Engineered architectured Materials, such as metamaterials with periodic patterns, achieve superior properties compared with their stochastic counterparts, such as the random microstructures found in natural materials. The primary research question focuses on the feasibility of learning advantageous microstructural features from stochastic microstructure samples to facilitate the generative design of periodic microstructures, resulting in unprecedented properties. Instead of relying on brainstorming-based, ad hoc design inspiration approaches, we propose an eXplainable Artificial Intelligence (XAI)-based framework to automatically learn critical features from the exceptional outliers (with respect to properties) in stochastic microstructure samples, enabling the generation of novel periodic microstructure patterns with superior properties. This framework is demonstrated on three benchmark cases: designing 2D cellular metamaterials to maximize stiffness in all directions, to maximize the Poisson’s ratio in all directions, and to minimize the thermal expansion ratio. The effectiveness of the design framework is validated by comparing its novel microstructure designs with known stochastic and periodic microstructure designs in terms of the properties of interest.