Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws
Convolution Neural Network Shock Detector for Numerical Solution of Conservation Laws
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DOI：
10.4208/cicp.oa-2020-0199
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发表时间：
2020-06
影响因子：
3.7
通讯作者：
Zheng Sun
中科院分区：
文献类型：
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作者：
Zheng Sun
． 我们提出了一种使用卷积神经网络（CNN）的通用不连续检测器，并将其应用于求解一维和二维的非线性守恒律。CNN检测器是用合成数据离线训练的。训练数据使用随机构造的分段函数生成，然后使用随机线性平流求解器对其进行处理，以计算实际中数值误差的情况。然后将检测器与高阶数值解算器配对。特别地，我们将麻烦细胞中的高阶WENO与光滑区域的高阶中心差结合起来。给出了大量的数值算例。我们观察到，与其他已知的麻烦细胞检测器方法相比，所提出的方法在不连续点附近产生明显更清晰的信号。
. 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.