A flux reconstruction model based on an artificial neural network

Abstract

In the present study, a multi-layer perceptron (MLP) model was applied to flux reconstruction. To determine if an MLP can be used as a general numerical model, the numerical characteristics of an MLP were investigated. To train MLPs, a training database was constructed without any actual flow data and input vectors of the database were normalized to avoid numerical extrapolation. A total of 4,800 MLPs were trained and evaluated by numerically solving the Sod problem and the Shu-Osher problem. For the Sod problem, the well-trained MLP produced more accurate flow solutions than WENO3 and WENO5 did. In contrast, the solutions from the MLP were more accurate than those of WENO3 and less accurate than WENO5 for the Shu-Osher problem. Nonetheless, the MLP successfully captured a small wave peak on the specific grid that WENO3 and WENO5 did not capture.