors, including an application strategy when the objective is an integral or a weighted sum.

Aug 5, 2026

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