Inverse design of elastic metamaterial plate with all-polarized odd-order topological bandgaps

Elastic metamaterial plates support rich polarization-components, high energy density, and strong miniaturization potential. However, most elastic metamaterial designs target only a single polarization, often the out-of-plane modes after modal separation, making it challenging to realize overlapping in-plane and out-of-plane complete bandgaps using conventional forward design. Here, we develop an inverse-design framework that treats in-plane and out-of-plane dispersion branches as distinct objectives. By combining the multi-objective genetic algorithm NSGA-II with a pixel-encoded topology representation, we generate unit-cells that achieve user-prescribed all-polarized bandgap combinations. The optimized designs exhibit clear polarization-selective band separation, enlarged common bandgaps, and odd-order bandgap topology for both polarizations. By lattice translation, we further obtain topological counterparts with opposite bulk polarization. Ribbon and finite-waveguide calculations confirm all-polarized topological interface modes.