Self-supervised AI for decoding and designing disordered metamaterials

Disordered microstructures are key to the distinct multifunctional properties of many natural materials. However, understanding the relationship between their microstructures and physical functions remains formidable, hindering engineering applications. Here, we introduce a physics-guided, self-supervised artificial intelligence (AI) framework called generative networks for disordered metamaterials (GNDM), trained on a progressively expanding dataset starting from a few initial samples. We integrate a formula writing module in the training process of neural networks to enforce the identification of the most selective set of hidden geometric invariants that dictate bulk properties. By inversely solving the formulae, GNDM manipulate disordered geometric features to extrapolate property space and design previously unknown structures via its generator module, validated by experiments. GNDM offers an all-in-one AI framework that closes the loop of feature extraction, property prediction, formula writing, and inverse design, unraveling the regulative role of disorder, a critical challenge in the study of metamaterials with complex microstructures.