Multi-Fidelity Surrogate Modeling via Hierarchical Kriging With Infinite-Width Bayesian Neural Network Correlation Function

Hierarchical Kriging (HK) is a promising surrogate model to fuse multi-fidelity data. In theory, HK can serve as predictor for problems with any number of input dimensions. In practice, for a problem with more than 1000 variables, it is often not affordable to build such HK model due to the high demand on the computer memory to store the spatial distance matrix and the heavy computational burden relating to the frequent inversion of the large correlation matrix. To mitigate the curse of dimensionality of HK for high-dimensional problems, an infinite-width Bayesian neural network correlation function is developed and incorporated to the HK model. Theoretical analysis demonstrates that the proposed correlation function is independent on the spatial distance and has no hyperparameters to be fine-tuned. Therefore, the demand on the consumption of computer memory and computility for the model construction can be reduced significantly. Real engineering problems, including the aerodynamic performance prediction of single axial flow compressor rotor with 31 variables, 3-stage compressor with 144 variables, and 10.5-stage compressor of 1512 variables, are established along with the collected problems to test the performance of the proposed method. Comparison among the proposed method and alternative methods are further conducted. It is observed that the proposed method performs competitive in terms of the modeling accuracy and significantly better with respect to modeling efficiency. On the 1512-dimensional problem of the prediction for the compressor pressure ratio, the proposed method can build most accurate model within 50 seconds on a personal laptop with a data set consisting of 15120 low-fidelity and 7560 high-fidelity sample data.