基于深度学习和梯度优化的弹性超材料设计

Elastic metamaterial design based on deep learning and gradient optimization

为了建立灵活通用的弹性超材料快速迭代设计框架,并实现考虑材料离散性的拓扑结构和材料参数同步优化,提出基于深度学习和梯度优化的设计方法.以变分自动编码器和带隙神经网络组成的设计网络作为框架,采用自动微分技术和梯度优化算法,利用梯度信息迭代调整设计变量;提出协同优化策略以考虑材料离散性,使结构优化的同时在材料库中选择最佳材料.基于所提方法分别进行约束条件下带隙宽度最大化和指定带隙区间设计,并探讨同步优化和拓扑构型的影响.结果表明,与材料和拓扑结构的单独优化相比,同步优化具有更优越的性能;在相同带隙目标和材料组成下,多层构型可以设计出更小尺寸的元胞.频域和时域分析的数值模拟结果表明,所设计的超材料结构在目标带隙范围内表现出明显的减振性能.

A novel design method based on deep learning and gradient optimization was proposed to establish a flexible and general framework for fast iterative design of elastic metamaterials and achieve simultaneous optimization of topology structure and material considering material discretization.The design network composed of variational autoencoders and band gap neural network was developed as the framework,and auto-differentiation techniques and gradient optimization algorithms were employed to iteratively tune the design variables with the gradient information.Furthermore,a co-optimization strategy was further proposed to consider the material discretization,so that the structure was optimized while the optimal material was selected from the material depot.Band gap width maximization under constraints and on-demand design were carried out respectively,and the effects of simultaneous optimization and topological configuration were explored.Results showed that the simultaneous optimization provided superior performance compared to separate optimization of materials and topology structures.Additionally,the multilayer configuration can achieve basic units with smaller sizes under the same objectives and material composition.Furthermore,the numerical simulation results of frequency and time domain analyses showed that the designed elastic metamaterials exhibited significant vibration damping performance in the target band gap range.