Data-driven methods have gained increasing attention in computational mechanics and design. This study investigates a two-scale data-driven design for thermal metamaterials with various functionalities. To address the complexity of multiscale design, the design variables are chosen as the components of the homogenized thermal conductivity matrix originating from the lower scale unit cells. Multiple macroscopic functionalities including thermal cloak, thermal concentrator, thermal rotator/inverter, and their combinations, are achieved using the developed approach. Sensitivity analysis is performed to determine the effect of each design variable on the desired functionalities, which is then incorporated into topology optimization. Geometric extraction demonstrates an excellent matching between the optimized homogenized conductivity and the extraction from the constructed database containing both architecture and property information. The designed heterostructures exhibit multiple thermal meta-functionalities that can be applied to a wide range of heat transfer fields from personal computers to aerospace engineering.

翻译：数据驱动方法在计算力学与设计中日益受到关注。本研究探讨了面向热超材料的多功能双尺度数据驱动设计。为应对多尺度设计的复杂性，设计变量选取为源自低尺度单胞的均质化热导率矩阵分量。通过所提出的方法实现了多种宏观功能，包括热隐身、热聚能、热旋转/反转及其组合。通过灵敏度分析确定各设计变量对目标功能的影响，并将其融入拓扑优化过程。几何提取结果表明，优化后的均质化热导率与包含结构及属性信息的数据库提取结果具有优异匹配性。所设计异质结构展现出多种热超常功能，可应用于从个人计算机到航空航天工程等广泛传热领域。