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Rotational invariance, a core design principle in graph neural networks (GNNs) for materials property prediction, has enabled remarkable accuracy for scalar quantities such as formation energy and band gap yet becomes a fundamental liability when the target property is a tensor of rank two or higher. Anisotropic elastic constants, which describe the directional stiffness of crystals and enter engineering design as a 6×6 Voigt matrix with up to 21 independent components in triclinic systems, must transform covariantly under rotation; any architecture that collapses all orientational information into a single invariant scalar cannot, in principle, recover the required tensorial structure. This failure-mode analysis articulates four distinct mechanisms by which invariance induces systematic error—diagonal indistinguishability, off-diagonal blindness, shear underspecification, and symmetry-induced degeneracy—and demonstrates how each arises directly from the interplay of global pooling, distance-only edge features, and symmetry averaging that characterize rotationally invariant models such as CGCNN, MEGNet, and SchNet. Detection principles based on equality tests, anisotropy-ratio checks, and differential error audits provide practitioners with practical diagnostics, while mitigation principles centered on equivariant architectures, directional encoding, and stress-tensor multi-task learning chart a clear path toward reliable tensorial prediction. The implications extend beyond elasticity to any directional property in low-symmetry crystals and call for a principled redesign of materials GNNs that treats invariance as a deliberate choice rather than a default.

Neural networks exhibit a pronounced spectral bias, preferentially converging to low-frequency components of target functions while struggling with high-frequency details, as governed by the neural tangent kernel and the frequency principle. In the domain of materials science, accurate prediction of atomic forces in periodic crystals is essential because high-frequency force components directly encode short-wavelength phonons that govern thermal transport, lattice thermal conductivity, phonon dispersion relations, and mechanical stability under strain. Periodic crystal graphs, formed by atoms connected through cutoff-based edges under periodic boundary conditions, amplify this spectral bias relative to molecular graphs or Euclidean data: the discrete spectrum of the graph Laplacian introduces pronounced gaps between low- and high-eigenvalue modes, and standard message-passing layers act as repeated low-pass filters that exponentially attenuate high-frequency signals. We develop a theoretical framework that decomposes force fields into graph-Laplacian eigenbasis components, couples the training dynamics to the neural tangent kernel on the crystal graph, and derives bounds on high-frequency force prediction error that grow exponentially with the spectral gap of the crystal graph. This analysis reveals why conventional graph neural networks systematically miss high-frequency forces and provides rigorous mathematical mechanisms—over-smoothing, spectral-gap bottlenecks, pooling-induced filtering, and limited receptive fields—that explain the failure. The resulting bounds and propositions imply concrete architectural modifications, including residual high-frequency pathways and spectral preconditioning, that can mitigate bias while preserving the inductive biases required for periodic materials modeling.

Machine learning interatomic potentials (MLIPs) are increasingly used to accelerate atomistic simulation in materials science, yet their evaluation remains dominated by test-set error measured on held-out data drawn from the same distribution as the training set. Although this practice often yields low mean absolute errors for energies and forces, it provides limited evidence that a model will remain reliable when applied to the distribution shifts that define real deployment settings, including new compositions, defect structures, elevated temperatures, and non-equilibrium trajectories. This article develops a conceptual framework that distinguishes transferability from in-distribution accuracy and defines it as the ability of an MLIP to preserve predictive fidelity within application-relevant tolerances under explicitly characterized shifts in the joint distribution of structures and quantum-mechanical labels. The framework identifies four canonical forms of shift in computational materials science—compositional, structural, thermodynamic, and dynamical—and shows why current benchmarking practices systematically obscure them. To address this limitation, the study proposes a shift-aware evaluation protocol built around five components: shift characterization, sensitivity analysis, extrapolation-distance estimation, robustness criteria, and standardized reporting. Within this framework, Maximum Mean Discrepancy is adapted as a quantitative diagnostic for pre-deployment assessment of train–target divergence, while transferability is evaluated through five complementary dimensions: accuracy under shift, graceful degradation, uncertainty alignment, physical consistency, and compositional extrapolation. By replacing the tacit IID assumption with an explicit framework for reasoning about distribution shift, this work offers a common basis for evaluating, reporting, and comparing MLIP transferability across benchmarks and deployment scenarios, thereby supporting more trustworthy AI-driven materials discovery.

