In this paper, we propose a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy minimization involving two weakly coupled components. This enables us to train two deep neural networks to represent two components of the solution in high-dimensional. The curse of dimensionality is alleviated by using the Monte-Carlo method to discretize the unfitted Nitsche energy function. We present several numerical examples to show the efficiency and accuracy of the proposed method.

翻译：在本文中,我们提出了一种极不合适的尼采方法,用于计算具有高度差异的极右侧界面问题。为了捕捉由界面造成的解决方案的不连续性,我们重新将该问题改写为一种能量最小化,涉及两个薄弱的连接组件。这使我们能够训练两个深神经网络,以代表高度解决方案的两个组成部分。通过使用蒙特-卡洛方法将不合格的尼采能源功能分解,可以减轻维度的诅咒。我们提出了几个数字例子,以显示拟议方法的效率和准确性。