Deep neural networks for parameterized homogenization in concurrent multiscale structural optimization
Deep neural networks for parameterized homogenization in concurrent multiscale structural optimization
复制标题
用于并行多尺度结构优化中参数化均匀化的深度神经网络
DOI：
10.1007/s00158-022-03471-y
复制
发表时间：
2023-01-01
影响因子：
3.9
通讯作者：
Najafi, Ahmad R.
中科院分区：
文献类型：
--
作者：
Black, Nolan;Najafi, Ahmad R.
并行多尺度结构优化是通过设计微尺度结构来提高宏观尺度结构性能的方法。多尺度设计空间必须考虑两个尺度上的变量，因此设计限制通常是可行优化所必需的。这项工作针对这些设计限制，旨在通过深度学习模型增加微结构的复杂性。深度神经网络（DNN）被实现为微尺度结构特性和材料形状导数（形状敏感性）的模型。DNN的深刻优势在于它能够将复杂的多维函数提取为显式，高效和可微的模型。与传统的参数化优化方法相比，DNN在结构优化框架中实现了足够的精度和稳定性。通过与界面感知有限元方法的比较，结果表明，足够精确的DNN收敛，通过反向传播产生稳定的形状敏感性近似。各种优化问题被认为是直接比较基于DNN的微尺度设计与界面丰富的广义有限元法（IGFEM）。利用这些发展，DNN被训练来学习二维和三维微观结构的数值均匀化，最多有30个几何参数。DNN的加速性能提供了更高的设计复杂性，用于在3D结构优化中设计生物启发的微架构。大量的基准设计实例表明，所提出的框架是一个有效的替代数值均匀化结构优化，解决纯材料设计和结构优化之间的差距差距。
Concurrent multiscale structural optimization is concerned with the improvement of macroscale structural performance through the design of microscale architectures. The multiscale design space must consider variables at both scales, so design restrictions are often necessary for feasible optimization. This work targets such design restrictions, aiming to increase microstructure complexity through deep learning models. The deep neural network (DNN) is implemented as a model for both microscale structural properties and material shape derivatives (shape sensitivity). The DNN's profound advantage is its capacity to distill complex, multidimensional functions into explicit, efficient, and differentiable models. When compared to traditional methods for parameterized optimization, the DNN achieves sufficient accuracy and stability in a structural optimization framework. Through comparison with interface-aware finite element methods, it is shown that sufficiently accurate DNNs converge to produce a stable approximation of shape sensitivity through back propagation. A variety of optimization problems are considered to directly compare the DNN-based microscale design with that of the Interface-enriched Generalized Finite Element Method (IGFEM). Using these developments, DNNs are trained to learn numerical homogenization of microstructures in two and three dimensions with up to 30 geometric parameters. The accelerated performance of the DNN affords an increased design complexity that is used to design bio-inspired microarchitectures in 3D structural optimization. With numerous benchmark design examples, the presented framework is shown to be an effective surrogate for numerical homogenization in structural optimization, addressing the gap between pure material design and structural optimization.