Accelerated discovery of ultraincompressible, superhard materials via physics-enhanced active learning

The discovery of ultraincompressible, superhard materials is constrained by the high computational cost of screening vast chemical spaces using density functional theory (DFT). To address this, we introduced a machine learning framework that integrates crystal graph convolutional neural networks (CGCNN) with physics-based atomic stiffness descriptors derived from bond-level mechanical models. This physics-enhanced approach achieves superior accuracy in predicting bulk and shear moduli while maintaining interpretability. By employing active learning to efficiently prioritize candidates from a pool of over 2.7 million inorganic crystals, we reduced the reliance on DFT validation and identified 632 ultraincompressible materials (bulk modulus > 400 GPa) and 15 superhard crystals (Vickers hardness > 40 GPa). Remarkably, over 90% of these ultraincompressible candidates and over 60% of these superhard materials are previously uncharacterized. Structural analysis revealed that ultraincompressibility predominantly emerges in low-symmetry intermetallic compounds showing strong Os/Re/Ir compositional preference, whereas superhard characteristics primarily associate with ceramic-based systems, including covalent compounds formed by light elements and transition metal-light element compounds exhibiting partial covalent bonding. Our methodology not only expands the known family of ultraincompressible, superhard materials but also overcomes a major scalability barrier in computational material discovery. These predictions, rigorously validated through DFT, establish a physics-grounded, data-driven pipeline to accelerate the exploration of extreme-performance materials for industrial applications.