Sequential learning is increasingly invoked in compositionally complex alloy modeling because the combinatorial scale of alloy design space, coupled with the cost of density-functional theory calculations and the staged nature of data acquisition, makes exhaustive one-shot training impractical. Yet under these conditions, neural networks are prone to catastrophic forgetting, whereby adaptation to newly introduced compositions, phases, or thermodynamic regimes degrades performance on previously learned ones. This article examines the conditions under which such failure emerges in compositionally complex alloys and shows that forgetting is not incidental but structurally induced by the interaction of shared representations, non-linear property landscapes, high compositional dimensionality, and sparse task-specific data. The analysis identifies four recurrent failure modes—elemental forgetting, concentration range collapse, phase space amnesia, and temperature-induced overwrite—and links them to underlying mechanisms of parameter interference, representation drift, output distribution shift, and gradient conflict. It further delineates the conditions that intensify these dynamics, including high compositional similarity, abrupt task transitions, rehearsal-free updates, and unstable optimization settings. By integrating detection criteria with mitigation strategies such as elastic weight consolidation, memory replay, modular architectures, and curriculum sequencing, the study provides a practical and conceptual framework for continual learning in alloy discovery. The central argument is that robust sequential learning in compositionally complex alloys requires forgetting-aware design at the levels of evaluation, architecture, and training protocol if materials machine learning is to support reliable lifelong modeling across expanding compositional spaces.

The term compositional generalization is increasingly invoked in machine learning for multi-principal element alloys (MPEAs), yet its meaning remains inconsistent and often conflated with interpolation or extrapolation. In standard machine learning, compositional generalization denotes the structured recombination of known components into novel configurations. Translating this concept to MPEAs is non-trivial due to their continuous composition space, permutation symmetries, and overlapping local atomic environments. Graph neural networks (GNNs), while effective for property prediction, are not inherently designed for such recombination beyond interpolation. This article identifies a resulting boundary problem and proposes an operational definition of compositional generalization based on four criteria: novel element–concentration co-occurrences, extrapolation beyond the convex hull of training compositions, controlled performance degradation, and permutation invariance. The framework clarifies widespread misuses of the term and provides a concrete basis for evaluating and designing models for MPEA discovery.

Smoothness constraints have become central to the training of machine-learning interatomic potentials, whether imposed explicitly through regularization or implicitly through Sobolev objectives that couple energies with forces. Although this strategy improves interpolation, stabilizes learned potential energy surfaces, and embeds physically motivated local structure, its broader consequence is more restrictive than current practice typically acknowledges. This article shows that smoothness does not merely regularize learning within the training domain; it also limits the model’s capacity to extrapolate beyond that domain in a mathematically structured way. Working in a Sobolev-space framework, the analysis demonstrates that extrapolation error grows at least exponentially with distance from the training set, with the growth rate controlled by the force-weighting parameter λ. On that basis, the article formalizes a set of fundamental trade-offs linking interpolation accuracy to extrapolation distance, force accuracy to energy extrapolation, strong smoothness priors to representational flexibility, and data efficiency to extrapolation range. The argument further identifies the mechanisms through which these tensions arise, including prior dominance, spectral filtering, gradient-matching interference, and optimization bias toward overly smooth solutions. The result is a unified theoretical account of why Sobolev-trained potentials perform so well near known configurations yet remain fragile in genuinely novel regions of configuration space. These findings reposition smoothness from a default virtue to a task-dependent design choice and establish the need for adaptive regularization, extrapolation-aware evaluation, and hybrid modeling strategies when machine-learning potentials are deployed in materials discovery settings that cannot avoid out-of-distribution prediction.

The standard practice in machine learning for small-crystal property prediction relies on random train-test splitting of datasets such as the Materials Project. This approach creates an illusion of generalization: models routinely report near-zero mean absolute errors on formation energies, band gaps, or elastic constants, yet these impressive figures reflect leakage of structural, compositional, and energetic information rather than genuine out-of-distribution capability. Random splitting fails because crystals are not independent and identically distributed; repeated prototypes, shared elemental combinations, local coordination environments, and clustered formation energies ensure that train and test sets remain statistically entangled even after random partitioning. We identify a typology of four generalization illusions—prototype, compositional, energy-range, and structural—that systematically mislead the field and explain why published “state-of-the-art” accuracies collapse under more rigorous evaluation regimes. The consequences are severe: wasted experimental validation efforts, inflated claims of progress, overinvestment in architectures that cannot extrapolate, and a delayed recognition of fundamental limitations in current graph-network approaches. We propose six alternative evaluation strategies—composition splits, prototype splits, time splits, structural dissimilarity splits, energy-extrapolation splits, and cross-database splits—that replace random partitioning with deliberate distribution shifts, thereby restoring scientific integrity to benchmark design in computational materials science.

