Unresolved gradients produce numerical oscillations and inaccurate results. The most straightforward solution to such a problem is to increase the resolution of the computational grid. However, this is often prohibitively expensive and may lead to ecessive execution times. By training a neural network to predict the shape of the solution, we show that it is possible to reduce numerical oscillations and increase both accuracy and efficiency. Data from the neural network prediction is imposed using multiple penalty terms inside the domain.

中文翻译：

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神经网络在粗网格上的增强计算

未解析的梯度会产生数值振荡和不准确的结果。解决此问题的最直接方法是提高计算网格的分辨率。但是，这通常非常昂贵，并且可能导致执行时间过长。通过训练神经网络来预测解决方案的形状，我们表明可以减少数值振荡并提高准确性和效率。来自神经网络预测的数据是使用域内的多个惩罚项来施加的。