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 constructed to lie outside the training distribution. Our results reveal a practical limitation of size-unaware uncertainty criteria and motivate size-aware calibration for more reliable OOD detection in large-scale atomistic simulations.
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