Designing Mixed-Category Stochastic Microstructures by Deep Generative Model-based and Curvature Functional-based Methods
Designing Mixed-Category Stochastic Microstructures by Deep Generative Model-based and Curvature Functional-based Methods
复制标题
通过基于深度生成模型和基于曲率函数的方法设计混合类别随机微观结构
DOI：
10.1115/1.4063824
复制
发表时间：
2023
影响因子：
3.3
通讯作者：
Xu, Hongyi
中科院分区：
文献类型：
--
作者：
Xu, Leidong;Naghavi Khanghah, Kiarash;Xu, Hongyi
弥合各种随机微结构之间的差距在微结构材料的设计表示中仍然是一个挑战。每个微结构类别都需要某些独特的数学和统计方法来定义设计空间(设计表示法)。在两类不同的随机微结构之间，设计表示方法通常是不相容的。在进行严格的计算设计之前，预先选择微结构类别和相关的设计表示方法是一种常见的做法，这限制了设计自由，阻碍了创新微结构设计的发现。为了解决这一问题，本文提出并比较了两种新的方法，即基于深度生成建模的方法和基于曲率泛函的方法，以了解它们在设计具有期望特性的混合类别随机微结构时的优缺点。对于基于深度产生式建模的方法，采用变分自动编码器生成一个非结构化的潜在空间作为设计空间。在基于曲率泛函的方法中，微结构的几何形状用曲率泛函表示，其中的函数参数被用作微结构设计变量。训练微结构设计变量-性能关系的回归变量，用于微结构设计优化。为了了解这两种方法在计算成本、连续过渡、设计可伸缩性、设计多样性、设计空间的维度、统计等价性的可解释性以及设计性能方面的相对优势，进行了比较研究。
Bridging the gaps among various categories of stochastic microstructures remains a challenge in the design representation of microstructural materials. Each microstructure category requires certain unique mathematical and statistical methods to define the design space (design representation). The design representation methods are usually incompatible between two different categories of stochastic microstructures. The common practice of preselecting the microstructure category and the associated design representation method before conducting rigorous computational design restricts the design freedom and hinders the discovery of innovative microstructure designs. To overcome this issue, this article proposes and compares two novel methods, the deep generative modeling-based method, and the curvature functional-based method, to understand their pros and cons in designing mixed-category stochastic microstructures for desired properties. For the deep generative modeling-based method, the variational autoencoder is employed to generate an unstructured latent space as the design space. For the curvature functional-based method, the microstructure geometry is represented by curvature functionals, of which the functional parameters are employed as the microstructure design variables. Regressors of the microstructure design variables–property relationship are trained for microstructure design optimization. A comparative study is conducted to understand the relative merits of these two methods in terms of computational cost, continuous transition, design scalability, design diversity, dimensionality of the design space, interpretability of the statistical equivalency, and design performance.