Does System Size Matter in Uncertainty Quantification for Machine Learning Interatomic Potentials?

Chayaphol Lortaraprasert, Nontawat Charoenphakdee, Wenwen Li, Yong-Bin Zhuang, Yuta Tsuboi

Machine-learning interatomic potentials (MLIPs) commonly use uncertainty estimates to flag out-of-distribution (OOD) configurations and select structures for active learning. A key question is whether the resulting structure-level uncertainty scores remain comparable across different system sizes. A common practice is to aggregate per-atom uncertainties by their mean or maximum and compare the resulting score against a fixed threshold, implicitly assuming such comparability. We test this assumption across several in-distribution (ID)/OOD pairs by characterizing both aggregations as a function of atom count. The two aggregations exhibit distinct size dependencies. Mean aggregation remains size-independent for homogeneous systems but loses sensitivity to defects in large cells. In contrast, maximum aggregation grows with system size for ID systems while remaining approximately flat for defect-containing systems, narrowing the ID-OOD gap in a manner consistent with extreme-value statistics. Although highly uncertain atoms in large structures may indicate novel local environments, retraining on these structures yields little improvement, in contrast to retraining on OOD structures…