基于深度Q网络的平面域Delaunay网格优化算法

Deep Q Network-Based Optimization Algorithm for Planar Delaunay Mesh

网格优化是Delaunay网格生成后的必要步骤,对于保证数值模拟的可靠性至关重要.为了改善平面域Delaunay网格的质量,提出一种基于深度Q网络(deep Q network,DQN)的网格优化算法.首先,对初始网格进行质量评估,选出不满足要求的单元结点,并将其按质量升序排列;其次,将结点移动描述为Markov决策过程,建立并训练DQN模型;再次,利用模型训练后的经验参数加速网格质量优化;最后,以实际的隧道、气缸体、机械零件等为背景构建测试算例,验证算法的适用性和可靠性,并与既有典型算法进行对比试验.研究结果表明,本文算法能显著提高畸变单元的质量,优化后的网格质量分布更为集中,且优化过程不会产生无效单元.

It is necessary to conduct mesh optimization after generating Delaunay mesh,which is essential to ensure the reliability of numerical simulation.To improve the quality of Delaunay mesh on the plane domain,a mesh optimization algorithm based on deep Q network(DQN)is proposed.Firstly,the quality of the initial mesh is evaluated,and the element nodes that do not meet the quality requirements are selected and arranged in ascending order of their quality.Secondly,the node movement is described as Markov decision process,and the DQN model is established and trained.Thirdly,the empirical parameters of the model training are used to accelerate the optimal mesh quality.Finally,several test examples from practical tunnel,cylinder block,mechanical parts,etc.,are employed to verify the applicability and reliability of the proposed algorithm.Compared with the existing typical algorithms,the test results show that the proposed algorithm can significantly improve the quality of poor elements,the quality distribution of optimized mesh will be more concentrated,and no invalid elements are produced during the optimization process.