Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws (Communications in Computational Physics, 2020)
We propose a universal discontinuity detector using convolution neural network (CNN) and apply it in conjunction of solving nonlinear conservation laws in both1D and 2D. The CNN detector is trained offline with synthetic data. The training dataare generated using randomly constructed piecewise functions, which are then processed using randomized linear advection solver to count for the cases of numericalerrors in practice. The detector is then paired with high-order numerical solvers. Inparticular, we combined high-order WENO in troubled cells with high-order centraldifference in smooth region. Extensive numerical examples are presented. We observethat the proposed method produces notably sharper and cleaner signals near the discontinuities, when compared to other well known troubled cell detector methods.