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Uncertainty quantification (UQ) has become indispensable for the trustworthy deployment of machine learning interatomic potentials (MLIPs) in materials science and molecular modeling, where predictions of energies, forces, and derived properties directly inform high-stakes decisions in materials discovery, long-time-scale molecular dynamics, and autonomous design workflows. Without reliable uncertainty estimates, MLIPs risk propagating errors that compromise simulation stability, mislead experimental prioritization, or produce unphysical results in extrapolation regimes critical to novel alloy or molecular discovery. This review synthesizes the literature on UQ methods specifically developed for or applied to MLIPs, drawing exclusively from the compiled reference set to provide a focused, critical overview of progress during this formative period. The scope is deliberately restricted to UQ techniques for interatomic potentials themselves (including GAP, DeepMD, ANI-series, SchNet-derived, and E(3)-equivariant models such as NequIP), excluding standalone ML property prediction unless the method directly supports force-field uncertainty. A systematic taxonomy organizes existing approaches into five methodological families—Bayesian and probabilistic methods, ensemble methods, Gaussian process and kernel methods, conformal prediction and frequentist methods, and heuristic and ad hoc methods—highlighting their distinct mathematical foundations and practical implementations in MLIP contexts. Hidden assumptions pervading these families are identified and dissected, including independence of atomic errors, Gaussianity of predictive distributions, homoscedasticity across chemical space, kernel-imposed smoothness in Gaussian processes, approximation quality in variational or Monte-Carlo inference, and exchangeability in conformal frameworks. These assumptions frequently remain unstated yet profoundly influence calibration and reliability when MLIPs are deployed in production simulations. Unresolved questions are articulated with precision: how to treat correlated uncertainties along molecular-dynamics trajectories, the absence of a true ground-truth uncertainty given DFT approximations, the prohibitive computational overhead of scalable UQ, evaluation under distribution shift, vectorial uncertainty for forces rather than scalar energies, detection of physical inconsistencies, and hierarchical fusion of model, data, and ab-initio uncertainties. Future outlook points toward integrated UQ-driven active learning, force-aware uncertainty representations, and hybrid methods that balance calibration, sharpness, and efficiency for next-generation autonomous materials engineering.

Reproducibility has emerged as a critical bottleneck in data-driven materials engineering, particularly as graph neural networks (GNNs) and associated uncertainty quantification (UQ) methods are increasingly embedded in high-stakes discovery pipelines. While advances in conformal prediction, Bayesian inference, and ensemble techniques have improved predictive reliability, their practical deployment remains constrained by fragmented workflows, opaque data provenance, and inconsistent reporting standards. This review reframes uncertainty-aware materials modeling through the lens of reproducible workflows, tracing the pipeline from dataset construction and curation to model training, calibration, and deployment. Drawing on peer-reviewed studies, we integrate methodological advances in UQ with emerging practices in data governance, experiment tracking, and model documentation. The analysis reveals that uncertainty estimates are only as trustworthy as the workflows that generate them: biases in dataset composition, undocumented preprocessing steps, and inconsistent calibration protocols systematically undermine reliability, even when state-of-the-art UQ methods are applied. We argue that reproducibility must be treated as a first-class design constraint, requiring standardized data provenance tracking, version-controlled training pipelines, and model cards that explicitly document uncertainty behavior, calibration performance, and failure modes. By linking UQ theory with reproducible systems design, this work establishes a framework for trustworthy materials graph learning in which uncertainty is not merely computed but auditable, interpretable, and transferable across applications.