Hierarchical diamond plate-lattice metamaterial: machine-learning co-optimisation of sound absorption and mechanics

Multifunctional lattice metamaterials that combine load- bearing and sound absorption are increasingly needed in lightweight manufacturing. Here we propose a modified hierarchical diamond plate-lattice metamaterial (DMH) that, at a fixed relative density, matches the mechanical performance of conventional lightweight composite architectures while delivering strong high-frequency absorption (α > 0.9 from 5.0 to 5.7 kHz; α = 1 at 5.4 kHz). To accommodate aerospace scenarios with shifting priorities, we develop a machine-learning multi-objective co-optimisation framework that tunes acoustic and structural metrics under design and manufacturability constraints. By benchmarking surrogate -optimiser combinations, we identify XGBoost coupled with NSGA-III as the most accurate and diversity-preserving pair for many-objective search. Across six inverse-design studies targeting randomly sampled vectors in a six-dimensional objective space, the framework retains high predictive fidelity and identifies Pareto-optimal solutions within the model's prediction range. Additively manufactured prototypes and experiments validate the predicted absorption and mechanical responses. The proposed DMH and workflow enable rapid, customisable design of load-bearing, sound-absorbing lattices for aerospace panels and lattice-reinforced structures.