In this paper, we propose a method for constructing a neural network viscosity in order to reduce the non-physical oscillations generated by high-order Discontiuous Galerkin (DG) methods. To this end, the problem is reformulated as an optimal control problem for which the control is the viscosity function and the cost function involves comparison with a reference solution after several compositions of the scheme. The learning process is strongly based on gradient backpropagation tools. Numerical simulations show that the artificial viscosities constructed in this way are just as good or better than those used in the literatur

翻译：本文提出一种构建神经网络粘性的方法，旨在抑制高阶不连续伽辽金（Discontinuous Galerkin, DG）方法产生的非物理振荡。为此，将问题重新表述为一个最优控制问题，其中控制变量为粘性函数，代价函数涉及格式多次迭代后与参考解的比较。该学习过程强依赖于梯度反向传播工具。数值模拟表明，以这种方式构造的人工粘性性能与文献中使用的传统方法相当或更优。