Abstract: To reduce the computational cost, the multi-fidelity metamodel methods that fusion analysis models with different computational cost and accuracy have been widely used in simulation-based engineering optimization. The existing multi-fidelity modeling methods still need a large number of high-fidelity and computationally expensive sample points especially for high-dimensional problems. Meanwhile, most of them are based on the Gaussian random process theory, and thus the time cost by hyper-parameter estimation increases significantly with the increase of dimension and nonlinearity of problems and the robustness is low. To address these issues, makes full use of the great potential of deep neural networks in high-dimensional information extraction and approximation, as well as the advantages of meta-learning theory in the field of small-sample learning, and develops a meta-learning based multi-fidelity deep neural network surrogate model (MLMF-DNN) method. Through several mathematical examples and the application of NACA0012 airfoil robust optimization problem, it is shown that the proposed MLMF-DNN approach is significantly improved in prediction accuracy and training time cost compared with the classical Co-Kriging method, especially for high-dimensional problems.

Key words: deep neural networks, meta-learning, multi-fidelity, surrogate model, robust optimization