Modified structure of deep neural network for training multi-fidelity data with non-common input variables

Abstract

Multi-fidelity surrogate (MFS) modeling technology, which efficiently constructs surrogate models using low-fidelity (LF) and high-fidelity (HF) data, has been studied to enhance the predictive capability of engineering performances. In addition, several neural network (NN) structures for MFS modeling have been introduced, benefiting from recent developments in deep learning research. However, existing multi-fidelity (MF) NNs have been developed assuming identical sets of input variables for LF and HF data, a condition that is often not met in practical engineering systems. Therefore, this study proposes a new structure of composite NN designed for MF data with different input variables. The proposed network structure includes an input mapping network that connects the LF and HF data's input variables. Even when the physical relationship between these variables is unknown, the input mapping network can be concurrently trained during the process of training the whole network model. Customized loss functions and activation variables are suggested in this study to facilitate forward and backward propagation for the proposed NN structures when training MF data with different inputs. The effectiveness of the proposed method, in terms of prediction accuracy, is demonstrated through mathematical examples and practical engineering problems related to tire performances. The results confirm that the proposed method offers better accuracy than existing surrogate models in most problems. Moreover, the proposed method proves advantageous for surrogate modeling of nonlinear or discrete functions, a characteristic feature of NN-based methods.