标题： 深度层次集方法用于斯蒂芬问题 显示英文标题

标题： Deep Level-set Method for Stefan Problems

摘要： 我们提出一种水平集方法，用于表征Stefan问题中固体占据的区域，包括有和没有表面张力的情况，这是基于其最近的概率重新表述。 水平集函数由一个前馈神经网络参数化，其参数通过Stefan生长条件的概率表述进行训练。 该算法可以处理液体过冷的Stefan问题，并通过沿移动边界模拟粒子以及对平均曲率的有效近似来捕捉表面张力效应。 我们在各种具有和不具有径向对称性的例子中展示了该方法的有效性。 显示英文摘要

摘要： We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a feed-forward neural network, whose parameters are trained using the probabilistic formulation of the Stefan growth condition. The algorithm can handle Stefan problems where the liquid is supercooled and can capture surface tension effects through the simulation of particles along the moving boundary together with an efficient approximation of the mean curvature. We demonstrate the effectiveness of the method on a variety of examples with and without radial symmetry.