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Deep graph neural networks (GNNs) have become a cornerstone of computational materials engineering because they can learn representations directly from crystal graphs. Yet a fundamental failure mode remains hidden when these models are applied to thermal transport: over-smoothing. After only a modest number of message-passing layers, node features converge to a single global vector, erasing the atom-resolved local environments that govern phonon scattering. The problem is dramatically amplified in large unit cells—structures containing 50 or more atoms, common in skutterudites, clathrates, and complex perovskites—because the graph diameter forces the model designer to choose between insufficient propagation depth (missing long-range interactions) and excessive depth (catastrophic smoothing). Lattice thermal conductivity κ emerges from local force constants, anharmonicity, and defect-sensitive scattering; over-smoothing replaces these variations with a featureless average, producing systematically erroneous predictions. This failure-mode analysis demonstrates that the central conflict is structural: thermal transport demands precisely the short- to medium-range distinctions that deep GNNs destroy. Four distinct failure modes are identified and mechanistically linked to the over-smoothing process. Detection principles based on feature similarity, depth sensitivity, and defect response are proposed. Mitigation strategies grounded in architectural modifications—residual connections, normalization, multi-scale pathways, and attention—are shown to preserve local information without sacrificing global coherence. The analysis reveals why standard crystal GNN architectures succeed for formation energies or band gaps yet fail systematically for thermal transport in realistic materials. By reframing over-smoothing as the dominant limitation rather than a minor training artifact, this work provides a conceptual roadmap for next-generation GNNs tailored to phonon physics.

Graph neural networks (GNNs) have transformed the modeling of periodic crystalline materials, enabling rapid prediction of formation energies, band gaps, elastic moduli, and interatomic forces directly from atomic coordinates. Early architectures including CGCNN and MEGNet established that message-passing on crystal graphs could rival density-functional theory (DFT) in speed while maintaining high accuracy for scalar properties. Subsequent advances introduced directional message passing (DimeNet, GemNet), equivariant architectures (E(3)-equivariant networks, MACE), graph attention mechanisms, and multi-scale approaches—each embodying distinct representational choices regarding node-edge features, symmetry handling, and information propagation. This systematic review synthesizes the literature not around incremental performance gains but around the fundamental representational trade-offs and hidden assumptions that govern model behavior in periodic systems. A taxonomy is developed organized by invariance versus equivariance, distance-only versus directional versus angular features, shallow versus deep message passing, and global pooling strategies. Four core trade-offs are analyzed: invariance against equivariance, local against global information capture, model depth against over-smoothing, and computational cost against expressivity. Beyond these, seven rarely articulated hidden assumptions are exposed—cutoff-radius sufficiency, primitive-cell representativeness, distance-only edge sufficiency, global-pooling adequacy, cubic-crystal benchmark bias, DFT-label perfection, and i.i.d. data assumptions—each critically limiting generalization to real-world materials discovery contexts. Empirical comparisons consistently favor newer architectures on standard benchmarks yet rarely isolate the contribution of individual design choices or report failure modes for low-symmetry crystals, extrapolation tasks, or long-range physics. Persistent gaps remain in long-range interaction modeling, uncertainty quantification, extrapolation capability, multi-property trade-offs, and interpretability. By reframing the crystal GNN literature through these lenses, this review offers a structured roadmap for future architecture development that prioritizes robustness and transparency over raw benchmark scores.