Open benchmark suites for machine learning interatomic potentials should include systematic failure cases as a core evaluation component rather than relying solely on leaderboard rankings based on average error metrics. Leaderboard-only benchmarks can obscure critical weaknesses, encourage overfitting to curated test sets, and provide limited guidance for real-world deployment. In contrast, failure-inclusive benchmarks reveal model limitations across challenging regimes such as compositional complexity, structural disorder, thermodynamic extremes, dynamical instability, numerical breakdown, and extrapolation beyond the training distribution. This position paper argues that making failure cases mandatory would improve transparency, support informed model selection, guide data acquisition, and strengthen reproducibility in materials machine learning. A practical typology of failure modes and a set of benchmark design principles are proposed to help shift evaluation from competitive ranking toward diagnostic understanding. Redesigning open benchmarks in this way is essential for building trustworthy and scientifically useful ML potentials.

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.

Phonon spectra offer a uniquely demanding benchmark for graph neural network (GNN) force fields because they interrogate the second-derivative structure of the potential energy surface that governs lattice dynamics, thermal transport, and vibrational stability in materials. Yet direct comparison between GNN-derived and density functional theory (DFT) phonon spectra is frequently compromised by spectral leakage introduced through finite supercell truncation, displacement amplitude selection, q-point undersampling, Fourier interpolation, and post-processing broadening. These numerical effects can either conceal genuine deficiencies in the learned force field or generate apparent discrepancies that do not reflect model behavior. This article develops a hierarchical, leakage-aware validation framework that addresses this problem through progressive levels of scrutiny. The framework begins with baseline agreement in energies and forces, then advances to phonon density of states validation, q-resolved dispersion analysis, and finally a reproducible multi-metric assessment of spectral similarity. Progression through the hierarchy is conditional rather than automatic, such that higher-level claims are only made once lower-level numerical stability and model fidelity have been established. To separate methodological artifact from true representational error, the framework embeds explicit diagnostics based on supercell convergence, displacement sweeps, q-mesh refinement, interpolation cross-checks, and residual spectral analysis. It further introduces a standardized reporting protocol designed to make phonon-based validation transparent, comparable, and reproducible across studies of machine-learning interatomic potentials. By formalizing leakage control as an integral part of validation rather than an afterthought, the framework closes a critical gap between high-fidelity DFT phonon workflows and contemporary ML force-field development, enabling more credible assessment of GNN transferability in computational materials science.

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.

Out-of-distribution (OOD) generalization has become a central claim in machine learning for materials discovery, yet its meaning remains unstable when crystalline materials are represented as graphs. In current practice, the term is applied to qualitatively different forms of domain shift without specifying which properties of the training support have actually been violated, rendering many OOD claims difficult to verify or compare. This article addresses that conceptual gap through a boundary-focused analysis of crystalline graph learning. It shows that prevailing usage conflates multiple non-equivalent shifts and argues that conventional vector-space definitions of OOD are inadequate for periodic, graph-structured materials data. In response, the paper identifies four primary dimensions along which crystalline graph distributions depart from training support: composition, structure, scale, and condition. It then proposes a dimension-explicit redefinition of OOD, together with measurable boundary criteria, operational detection rules, and a per-dimension domain-shift score that can be computed from characterized training distributions. Boundary cases and gray zones are examined to clarify how formally defined thresholds should be interpreted in practice. By distinguishing OOD from anomaly detection, novelty detection, extrapolation, and domain adaptation, the framework establishes a more precise conceptual foundation for evaluating generalization in crystalline materials machine learning. The central contribution is not a new predictive model, but a falsifiable vocabulary for reporting domain shift. Adopting dimension-specific OOD reporting would make claims of robustness more reproducible, benchmark design more informative, and model evaluation more scientifically defensible in AI-driven materials discovery.

Equivariant graph neural networks have become central to data-efficient modeling of interatomic potentials, yet the mechanism underlying their empirical advantage remains insufficiently quantified. This work establishes a theoretical link between E(3)/SE(3) equivariance and sample complexity reduction in materials GNNs. By constraining the hypothesis space to functions that respect physical symmetries, equivariant architectures eliminate orbit-related redundancy and reduce the effective dimension of the learning problem. Within a PAC-style framework, we derive a bound showing that the sample complexity of an equivariant hypothesis class is reduced relative to its unrestricted counterpart by a factor proportional to the symmetry group size |G|, up to logarithmic terms. For discrete crystallographic groups, this yields finite reductions (e.g., 48× for cubic symmetry), while for continuous groups such as SO(3), the reduction becomes unbounded in the finite-data regime. The analysis relies on group-averaging projections and the induced contraction of VC dimension. These results provide a quantitative explanation for the observed data efficiency of architectures such as NequIP, MACE, and Allegro, and clarify the limitations of non-equivariant baselines such as SchNet. The framework situates symmetry as a statistically optimal inductive bias and offers principled guidance for designing data-efficient models in materials discovery.

