Fig. 5: Robustness for single-target and dual-target customization tasks.

a–d Probability distributions of generated resonant frequencies for the X-tilting, Y-tilting, Rotational, and Flexural mode, respectively. Three target frequencies are assigned for each mode: a 0.18 MHz, 0.61 MHz, 1.04 MHz for the X-tilting mode, b 0.18 MHz, 0.61 MHz, 1.04 MHz for the Y-tilting mode, c 0.25 MHz, 0.48 MHz, 0.71 MHz for the Rotational mode, and d 0.53 MHz, 1.65 MHz, 2.77 MHz for the Flexural mode. For each target, 300 designs are generated. The average accuracy for the physically feasible targets is 99.5%, 99.4%, 99.6%, and 99.4% for the X-tilting, Y-tilting, Rotational, and Flexural mode, respectively. For the physically infeasible targets, the closest frequencies generated are 0.27 MHz, 1.00 MHz (X-tilting), 0.25 MHz, 0.99 MHz (Y-tilting), 0.26 MHz, 0.67 MHz (Rotational), and 0.71 MHz, 2.65 MHz (Flexural). These designs exhibit performances that are close to or even beyond the boundaries of the dataset, which are 0.25 MHz, 0.99 MHz (X-tilting), 0.24 MHz, 0.98 MHz (Y-tilting), 0.23 MHz, 0.64 MHz (Rotational), and 0.65 MHz, 2.57 MHz (Flexural). e Dual-target test for physically feasible frequencies of 0.61 MHz for both X-tilting and Y-tilting modes, with the 600 generated designs clustering tightly around the target. The average accuracy is 97.7%. f Dual-target test for physically infeasible frequencies of 1.04 MHz for both X-tilting and Y-tilting modes, showing a band-like distribution of solutions parallel to the line y = -x, with the 600 generated designs demonstrating an average accuracy of 77.2%.