While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods as a local estimate of solution regularity generally is required. In this work we demonstrate how to train and use a local artificial neural network to estimate the local solution regularity and demonstrate the efficiency of nonlinear artificial viscosity methods based on this in the context of Fourier spectral methods. We compare with entropy viscosity techniques and illustrate the promise of the neural network based estimators when solving one- and two-dimensional conservation laws, including the Euler equations.

尽管在使用基于高阶元素的方法求解守恒定律时，非线性粘度已被广泛用于控制振荡，但由于通常需要对求解规律性进行局部估计，因此此类技术不太容易直接应用于全局频谱方法。在这项工作中，我们演示了如何训练和使用局部人工神经网络来估计局部解的规律性，并在傅立叶谱方法的背景下证明基于此的非线性人工黏度方法的效率。我们与熵粘度技术进行了比较，并说明了基于一维和二维守恒律（包括欧拉方程）的基于神经网络的估计器的前景。