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.

Uncertainty quantification in machine learning (ML) interatomic potentials remains fundamentally limited by the conflation of epistemic uncertainty, arising from incomplete sampling of configuration space, and aleatoric uncertainty, embedded in reference data generated by density-functional theory. Existing approaches provide internally consistent uncertainty estimates but collapse these distinct sources into a single scalar, obscuring the mechanisms governing model reliability and limiting principled decision-making. This work introduces a modular, architecture-agnostic framework that enforces explicit separation of epistemic and aleatoric contributions at the level of model design rather than post hoc analysis. The framework defines five interoperable components—a shared feature extractor, dedicated epistemic and aleatoric modules, an aggregation mechanism, and a calibration stage—whose interactions preserve disentanglement throughout training, inference, and downstream application. The resulting formulation transforms uncertainty into an operational diagnostic. Epistemic uncertainty identifies regions where additional data acquisition is informative, whereas aleatoric uncertainty defines the intrinsic accuracy ceiling imposed by the reference method. This separation restructures active learning by directing sampling toward reducible error, enables meaningful comparison between models through their uncertainty composition, and grounds performance evaluation relative to an explicit noise floor. The framework further introduces operational criteria that provide falsifiable tests of successful separation, ensuring that reported uncertainties remain interpretable and consistent across architectures. By decoupling learnable structure from irreducible variability, the proposed approach establishes a principled foundation for uncertainty-aware ML potentials, supporting more efficient data allocation, more reliable atomistic simulations, and more rigorous standards for model development in computational materials science.

E(3)-equivariant networks have become central to materials machine learning because they encode spatial symmetries and achieve high accuracy for non-magnetic systems. Their underlying assumptions, however, break down for magnetic ordering, where spin degrees of freedom, time-reversal symmetry breaking, and near-degenerate magnetic states are essential to the physics but absent from coordinate-only representations. This paper argues that the mismatch between E(3) symmetry and the magnetic space-group structure of real materials makes standard equivariant architectures fundamentally unreliable for magnetic ordering tasks. We show that this mismatch produces systematic failures, including the collapse of distinct magnetic states, the erasure of hidden degeneracies, and the inability to capture finite-temperature ordering phenomena. By framing these limitations in symmetry-theoretic terms, the analysis clarifies why architectural modifications that incorporate spin, time reversal, and multi-valued outputs are necessary for physically faithful prediction in magnetic materials discovery.

Material similarity functions as the implicit premise underlying domain adaptation in materials informatics, yet it remains largely undefined, rendering transfer claims difficult to evaluate and compare. This work establishes a task-dependent, operational definition of material similarity for composition-transfer learning, grounded in four orthogonal dimensions: composition, structure, property behavior, and local atomic environment. By examining current usage patterns, it reveals systematic ambiguities arising from single-dimension interpretations and demonstrates how these ambiguities contribute to inconsistent transfer outcomes. The proposed framework introduces threshold-based criteria and a weighted similarity score that jointly determine when transfer is justified, alongside boundary conditions that constrain successful adaptation. Gray zones and edge cases are analyzed to show how trade-offs across dimensions must be explicitly quantified rather than implicitly assumed. The resulting formulation repositions similarity as a measurable, task-specific precondition rather than a descriptive label, enabling pre-transfer validation and standardized reporting. This shift provides a conceptual foundation for reproducible domain adaptation, aligning materials machine learning with more rigorous principles of transferability and model generalization.

This theoretical study establishes a materials-specific depth limit for graph neural networks used in crystal property prediction by showing that early-layer gradient norms decay as ρ raised to the remaining propagation depth, where ρ denotes the spectral radius of the normalized message-passing operator. Because ρ remains strictly below unity for connected crystal graphs, repeated aggregation induces exponential attenuation of backward signals and renders optimization ineffective beyond a critical number of layers. For representative crystal topologies with ρ ≈ 0.9, the practically trainable regime contracts to roughly 10–20 layers, well below the depth that would be required to resolve genuinely long-range order in large unit cells, defective lattices, or disordered materials. The bound follows directly from spectral decomposition and therefore holds independently of weight initialization and, at the leading-order level, independently of activation choice. The analysis further distinguishes vanishing gradients from over-smoothing, clarifies how coordination environment, connectivity, normalization, graph size, and symmetry reshape the depth ceiling, and situates the result within the broader theoretical literature on recurrent networks and graph learning. The central implication is that depth cannot be treated as a universally beneficial scaling axis in materials GNNs. Instead, reliable model design requires spectrally informed architectural choices, including residual pathways, adaptive depth control, and shallow message passing combined with explicit long-range representations. By linking crystal graph topology to backward propagation dynamics, this work provides a rigorous theoretical basis for depth-aware model design in computational materials discovery.

