论文标题
可压缩流体动力学的六点神经元的ENO（NENO6）方案
A six-point neuron-based ENO (NENO6) scheme for compressible fluid dynamics
论文作者
论文摘要
在这项工作中，我们引入了一个深层的人工神经网络（ANN），该网络可以检测不连续性的位置，并基于一组平稳且不连续的训练数据来构建六点ENO型方案。虽然构建了一组候选宽度宽度的模具，但ANN而不是经典的平滑度指示器被部署以进行类似ENO的子模具选择。候选通量与重新归一化线性权重的凸组合形成了六点神经元基于基于神经元的ENO（NENO6）方案。本方法的灵感来自[Fu等人，计算物理学杂志305（2016）：333-359]，其中最终的重建模具从最终的重建模板中删除了含有不连续性的候选模具的贡献。二进制候选模具分类由训练有素的ANN高保真进行。与其他基于ANN的方案相比，提出的框架显示出提高的一般性和鲁棒性。通过检查具有不同管理法律的一维基准案例，并与Weno-Cu6和TenO6-OPT方案进行比较，可以证明拟议的NENO6方案的一般性和性能。
In this work, we introduce a deep artificial neural network (ANN) that can detect locations of discontinuity and build a six-point ENO-type scheme based on a set of smooth and discontinuous training data. While a set of candidate stencils of incremental width is constructed, the ANN instead of a classical smoothness indicator is deployed for an ENO-like sub-stencil selection. A convex combination of the candidate fluxes with the re-normalized linear weights forms the six-point neuron-based ENO (NENO6) scheme. The present methodology is inspired by the work [Fu et al., Journal of Computational Physics 305 (2016): 333-359] where contributions of candidate stencils containing discontinuities are removed from the final reconstruction stencil. The binary candidate stencil classification is performed by a well-trained ANN with high fidelity. The proposed framework shows an improved generality and robustness compared with other ANN-based schemes. The generality and performance of the proposed NENO6 scheme are demonstrated by examining one- and two-dimensional benchmark cases with different governing conservation laws and comparing to those of WENO-CU6 and TENO6-opt schemes.
