TY - JOUR
T1 - Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws
AU - Sun , Zheng
AU - Wang , Shuyi
AU - Chang , Lo-Bin
AU - Xing , Yulong
AU - Xiu , Dongbin
JO - Communications in Computational Physics
VL - 5
SP - 2075
EP - 2108
PY - 2020
DA - 2020/11
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2020-0199
UR - https://global-sci.org/intro/article_detail/cicp/18405.html
KW - Deep neural network, convolution neural network, discontinuity detection, troubled cell, hybrid method, hyperbolic conservation laws.
AB - <p style="text-align: justify;">We propose a universal discontinuity detector using convolution neural network (CNN) and apply it in conjunction of solving nonlinear conservation laws in both
1D and 2D. The CNN detector is trained offline with synthetic data. The training data
are generated using randomly constructed piecewise functions, which are then processed using randomized linear advection solver to count for the cases of numerical
errors in practice. The detector is then paired with high-order numerical solvers. In
particular, we combined high-order WENO in troubled cells with high-order central
difference in smooth region. Extensive numerical examples are presented. We observe
that the proposed method produces notably sharper and cleaner signals near the discontinuities, when compared to other well known troubled cell detector methods.</p>