Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization

TL;DR

This paper reviews machine learning-based multi-fidelity methods for uncertainty quantification and optimization, emphasizing graph neural networks and Bayesian optimization, and discusses current advances, gaps, and future research directions.

Contribution

It provides a comprehensive overview of emerging multi-fidelity machine learning techniques, highlighting novel approaches like graph neural networks and unified optimization strategies.

Findings

Multi-fidelity graph neural networks enhance uncertainty quantification.

Multi-fidelity Bayesian optimization effectively balances cost and accuracy.

The paper identifies key gaps and future research opportunities in the field.

Abstract

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.