A Straightforward Gradient-Based Approach for High-Tc Superconductor Design: Leveraging Domain Knowledge via Adaptive Constraints

Materials design aims to discover novel compounds with desired properties. However, prevailing strategies face critical trade-offs. Conventional element-substitution approaches readily and adaptively incorporate various domain knowledge but remain confined to a narrow search space. In contrast, deep generative models efficiently explore vast compositional landscapes, yet they struggle to flexibly integrate domain knowledge. To address these trade-offs, we propose a gradient-based material design framework that combines these strengths, offering both efficiency and adaptability. In our method, chemical compositions are optimised to achieve target properties by using property prediction models and their gradients. In order to seamlessly enforce diverse constraints, including those reflecting domain insights such as oxidation states, discretised compositional ratios, types of elements, and their abundance, we apply masks and employ a special loss function, namely the integer loss. Furthermore, we initialise the optimisation using promising candidates from existing dataset, effectively guiding the search away from unfavourable regions and thus helping to avoid poor solutions. Our approach demonstrates a more efficient exploration of superconductor candidates, uncovering candidate materials with higher critical temperature than conventional element-substitution and generative models. Importantly, it could propose new compositions beyond those found in existing databases, including new hydride superconductors absent from the training dataset but which share compositional similarities with materials found in literature. This synergy of domain knowledge and machine-learning-based scalability provides a robust foundation for rapid, adaptive, and comprehensive materials design for superconductors and beyond.