Machine learning interatomic potentials have become central tools in computational materials engineering, promising accurate and scalable predictions of alloy properties. Benchmarks in the field routinely report impressive accuracies, such as energy mean absolute errors below 20 meV/atom and low force root-mean-square errors, leading many papers to conclude that their models generalize well to alloy systems. Yet when these same potentials are deployed on real-world disordered alloys—such as binary solid solutions or multi-principal-element high-entropy alloys—the accuracy collapses, often by an order of magnitude. The root cause lies in the benchmarking pipeline itself: training and testing occur almost exclusively on ordered crystal structures drawn from databases of intermetallic compounds, while disordered configurations, which dominate practical applications, are never evaluated. This critical critique identifies four primary sources of systematic overestimation. First, the near-universal reliance on ordered training and test sets creates an illusion of generalization that fails the moment configurational disorder is introduced. Second, random or composition-based splits on ordered data allow models to memorize recurring structural motifs rather than learn transferable physics. Third, even when special quasirandom structures are employed as proxies for disorder, their periodic nature and limited sampling of local environments produce a misleading “SQS mirage.” Fourth, energy-only metrics mask severe force-prediction failures that render molecular-dynamics simulations unstable in disordered systems. These benchmarking flaws have concrete consequences: overconfidence among practitioners, misallocation of experimental resources, and slowed progress in high-entropy alloy design. By drawing on the literature, this article demonstrates that the ordered-to-disordered gap is not an edge case but a fundamental and under-reported limitation. It proposes concrete reforms—mandatory disordered test sets, configurational sampling protocols, and separate reporting of ordered versus disordered performance—to restore credibility to ML potential benchmarks. Until these changes are adopted, claims of “alloy-ready” potentials should be treated with skepticism. The field must move beyond ordered-crystal comfort zones if machine-learned potentials are to deliver on their promise for the compositionally complex materials that define modern materials science.

Embedding domain knowledge into materials graph neural networks (GNNs) is not an optional enhancement for performance tuning; it is a fundamental requirement for models that must extrapolate reliably, operate with acceptable sample efficiency, and deliver physically consistent predictions. Purely data-driven architectures, which treat materials systems as generic graphs without built-in physical inductive biases, consistently fail when deployed beyond their training distributions — precisely the regime in which materials discovery operates. This Perspective articulates a clear position: the continued reliance on unconstrained, black-box GNNs represents a dead end for computational materials engineering. Three interlocking reasons compel this stance. First, materials discovery demands extrapolation to unseen compositions, structures, and conditions; unconstrained models offer no guarantees beyond interpolation. Second, density-functional theory (DFT) data remain scarce and computationally prohibitive, rendering sample-inefficient architectures unsustainable. Third, predictions must obey conservation laws, symmetry requirements, and thermodynamic limits; violations render long-term simulations unstable and untrustworthy. Four classes of domain knowledge must be embedded as hard constraints: (1) symmetry (E(3) equivariance, permutation invariance, space-group symmetries), (2) conservation laws (energy conservation, momentum balance), (3) physical scales and units (bounded energies, forces, and lengths), and (4) locality and smoothness principles (finite cutoffs, hierarchical many-body interactions). Recent literature provides compelling evidence that physics-constrained models — notably equivariant architectures — achieve comparable accuracy with an order-of-magnitude reduction in training data while maintaining physical consistency. Conversely, ignoring these constraints leads to extrapolation collapse, massive data waste, unphysical molecular-dynamics drift, and models that cannot be interpreted or transferred. The materials community must therefore treat physics-constrained design as the default, not an afterthought. We recommend concrete standards for model development, benchmark construction, and peer review. Only by making domain knowledge non-optional can machine learning accelerate, rather than merely decorate, the discovery of next-generation materials.

