Deep Learning-Accelerated inverse design of NURBS-Based phononic crystals with customized bandgaps

Phononic crystals (PnCs) enable effective control of elastic wave propagation through the formation of frequency bandgaps, but their design is computationally demanding due to the complex relation between geometry and dynamic behavior. To address this challenge, this study proposes a deep learning–accelerated inverse design framework for non-uniform rational B-spline (NURBS)-based phononic crystals. In the proposed approach, a NURBS parameterization scheme is employed to represent the unit-cell geometry using control points and weights, enabling smooth, fabricable, and highly flexible curved-edge design. A deep neural network (DNN) is trained to accurately predict the full dispersion relations of PnCs, replacing finite element (FE) analysis with millisecond-level inference. The trained model is integrated with an improved real-coded genetic algorithm (IRGA) to perform global optimization under multiple objective functions, including single-bandgap maximization, dual-bandgap enhancement, target-frequency bandgap control, and dispersion customization. The results demonstrate that the DNN surrogate achieves an R2 of 0.996, with 84.2% of test samples exhibiting a mean relative error below 4.5%. The DNN–IRGA framework efficiently identifies optimized geometries that exhibit desired bandgap properties, validated by FE simulations and a 3D-printed experimental specimen showing strong attenuation (up to − 85 dB) within the predicted bandgap. This work establishes a unified framework that bridges geometric parameterization, deep learning prediction, and inverse optimization, providing a powerful tool for rapid and customizable bandgap design of two-dimensional NURBS-based phononic crystals.