Machine learning-enabled development of high performance gradient-index phononic crystals for energy focusing and harvesting

Gradient-index (GRIN) phononic crystals (PnCs) offer an excellent platform for various applications, including energy harvesting via wave focusing. Despite its versatile wave manipulation capability, the conventional design of GRIN PnCs has thus far been limited to relatively simple shapes, such as circular holes or inclusions. In this study, we propose a GRIN PnC comprising of unconventional unit cell designs derived from machine learning-based optimization for maximizing elastic wave focusing and harvesting. A deep neural network (NN) is trained to learn the complicated relationship between the hole shape and intensity at the focal point. By leveraging the fast inference of the trained NN, the genetic optimization approach derives new hole shapes with improved focusing performance, and the NN is updated by augmenting the new dataset to enhance the prediction accuracy over a gradually extended range of performance via active learning. The optimized GRIN PnC design exhibits 3.06 times higher wave energy intensity compared to the conventional GRIN PnC with circular holes. The performance of the best GRIN PnC within the allowable range of our machining tools was validated against experimental measurements, which shows 1.35 and 2.35 times higher focused wave energy intensity and energy harvesting output, respectively.