Equivariant neural networks have emerged as a transformative paradigm in computational materials science and molecular modeling, embedding rotational, translational, and permutational symmetries directly into the network architecture rather than learning them from data.A rapid sequence of innovations—from Tensor Field Networks to NequIP , MACE, Allegro, and the e3nn framework —has produced architectures that deliver state-of-the-art accuracy in interatomic potential prediction while dramatically reducing data requirements compared with invariant or non-symmetric baselines. This review synthesizes the architectural lineage of E(3)- and SE(3)-equivariant models developed specifically for materials and molecular systems, critically examines the theoretical guarantees provided by group and representation theory (universality, sample-complexity reduction, exact symmetry preservation, and conservation-law compliance), and contrasts these guarantees with empirical outcomes reported on standard atomistic benchmarks. Although equivariant networks provably approximate any continuous equivariant function and enforce exact roto-translational symmetry by construction, their practical advantages are most pronounced in the low-data regime and for vectorial properties such as forces. Limitations persist in composition-space extrapolation, long-range interaction modeling, magnetic systems, and computational scaling for higher-order equivariance. By systematically cataloguing these guarantees and gaps across 45 peer-reviewed contributions published 2017–2023, the review identifies a clear disconnect between mathematical assurances derived under idealized assumptions and the realities of finite datasets, complex material compositions, and large-scale simulations. The analysis concludes with open questions on optimal equivariance order, multi-group symmetry handling, and rigorous generalization bounds for continuous groups, offering a roadmap for future theoretical and practical advances in data-driven materials engineering.

High-entropy alloys (HEAs) and multi-principal element alloys (MPEAs) occupy an enormous compositional space that conventional computational approaches cannot fully explore. A five-element system with 10 % concentration steps already contains millions of distinct nominal compositions, each further multiplied by exponentially many atomic configurations arising from configurational disorder. Machine learning (ML) interatomic potentials have been proposed as a scalable solution to accelerate property prediction and materials design in this vast space. Yet the compositional generalizability of these potentials—their capacity to make reliable predictions for compositions and local environments lying outside the training distribution—remains largely unexamined in a systematic way. Most existing benchmarks focus on interpolation within narrow ranges of ordered or equiatomic compounds, leaving critical extrapolation scenarios untested. This conceptual framework article identifies four distinct but interrelated dimensions of compositional generalizability in HEA ML potentials: (i) element extrapolation, (ii) concentration interpolation, (iii) multi-element recombination, and (iv) local environment diversity. It proposes a four-component assessment framework—training-set characterization, test-set design, dimension-specific generalization metrics, and a structured validation protocol—that enables researchers to quantify generalization gaps without relying on performance numbers or simulation results. For each dimension, explicit validation strategies and success criteria are defined, grounded in the literature on special quasirandom structures, graph-network representations, and equivariant architectures. The framework is deliberately conceptual, emphasizing definitions, relationships among components, assessment criteria, and diagnostic reasoning rather than empirical data. By adopting this framework, the community can move beyond ad-hoc testing and develop ML potentials that truly generalize across the high-dimensional alloy landscape. The implications extend to more reliable high-throughput screening, accelerated discovery of novel HEAs, and clearer guidance for training-set design and model architecture choices. Ultimately, systematic assessment of compositional generalizability will help ensure that ML potentials fulfill their promise for complex concentrated alloys.

Transfer learning has become a dominant paradigm for addressing the persistent small-data limitation in computational materials science, particularly through pre-training graph neural networks on large-scale repositories and subsequent fine-tuning on task-specific datasets. This strategy assumes that universal atomic-scale representations—such as local coordination environments, bonding characteristics, and elemental embeddings—transfer effectively across domains. However, accumulating empirical evidence reveals a systematic and reproducible failure: in small-data regimes, fine-tuned models frequently underperform both zero-shot pre-trained models and models trained from scratch. This work presents a comprehensive failure-mode analysis demonstrating that such collapse is not incidental but structurally inevitable under common conditions in materials applications. Four interdependent mechanisms are identified—catastrophic forgetting, negative transfer, representation distortion, and overfitting amplification—arising from irreducible source–target domain mismatch, feature entanglement in equivariant graph architectures, and the statistical insufficiency of target datasets typically containing fewer than 10³ samples. Under these constraints, the corrective signal provided by target data is inadequate to overcome entrenched source biases or to reconfigure internal representations. Drawing exclusively on consolidated literature, we show that transfer learning failure emerges when domain similarity falls below critical thresholds and when data scarcity prevents stable optimization. The study further formalizes operational diagnostics—including baseline benchmarking, source-validation tracking, and learning-rate sensitivity analysis—and introduces mitigation strategies such as progressive unfreezing, elastic weight consolidation, replay-based regularization, and similarity-gated transfer decisions. By reframing transfer learning as a high-risk, condition-dependent strategy rather than a default solution, this work provides a principled foundation for robust model deployment in materials informatics. It challenges prevailing assumptions of universal transferability and advocates for systematic failure-mode reporting to ensure reliability in machine-learned interatomic potentials and property prediction workflows.

