  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.
