Multi-fidelity transonic aerodynamic loads estimation using Bayesian neural networks with transfer learning

Multi-fidelity surrogate models are of particular interest in aerospace applications, as they combine the computational efficiency of low-fidelity simulations with the accuracy of high-fidelity models. This methodology, often implemented via data fusion, aims to reduce the cost of data generation while preserving predictive accuracy. Despite the widespread use of traditional machine learning techniques to improve surrogates and perform data fusion tasks, there remains a need for novel approaches that further improve predictive reliability—particularly in terms of uncertainty quantification—without substantially increasing the computational cost of generating high-fidelity training samples. In this study, we propose a Bayesian neural network framework designed for multi-fidelity prediction of transonic aerodynamic data, employing transfer learning to integrate computational fluid dynamics data of varying fidelities. The probabilistic nature of the model allows also quantification of the uncertainty in the input space, making it well suited for analyzing the inherently complex and nonlinear behavior of the transonic aerodynamic responses under investigation. Our results demonstrate that the proposed multi-fidelity Bayesian model outperforms classical data fusion Co-Kriging method, both in accuracy and generalization capabilities on unseen data. • Bayesian Neural Network estimates uncertainty for nonlinear aerodynamic loads. • Multi-fidelity enhances model accuracy exploiting sparse high-fidelity data. • Data fusion with transfer learning effectively integrates multiple fidelity data. • It outperforms Co-Kriging in accuracy and uncertainty estimation. • Method validated on transonic wing and eVTOL with rotor-wing interactions.