论文标题
使用双模型神经网络加速基于梯度的拓扑优化设计
Accelerating gradient-based topology optimization design with dual-model neural networks
论文作者
论文摘要
拓扑优化（TO）是一种自由形式设计中的常见技术。但是，由于需要重复的前向计算和/或灵敏度分析，通常使用高维模拟（例如有限元分析（FEA））进行的，基于常规的设计方法遭受了高计算成本的影响。在这项工作中，神经网络被用作有效的替代模型，用于远期和灵敏度计算，以极大地加速拓扑优化的设计过程。为了提高灵敏度分析的准确性，构建了经过正向和灵敏度数据训练的双模型神经网络，并通过惩罚方法（SIMP）方法集成到固体各向同性材料中以替代FEA。在两个基准设计问题（即最低符合性设计和超材料设计）上证明了加速SIMP方法的性能。在64x64大小的问题中获得的效率是正向计算的137倍，灵敏度分析的效率为74倍。此外，研究和开发了适合设计的有效数据生成方法，从而节省了训练时间。在这两个基准设计问题中，只有2000年培训数据只能达到95％的设计准确性。
Topology optimization (TO) is a common technique used in free-form designs. However, conventional TO-based design approaches suffer from high computational cost due to the need for repetitive forward calculations and/or sensitivity analysis, which are typically done using high-dimensional simulations such as Finite Element Analysis (FEA). In this work, neural networks are used as efficient surrogate models for forward and sensitivity calculations in order to greatly accelerate the design process of topology optimization. To improve the accuracy of sensitivity analyses, dual-model neural networks that are trained with both forward and sensitivity data are constructed and are integrated into the Solid Isotropic Material with Penalization (SIMP) method to replace FEA. The performance of the accelerated SIMP method is demonstrated on two benchmark design problems namely minimum compliance design and metamaterial design. The efficiency gained in the problem with size of 64x64 is 137 times in forward calculation and 74 times in sensitivity analysis. In addition, effective data generation methods suitable for TO designs are investigated and developed, which lead to a great saving in training time. In both benchmark design problems, a design accuracy of 95% can be achieved with only around 2000 training data.
