Insect wings are formed by intricate combinations of flexible membranes and rigid veins; such a structure enables excellent flight performance, adaptability to aerodynamic forces, and biological functions. Comprehensive understanding of the interplay between wing patterning and flight dynamics has however not been achieved yet due to enormous variability of natural patterns and the extreme complexity of the modeling wing-air interactions. Therefore, the design of a pattern for artificial flexible wings is challenging. In contrast to other studies mimicking biological patterns of insect wings, we propose usage of metamaterials principles to enable controllable dynamics, and machine-learning techniques to solve a related multi-parameter design optimization problem. We demonstrate the advantages of this hybrid approach by finding practical patterns with improved target property – enhanced lift. The obtained designs were manufactured by means of a low-cost fused deposition modeling (FDM) 3D-printer from a single commercially available thermoplastic polyurethane (TPU) and revealed the required balance between the rigidity of metamaterial “veins” and the flexibility of the wing base. Extensions of our approach to other designs or analyses of other moving structures offer straightforward benefits in tackling a wide range of computationally complex aerodynamic and vibroacoustic problems.