We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable refinement criteria to be possibly employed within adaptive refinement strategies. We propose two refinement strategies that exploit the use of CNNs to classify elements' shape, at a low computational cost. We test the proposed idea considering two families of finite element methods that support arbitrarily shaped polygonal elements, namely Polygonal Discontinuous Galerkin (PolyDG) methods and Virtual Element Methods (VEMs). We demonstrate that the proposed algorithms can greatly improve the performance of the discretization schemes both in terms of accuracy and quality of the underlying grids. Moreover, since the training phase is performed off-line and is problem independent the overall computational costs are kept low.
翻译:我们提出了在进化神经网络的基础上完善多边形网格的新战略。我们表明,CNN可以成功地用于正确识别多边形元素的“形状”以便设计适应性完善战略中可能采用的适当完善标准。我们提出了两项完善战略,利用CNN对元素的形状进行分类,而计算成本较低。我们测试了考虑两种支持任意形状多边形元素的有限元素方法,即多边形不连续的Galerkin(PollyDG)方法和虚拟元件方法(VEMS)的组合。我们证明,拟议的算法可以极大地提高离散计划在基础电网的准确性和质量方面的性能。此外,由于培训阶段是离线进行的,而且存在独立问题,因此总体计算成本一直较低。