Solution reconstruction for computational fluid dynamics via artificial neural network

Abstract

The potential of using an artificial neural network (ANN) to reconstruct the solution for CFD was investigated. From various ANN models, the multi-layer perceptron (MLP) model was adopted. At first, to examine the potential feasibility of using MLP for reconstruction, the numerical characteristics of MLP were investigated. Then training database alpha was created from the input-output relationship of WENO3, followed by database beta (which maps the WENO3 input to the WENO7 output). A total of 6000 MLPs and 10000 MLPs were trained by Database alpha and beta, respectively. To assess the capability of the present MLPs to handle strong discontinuity, the Sod problem was solved. Then the Shu-Osher problem was solved to evaluate the performance for a more general flow problem involving shocks and sinusoidal density waves. The well-trained MLP from database beta, which yielded the most accurate solutions for both problems, was further assessed by solving the interacting blast waves problem and the supersonic channel test case on unstructured grids. The well-trained MLP yielded more accurate solutions for all test cases compared to WENO3 without extending the stencil. It was concluded that the MLP can potentially reconstruct the solution more accurately than existing reconstruction schemes.