Topology-Informed Active Learning for Sequential Materials Screening

The discovery of metal--organic frameworks (MOFs) requires searching an enormous space of candidate structures, where every property evaluation requires an expensive molecular simulation. We introduce an active learning framework whose surrogate models are built on topological representations of pore structure obtained by persistent homology, a data analysis tool that records how the accessible pore space changes across all length scales. On a pool of 10,000 hypothetical MOFs screened for xenon and krypton uptake, we show that (i) topological surrogates are substantially better calibrated than geometric descriptor baselines, with 95\% prediction interval coverage rising from $\approx 0.55$ to $\approx 0.94$; (ii) hybrid surrogates combining topological and geometric information consistently outperform either representations alone, recovering up to $1.7\times$ more of the true top performing MOFs under region-based active learning. Our results establish persistent homology as a practical and effective representation for sequential materials discovery.