# Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization

arXiv: https://arxiv.org/abs/2410.23482 · HTML: https://mlsanity.com/paper/2410.23482/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 10 of 10)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [Epsilon-Greedy Thompson Sampling to Bayesian Optimization](https://mlsanity.com/paper/2403.00540/) (2024)
- [Optimizing Posterior Samples for Bayesian Optimization via Rootfinding](https://mlsanity.com/paper/2410.22322/) (2024)
- [Automated design of nonreciprocal thermal emitters via Bayesian optimization](https://mlsanity.com/paper/2409.09192/) (2024)
- [Gaussian Process Thompson Sampling via Rootfinding](https://mlsanity.com/paper/2410.08071/) (2024)

## Built on by (most cited first, 3 of 3)

- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)
- [Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models](https://mlsanity.com/paper/2510.06439/) (2025)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)

## Abstract (arXiv)

In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate predictions but require significant computational resources, and low-fidelity models, which are computationally efficient but less accurate. Multi-fidelity methods integrate high- and low-fidelity models to balance computational cost and predictive accuracy. This perspective paper provides an in-depth overview of the emerging field of machine learning-based multi-fidelity methods, with a particular emphasis on uncertainty quantification and optimization. For uncertainty quantification, a particular focus is on multi-fidelity graph neural networks, compared with multi-fidelity polynomial chaos expansion. For optimization, our emphasis is on multi-fidelity Bayesian optimization, offering a unified perspective on multi-fidelity priors and proposing an application strategy when the objective function is an integral or a weighted sum. We highlight the current state of the art, identify critical gaps in the literature, and outline key research opportunities in this evolving field.