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Volume 28, Issue 5
Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws

Zheng Sun, Shuyi Wang, Lo-Bin Chang, Yulong Xing & Dongbin Xiu

DOI: 10.4208/cicp.OA-2020-0199

Commun. Comput. Phys., 28 (2020), pp. 2075-2108.

Published online: 2020-11

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  • Abstract

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.

  • Keywords

Deep neural network, convolution neural network, discontinuity detection, troubled cell, hybrid method, hyperbolic conservation laws.

  • AMS Subject Headings

35L65, 35L67, 65M06, 65M99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-2075, author = {Sun , ZhengWang , ShuyiChang , Lo-BinXing , Yulong and Xiu , Dongbin}, title = {Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {5}, pages = {2075--2108}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0199}, url = {http://global-sci.org/intro/article_detail/cicp/18405.html} }
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 -

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.

Sun , ZhengWang , ShuyiChang , Lo-BinXing , Yulong and Xiu , Dongbin. (2020). Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws. Communications in Computational Physics. 28 (5). 2075-2108. doi:10.4208/cicp.OA-2020-0199
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