Multi-objective design of 3-D phononic metamaterials using graph-based reinforcement learning

The proposed framework, GraphPhononic, introduces a pioneering, unified approach for the inverse design of 3-D truss metamaterials with tailored band structures. Moving beyond conventional 2-D pixel-based and basic 3-D parameterized methods focused on single-objective bandgap placement, GraphPhononic enables the direct and simultaneous engineering of both longitudinal acoustic (LA) and transverse acoustic (TA) branches within elastic media. This framework employs graph neural networks and multi-objective reinforcement learning to facilitate precise, adaptable manipulation of frequency-dependent dispersion relations. A diverse dataset of approximately 4000 unique truss topologies and their associated band structures forms the foundation for generalization and robust discovery. As band structures are fundamentally quasi-material and size invariant, this dataset is highly transferable, allowing solutions to be seamlessly adapted to diverse practical constraints, including variations in material choice, structural demands, and operational frequency conditions. This scalability ensures optimized solutionsmaintain effectiveness across a wide spectrum of real-world applications. In brief, GraphPhononic empowers the design of materials for mode-selective vibration isolation, directional wave guidance, and tunable dynamic moduli, providing researchers with an extensible toolkit to advance current applications and shape future innovations in automotive, aerospace, and materials science.