论文标题
Voronoi多边形的庞加莱常数的人工神经网络评估
Artificial Neural Network evaluation of Poincaré constant for Voronoi polygons
论文作者
论文摘要
我们提出了一种基于人工神经网络的方法，该方法了解了庞加莱不平等中常数对voronoi网格多边形元素的依赖性，这是对该元素的某些几何指标的依赖性。这种算法的成本主要驻留在数据预处理和学习阶段中，可以一劳永逸地离线执行，构建一种有效的计算常数方法，这是在基于数值网格的方案的基于数值网格的方案中的后验误差估计中所需的。
We propose a method, based on Artificial Neural Networks, that learns the dependence of the constant in the Poincaré inequality on polygonal elements of Voronoi meshes, on some geometrical metrics of the element. The cost of this kind of algorithms mainly resides in the data preprocessing and learning phases, that can be performed offline once and for all, constructing an efficient method for computing the constant, which is needed in the design of a posteriori error estimates in numerical mesh-based schemes for the solution of Partial Differential Equations.
