Fig. 5: Optimized \({E}_{11}^{max}\) microstructures (ODFs) in the orientation space for an example of cubic material and an example of hexagonal material discovered by different methods.

An example of cubic material ID = 15716 discovered by a Best-of-∣ODF∣, b Gradient-based method, c Previous ML-based method, d–f AI-driven framework. An example of hexagonal material ID = 14815 discovered by g Best-of-∣ODF∣, h Gradient-based method, i Previous ML-based method, j–l AI-driven framework.