Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization

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 multifidelity polynomial chaos expansion. For optimization, our emphasis is on multifidelity 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. Keywords multi-fidelity modeling uncertainty quantification Bayesian optimization 1 Introduction When studying a physical system, analysts often have access to multiple computational models. These models are typically classified as either high-fidelity or low-fidelity, depending on their predictive accuracy. High-fidelity models (HFMs) offer precise predictions of the system's behavior, meeting specific accuracy metrics, but they are computationally demanding.