Review on Data‐ and Mathematics‐Driven Optimization for Metamaterial Lattice Structures

Lattice structures, as pivotal constituents of metamaterials, receive extensive utilization in emerging engineering domains like aerospace, automotive, and biomedicine due to their distinctive mechanical properties. However, stringent engineering requirements necessitate the further optimization of the structures. In recent years, numerous inverse design methodologies oriented toward targeted performance and seeking optimal solutions have been reported which can be theoretically divided into data‐driven and mathematics‐driven strategies. This review presents lattice structures classified by Poisson's ratio and introduces inverse design methodologies at two distinct scales. Data‐driven strategies represented by artificial intelligence and mathematics‐driven strategies represented by topology optimization receive equal attention, and their characteristics are evaluated objectively, while their advantages and limitations are systematically compared. Concurrently, integration and collaboration between the two strategies are focused, resulting in the development of three hybrid optimization frameworks and one modular two‐scale design approach, whose engineering applicability is discussed. Finally, the current limitations and future opportunities for lattice structure design are summarized. This work places both strategies within a single discourse for the first time, guiding their selection, application, and integration and thereby exerts a forward‐looking influence on the evolution of design methodology.