An active learning multi-fidelity metamodel method considering arbitrary fidelity level

As engineering problems such as aircraft design become increasingly complex, multi-fidelity deep-learning-based metamodels are increasingly used to reduce computational cost and tackle high-dimensional regression. Existing approaches typically address either hierarchical or non-hierarchical fidelity relations and employ distinct fusion schemes for each, leaving hybrid fidelity settings—where some low-fidelity models can be clearly ranked while others have comparable accuracy—inefficiently treated. This paper proposes an active-learning multi-fidelity deep learning metamodeling method that accommodates arbitrary fidelity configurations within a unified, simple network architecture. An incremental-learning multi-fidelity Bayesian neural network with an omnidirectional information transmission matrix is introduced to enable flexible multi-fidelity fusion. A complementary active learning strategy selects cost-effective samples by balancing predictive uncertainty and spatial diversity. The method is evaluated on several mathematical benchmarks with different numbers of fidelity levels and on a robust aerodynamic optimization of the 52-dimensional ONERA M6 wing with hybrid fidelity and under uncertain flow conditions. For the ONERA M6 case, it reduces computational cost by 20.5 % relative to using only high-fidelity data while maintaining comparable accuracy.