Controllable and scalable gradient-driven optimization design for two-dimensional metamaterials based on deep learning

Abstract

A novel gradient-driven rapid optimization design method based on deep learning is proposed to design two-dimensional irregular elastic metamaterials (EMMs). We develop a design network comprising a conditional topology generator (TG) and a bandgap predictor (BGP). TG is applied to controllably generate candidate topological structures with geometric constraints, while BGP serves as a surrogate model linking EMM structures with their bandgaps. Utilizing automatic differentiation techniques, the error gradients of design variables are computed on the design network and then passed to gradient-driven optimization algorithms to optimize the design variables until the target bandgap is achieved. The design variables in optimization algorithms are independent of the design network’s input features, allowing adaptation to changes in design factors without retraining the network, thereby providing scalability. The testing results show that the proposed method can efficiently and rapidly design EMM structureswith significant consistency to target bandgaps. Additionally, further comparative analysis reveals that the irregular topological structures enable bandgap broadening, generation of new bandgaps, and band flattening. The proposed method demonstrates remarkable feasibility and efficiency in the design of irregular EMM structures, and offers practical controllability and scalability.