论文标题
具有局部融合输入（NNLCI）的神经网络用于解决保护法，第二部分：2D问题
Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems
论文作者
论文摘要
在我们先前的工作[ARXIV：2109.09316]中，引入了具有基于依赖性领域和收敛序列的输入的神经网络方法，以求解一维保护法，尤其是Euler系统。为了在给定的时空位置预测高保真解决方案，从融合序列中的两种保护定律的解决方案，从低成本数值方案计算出来，以及在时空位置依赖性的局部域中作为神经网络的输入。在目前的工作中，我们将方法扩展到二维Euler系统并引入变化。数值结果表明，这些方法不仅在一个维度[ARXIV：2109.09316]中很好地工作，而且在二维中表现良好。尽管局部输入数据涂抹了，但神经网络方法仍能够准确预测溶液的冲击，触点和平滑区域。神经网络方法是有效的且相对易于训练，因为它们是本地求解器。
In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a high-fidelity solution at a given space-time location, two solutions of a conservation law from a converging sequence, computed from low-cost numerical schemes, and in a local domain of dependence of the space-time location, serve as the input of a neural network. In the present work, we extend the methods to two dimensional Euler systems and introduce variations. Numerical results demonstrate that the methods not only work very well in one dimension [arXiv:2109.09316], but also perform well in two dimensions. Despite smeared local input data, the neural network methods are able to predict shocks, contacts, and smooth regions of the solution accurately. The neural network methods are efficient and relatively easy to train because they are local solvers.
