Non-intrusive reduced order modeling for flowfield reconstruction based on residual neural network

Abstract

A non-intrusive reduced order model is proposed based on residual neural network for parametrized flows. Specifically, a map from the flow parameters or the flowfield of a designed simplified problem to the flowfield of the target problem is constructed using the residual neural network in the offline stage. With this map, the unknown flowfield of the target problem can be reconstructed online as long as the flow parameters are provided or the simplified problem is solved properly. In this fashion, the efficiency of the reduced order model is ensured. Compared with the feedforward neural network utilized in other non-intrusive reduced order models, residual neural network has an additional shortcut connection, which is capable of providing a rough prediction and helping improve the accuracy of the model. To relieve the computational burden of training the residual neural network, proper orthogonal decomposition is employed to compress the flowfields of the simplified problem and target problem. In addition, a novel two-step training strategy is proposed to decouple the training of the shortcut connection and the fully connected layers in the residual neural network, which contributes to the superiority of the shallow residual neural network in this paper. Several typical cases are conducted to examine the performance of the proposed method, including the compressible NACA0012 airfoil flow, the compressible M6 wing flow and the unsteady cylinder flow. The results demonstrate that the proposed model is superior to a model based on the feedforward neural network in terms of accuracy and robustness, especially for problems of high sensitivity with respect to flow parameters.