WCNS3-MR-NN: A machine learning-based shock-capturing scheme with accuracy-preserving and high-resolution properties

Machine learning-based techniques have been introduced to help enhance the performance of high-order shock-capturing schemes in recent years. In this work, a novel neural network is devised to address the accuracy reduction issue faced by previous machine learning-based schemes. By fully leveraging the features of multi-resolution strategy, optimal accuracy of the original numerical scheme can be formally preserved at all grid levels by the proposed WCNS3-MR-NN scheme. Meanwhile, the present scheme is designed to achieve high-resolution property and robust shock-capturing ability simultaneously. Analysis and numerical experiments are presented for validation. The results confirm that WCNS3-MR-NN maintains its optimal accuracy even at the presence of extreme points, and demonstrates excellent performance across a wide range of benchmark cases.