DNN-based shape optimization of gradient-index phononic crystals with sensitivity analysis for tunable focal position and robust energy harvesting

Gradient-index (GRIN) phononic crystals (PnCs) enable energy harvesting (EH) by focusing elastic waves into electrical energy. Efficient EH requires maximizing focused wave intensity, typically achieved by tuning the GRIN PnCs unit-cell shape. However, existing designs often exhibit energy concentration near the GRIN lens boundary and incorporate narrow gaps and sharp corners, making them susceptible to manufacturing errors and limiting their practical applicability. Understanding the potential performance changes caused by manufacturing errors is important because geometrical alterations can compromise wave-focusing performance. Therefore, this study aims to optimize the unit-cell shape toward maximum focused intensity at the desired locations for EH devices. To assess manufacturability, the effects of minor geometric variations on the focal position and focused intensity are evaluated via a sensitivity analysis. The optimal shape is derived using a deep neural network (DNN) surrogate model trained to predict focal position and focused intensity. This model accelerates a genetic algorithm (GA) used to perform the optimization. Our optimized designs exhibit 1.5 to 2.0 times higher focused intensity across the target focal positions compared with the conventional design. Thus, these optimal shapes, along with their sensitivity analysis results, provide practical guidelines for defining manufacturing tolerances and achieving consistent, efficient EH performance.