This paper presents a machine-learning approach for determining the optimal anisotropy in a computational mesh, in the context of an output-based adaptive solution procedure. Artificial neural networks are used to predict the desired element aspect ratio from readily accessible features of the primal and adjoint solutions. Whereas the sizing of the element is still based on an adjoint-weighted residual error estimate, the network augments this information with element stretching magnitude and direction, at lower computational and implementation costs compared to a more rigorous approach: mesh optimization through error sampling and synthesis (MOESS). The network is trained to provide anisotropy information in the form of a normalized metric field, computed from primal, adjoint, and error indicator features. MOESS-optimized meshes for a variety of steady aerodynamic flows governed by the Reynolds-averaged Navier-Stokes equations in two dimensions provide data for training several multi-layer perceptron networks, which differ in size and inputs. The networks are then deployed and tested by driving complete mesh adaptation sequences, and the results show improvements in mesh efficiency compared to pure primal Hessian-based anisotropy detection and in many cases to MOESS itself.

本文提出了一种基于学习的自适应求解程序，用于确定计算网格中的最佳各向异性的机器学习方法。人工神经网络用于根据原始溶液和伴随溶液的易于访问的特征来预测所需的元素长宽比。尽管元素的大小仍然基于伴随加权的残差误差估计，但与更严格的方法相比，网络通过元素拉伸的幅度和方向来扩展此信息，从而降低了计算和实现成本：通过错误采样和综合进行网格优化（MOESS）。训练网络以提供归一化度量值字段形式的各向异性信息，该度量值是根据原始，伴随和错误指示符特征计算得出的。由MOESS优化的网格用于二维的雷诺平均Navier-Stokes方程控制的各种稳定的空气动力学流动，为训练几个多层感知器网络提供了数据，这些感知器网络的大小和输入不同。然后，通过驱动完整的网格自适应序列来部署和测试网络，结果表明，与纯基于原始Hessian的各向异性检测相比，网格效率有所提高，在许多情况下，与MOESS本身相比也有所提高。