The synergy of geometric tolerance factor and machine learning in discovering stable materials

Assessing stability remains a fundamental prerequisite for deploying materials across a wide range of applications, including batteries, catalysts, and photovoltaics. However, first-principles stability checks such as phonon dispersion and energy above hull calculations typically require days to weeks of computing time per composition, creating a critical bottleneck for truly high-throughput discovery. In this Perspective, we highlight the underutilized potential of geometric tolerance factors (T_f) as lightweight yet informative indicators for rapid stability assessment. First, we review the T_f developed for representative materials systems, including perovskites, spinels, and garnets, and analyze recent cases where such indicators have been integrated into AI-driven materials discovery. Then, we identify key open challenges in designing T_f that is both accurate and generalizable, as well as in effectively incorporating them into AI frameworks. The potential solutions, including active learning for multi-composition structure, electron density profile-based learning for ionic radii estimation, diffusion model for thermodynamic and kinetic stability, are proposed to address these challenges. The synergy between T_f-based heuristics and advanced AI models has the potential to triage vast compositional spaces before committing to expensive first-principles stability validation, thereby enabling broader innovations in materials design and deployment.