The reliability of machine-learned (ML) interatomic potentials in phase space sampling depends critically on whether sampled configurations lie within the interpolative domain of the training data or extend into extrapolative regimes. Despite its central importance, the interpolation–extrapolation distinction remains inconsistently defined across the literature. Existing single-metric approaches—such as convex-hull composition checks, descriptor-space distances, uncertainty estimates, and local-environment similarity—capture only partial aspects of high-dimensional configuration space and frequently yield conflicting classifications. This lack of a rigorous, unified boundary undermines active learning strategies, uncertainty quantification, benchmarking, and the safe deployment of ML potentials in safety-critical applications. This boundary/definitional article introduces a unified and operational framework that delineates the interpolation–extrapolation boundary through four independent and jointly necessary criteria: (C1) compositional coverage, (C2) local-environment similarity, (C3) configurational co-occurrence, and (C4) thermodynamic condition. A configuration is defined as interpolative only when all four criteria are simultaneously satisfied; violation of any criterion constitutes extrapolation. To replace binary classification, the framework further introduces a graded hierarchy of extrapolation—mild, moderate, and severe—based on the number and magnitude of violations. The proposed definitions are deliberately operational, relying exclusively on information available during training-set construction or simulation runtime, and are agnostic to model architecture. Their adoption enables standardized reporting, stratified benchmarking, improved calibration of uncertainty estimates, and more targeted active-learning workflows. By establishing a clear and reproducible boundary, the framework provides a principled foundation for evaluating model reliability during phase space exploration. This work advances the epistemic rigor of ML-driven materials modeling and supports the responsible and transparent deployment of data-driven interatomic potentials.

Transfer learning across chemical spaces is widely used in materials graph neural networks, yet its success declines sharply as source and target domains diverge. This work frames that limitation in information-theoretic terms by modeling chemical spaces as probability distributions over composition, structure, and properties. We identify mutual information between source and target as the key determinant of transferability and derive a conceptual lower bound on target error governed by source error, shared information, and irreducible noise. The analysis explains why transfer succeeds under strong elemental and structural overlap but fails when chemical spaces are weakly aligned. It also yields a practical criterion: assess domain overlap before fine-tuning. By establishing transferability as an information-constrained problem, the study provides a principled basis for deciding when adaptation is justified in materials GNNs.

“State-of-the-art” (SOTA) claims in materials graph neural networks are typically grounded in marginal improvements on standard benchmarks, yet such gains often reflect properties of the evaluation protocol rather than advances in generalization. This analysis demonstrates that widely used practices—particularly random train–test splits, inconsistent baselines, and selective reporting—systematically inflate reported performance. At the same time, critical constraints, including interpolation-dominated evaluation, computational cost, limited extrapolation, and dataset bias, remain largely unacknowledged. Drawing on the 2017–2023 literature, the study shows that these artifacts and omissions distort how progress is measured and interpreted. By reframing SOTA as a context-dependent rather than universal claim, it proposes a shift toward multi-split, multi-metric, and reproducible evaluation that more accurately reflects real-world materials discovery conditions.

Generative models for materials inverse design, including variational autoencoders, generative adversarial networks, and diffusion models, have rapidly emerged as powerful tools for proposing crystal structures conditioned on target properties. Yet, despite significant methodological progress, evaluation practices remain fragmented and inconsistent, limiting comparability and obscuring genuine scientific advancement. This review introduces a unified five-dimensional taxonomy—validity, novelty, diversity, property optimization, and stability—and uses it to diagnose systematic distortions in current reporting. Across the literature, metrics are defined heterogeneously, diversity is frequently omitted, stability is selectively assessed, and baseline comparisons are often absent. These inconsistencies inflate reported performance and prevent reliable benchmarking. In response, a minimal reporting standard is proposed, requiring transparent multi-metric evaluation, explicit dataset and split disclosure, baseline-controlled property assessment, distribution-level reporting, and computational-cost transparency. Establishing such community-agreed protocols is essential for transforming generative materials research into a reproducible, comparable, and cumulatively advancing field.

