High-dimensional Bayesian optimization for metamaterial design

Metamaterial design, encompassing both microstructure topology selection and geometric parameter optimization, constitutes a high-dimensional optimization problem, with computationally expensive and time-consuming design evaluations. Bayesian optimization (BO) offers a promising approach for black-box optimization involved in various material designs, and this work presents several advanced techniques to adapt BO to address the challenges associated with metamaterial design. First, variational autoencoders (VAEs) are employed for efficient dimensionality reduction, mapping complex, high-dimensional metamaterial microstructures into a compact latent space. Second, mutual information maximization is incorporated into the VAE to enhance the quality of the learned latent space, ensuring that the most relevant features for optimization are retained. Third, trust region-based Bayesian optimization (TuRBO) dynamically adjusts local search regions, ensuring stability and convergence in high-dimensional spaces. The proposed techniques are well incorporated with conventional Gaussian processes (GP)-based BO framework. We applied the proposed method for the design of electromagnetic metamaterial microstructures. Experimental results show that we achieve a significantly high probability of finding the ground-truth topology types and their geometric parameters, leading to high accuracy in matching the design target. Moreover, our approach demonstrates significant time efficiency compared with traditional design methods.