Bayesian Synthesis of Models and Data in Fluid Mechanics

Abstract

Computational fluid dynamics (CFD) relies on a hierarchy of models balancing physical fidelity and computational cost. While high-fidelity simulations such as direct numerical simulation (DNS) or large-eddy simulation (LES) provide detailed physical insight, their computational expense limits their use in engineering design and optimization. Conversely, homogenized models such as Reynolds-Averaged Navier–Stokes (RANS) equations introduce modeling assumptions that may compromise predictive accuracy. In recent years, machine learning has emerged as a powerful tool for bridging this gap by extracting information from high-fidelity data and embedding it into reduced-order models or surrogate representations. Bayesian machine learning provides a principled probabilistic framework for this task, enabling model calibration, uncertainty quantification, model selection, and aggregation. This paper describes recent developments in Bayesian approaches for model/data fusion in fluid mechanics, with a particular focus on turbulence modeling, model aggregation strategies, and multi-fidelity surrogate modeling for design optimization. Original application examples are provided for turbomachinery flow prediction and design. Perspectives and open challenges for trustworthy artificial-intelligence-assisted CFD are also discussed.