Inverse design of TPMS lattices with targeted phononic bandgaps using multi-objective Bayesian optimization

This study introduces a machine learning based multi-objective Bayesian optimization framework for the inverse design of phononic bandgaps in triply periodic minimal surface lattices. High fidelity finite element dispersion analyses are conducted for seven TPMS topologies in matrix and network forms, enabling the identification of configurations that support elastic bandgaps. The results reveal that only network gyroid, primitive, diamond, and Neovius lattices exhibit significant and tunable bandgaps over wide frequency ranges. A dataset of 1158 dispersion analyses is generated and refined through outlier removal, yielding 948 high quality samples. These data are used to train a dual output neural network surrogate relating TPMS topology, unit cell size, and volume fraction to bandgap center frequency and bandwidth. The model achieves R² values of 0.92 for center frequency and 0.91 for bandwidth, while reducing evaluation cost by more than three orders of magnitude compared with finite element analysis. The surrogate is integrated into a multi-objective Bayesian optimization scheme based on Gaussian process posteriors and Expected Hypervolume Improvement to address the inverse design problem. The optimization converges to Pareto-optimal solutions for a target bandgap with a 10 kHz center frequency and 1 kHz bandwidth.