Adaptive Multi-Fidelity Composite Deep Neural Networks

Data-driven deep learning modeling has been applied in different disciplines such as mechanics and materials. The computational accuracy of deep learning modeling requires a large amount of high-fidelity data. In many real-world applications, only a small number of expensive high-fidelity data are available while the cheap low-fidelity data are sufficient, which leads to poor accuracy as the number of high-fidelity data is not sufficient. Recently developed multi-fidelity deep neural networks achieve high accuracy when the number of high-fidelity data is small by fusing multi-fidelity data. However, the accuracy of existing multi-fidelity deep neural networks depends on the regularization of the hyperparameters. When the regularization is too strong, the model has difficulty in fitting nonlinear correlations; while the regularization is too small, overfitting occurs for cases with linear correlation between multi-fidelity data. Generally, high-fidelity data for validation in multi-fidelity modeling are not available since the number of high-fidelity data is quite small. The optimal regularization is difficult to obtain. To this end, we proposed an improved multi-fidelity model, referred to as adaptive multi-fidelity compo-site neural networks, by modifying the loss function of existing multi-fidelity neural networks. This model can adaptively approximate the linear or nonlinear correlation between multi-fidelity data with less dependence on the regularization coefficients, which improves the robustness of modeling. The proposed model shows good accuracy and robustness in several benchmark examples as well as a demo application of the aerodynamics.