Phononic Metamaterial Design via Transfer Learning-Based Topology Optimization Framework

Abstract Phononic metamaterials are widely used to attenuate wave propagation. However, designing the structure of phononic metamaterial remains a challenge. In this work, we proposed a transfer learning-based design framework to accelerate the design of phononic metamaterials with wide bandgaps. First, we establish a transfer learning model with convolutional layers. This model leverages the knowledge learned from the structure-elasticity dataset to predict the structure-phononic property relationship. We demonstrate that the transfer learning model achieves good prediction accuracy with limited training data. We also discuss the feasibility of using the structure-elasticity model to benefit the design optimization of phononic metamaterials. Then we propose a transfer learning-based design framework for the topology optimization of cellular metamaterial for optimal phononic properties (bandgap width). Parametric optimization is conducted to find the optimal structure features that lead to the widest bandgap. The structure features are represented by an embedding layer shared by the structure-elasticity and the structure-phononic property models. Next, the corresponding elastic stiffness constants are obtained via the structure-elasticity model. Then topology optimization is employed to generate the metamaterial structural images corresponding to the target elastic stiffness constant values. The effectiveness of the proposed design framework is validated by comparing the performances of design candidates with existing designs.