  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.