Benchmarking has become central to the development of machine learning interatomic potentials (MLIPs), yet the epistemic reliability of reported comparisons remains insufficiently scrutinized. This review synthesizes prevailing practices and demonstrates that current evaluation protocols systematically misrepresent model progress. A coherent taxonomy of methodological failure emerges, spanning opaque data handling, structurally flawed train–test partitioning, restricted metric selection, weak baseline construction, limited reproducibility, and the near absence of extrapolation analysis. Under these conditions, widely cited performance indicators—such as sub-10 meV/atom energy MAE or sub-0.1 eV/Å force RMSE—primarily capture interpolation within constrained training distributions, offering limited insight into generalization, dynamical stability, or deployment viability. A related deficiency lies in the systematic exclusion of physically and computationally salient regimes, including long-range interactions, finite-temperature behavior, low-symmetry and disordered structures, calibrated uncertainty, defect-rich configurations, and explicit cost–accuracy trade-offs. Existing benchmark suites, including Materials Project–derived datasets, QM9 adaptations, COMP6, and bespoke collections, inherit these constraints, reinforcing an evaluative paradigm that privileges narrow optimization over robust, application-relevant performance. Recasting benchmark outcomes as contingent on methodological design rather than intrinsic model capability reveals how evaluation choices implicitly structure model rankings. In response, this work advances a set of directly implementable standards: diversified splitting strategies, distribution-aware multi-metric reporting, transparent baseline inclusion, controlled extrapolation regimes, complete reproducibility artifacts, and normalized cost accounting. Aligning benchmarking practice with these principles is necessary to transition from incremental leaderboard gains toward reliable and transferable interatomic potentials for materials discovery.

High-risk materials predictions in fields such as nuclear reactor design, aerospace component qualification, and advanced energy storage systems demand not only accurate property forecasts but also uncertainty estimates that can be trusted under regulatory scrutiny. Materials graph neural networks have emerged as powerful tools for property prediction across composition and structure spaces, yet the overwhelming majority output a single scalar uncertainty that conflates two fundamentally different sources: epistemic uncertainty arising from incomplete or sparse training data and aleatoric uncertainty arising from irreducible noise in the underlying data-generation process itself. This conceptual framework paper demonstrates that failure to separate these uncertainty types leads to flawed risk assessments and inefficient decision-making. Epistemic uncertainty signals the need for additional data collection or targeted active learning, whereas aleatoric uncertainty signals the need for higher-fidelity data sources such as improved density-functional approximations or experimental validation. The proposed modular framework equips materials graph networks with dedicated estimators for each uncertainty type, an aggregator that applies risk-adjusted safety margins, a decision gate that triggers appropriate remediation actions, and a calibration certificate required for deployment in safety-critical contexts. Operational criteria are defined to validate the separation in practice, including data-scaling behavior, source-identification tests, and active-learning efficiency. By enabling precise mapping of uncertainty to actionable protocols, the framework bridges a critical gap between current uncertainty-quantification practices in graph neural networks and the stringent reliability requirements of high-risk materials engineering. It builds directly on foundational distinctions introduced for deep learning while adapting them to the unique challenges of crystal-graph representations and multi-fidelity materials data. The result is a conceptual blueprint that supports safer model deployment, more efficient discovery campaigns, and clearer pathways to regulatory approval.

Active learning is widely used in materials discovery to reduce the number of expensive density functional theory calculations required for surrogate-model training. Its dominant acquisition rule, uncertainty sampling, assumes that the most uncertain configuration will also yield the greatest information gain. Although this logic performs well for many bulk properties, it breaks down for defect formation energies. In this setting, uncertainty sampling repeatedly selects uninformative structures, misallocates computational budget, and fails to reach the defective configurations that govern vacancy, interstitial, and substitutional behavior in technologically important materials. This failure reflects a structural mismatch between the acquisition rule and defect physics. Defect configurations are rare in configuration space, energetics are highly localized, and DFT labels often contain substantial aleatoric noise from finite-size effects, charge corrections, and supercell artifacts. These conditions weaken the link between predictive uncertainty and useful learning signal, while representation bias in models trained mainly on perfect crystals further erodes selectivity. This study develops a failure-mode analysis of uncertainty sampling for defect formation energies, identifying recurrent breakdowns in sampling, representation, calibration, and budget use. It also outlines practical detection principles and defect-aware mitigation strategies, including initialization with defective structures, hybrid acquisition functions, epistemic-only scoring, and budget partitioning. The central implication is that active learning for defect discovery cannot rely on generic uncertainty-based querying. Effective acceleration in this domain requires acquisition strategies designed around the rarity, locality, and noise structure of defect energetics.