Designing 3D Thermal Metamaterials at Gigavoxel Resolution on a Single Computer via Hybrid CPU‐GPU Architectures

ABSTRACT Thermal metamaterials enable engineered control of heat transport in advanced systems by tailoring effective thermal conductivity. However, inverse design at truly 3D gigavoxel‐scale resolution remains largely unexplored, even though thermal functionalities often depend on fine‐scale features, sharp spatial variations, and complex anisotropies that are poorly captured on coarse grids. Pushing inverse optimization to gigavoxel resolution on a single computer is particularly challenging. In this paper, we develop a novel high‐performance computational framework for gigavoxel‐resolution inverse optimization of 3D thermal metamaterials on a single computer. The framework rests on two key components: (i) a novel out‐of‐core data structure that jointly exploits host (CPU) and device (GPU) memory to accommodate extreme‐resolution fields, and (ii) an efficient data‐transport scheme that overlaps communication with computation to sustain high throughput during PDE solves and sensitivity evaluations. By enabling high‐resolution optimization, our method improves the fidelity of the designed conductivity distributions, better resolves fine structural details that govern heat‐flow pathways, and reduces discretization‐induced performance loss. Numerical studies demonstrate that the proposed approach substantially enhances scalability and practical accessibility while maintaining high design accuracy. This advancement bridges a critical gap in the field and opens new possibilities for the practical engineering of next‐generation thermal metamaterials.