A new adaptive multi-fidelity metamodel method using meta-learning and Bayesian deep learning

To reduce the computational cost, multi-fidelity (MF) metamodel methods have been widely used in engineering optimization. Most of these methods are based on the standard Gaussian random process theory; thus, the time cost required for hyperparameter estimation increases significantly with an increase in the dimension and nonlinearity of the problems especially for high-dimensional problems. To address these issues, by exploiting the great potential of deep neural networks in high-dimensional information extraction and approximation, a meta-learning-based multi-fidelity Bayesian neural network (ML-MFBNN) method is developed in this study. Based on this, to further reduce the computational cost, an adaptive multi-fidelity sampling strategy is proposed in combination with Bayesian deep learning to sequentially select the highly cost-effective samples. The effectiveness and advantages of the proposed MF-MFBNN and adaptive multi-fidelity sampling strategy are verified through eight mathematical examples, and the application to model validation of computational fluid dynamics and robust shape optimization of the ONERA M6 wing.