Atomistic simulations, particularly molecular dynamics (MD), have become indispensable tools for materials discovery, drug design, and understanding fundamental physical phenomena. However, the reliability of these simulations hinges critically on the accuracy of interatomic potentials—mathematical functions that approximate the complex quantum mechanical interactions between atoms. Despite decades of development, significant discrepancies persist between simulation predictions and experimental observations, often spanning orders of magnitude in critical applications such as nanofluidics, catalysis, and mechanical properties . These discrepancies arise fundamentally from the approximate nature of interatomic potential formulations, whether classical empirical potentials or modern machine learning interatomic potentials (MLIPs). The consequences of unquantified uncertainty can be severe: materials designed in silico may fail in practice, computational screening may miss promising candidates, and scientific conclusions may rest on numerically unstable foundations.
\nThe field of uncertainty quantification (UQ) for atomistic simulations has therefore emerged as a critical research frontier, with the goal of providing rigorous, computationally tractable estimates of prediction reliability. Traditional approaches have focused primarily on quantifying uncertainty within the parameter space of a single potential functional form—estimating how parameter calibration affects predictions. However, this paradigm fundamentally neglects a potentially larger source of error: systematic bias arising from the choice of functional form itself. Different potential formulations—whether Lennard-Jones, embedded atom method (EAM), spectral neighbor analysis method (SNAP), or various neural network architectures—encode different physical approximations and inductive biases that can lead to systematically divergent predictions even when individually well-calibrated.
\nThe proliferation of MLIPs has intensified this challenge. Frameworks such as DeePMD, MACE, NequIP, Allegro, CHGNet, EquiformerV2, SevenNet, and ACE now offer unprecedented accuracy for specific systems, yet each carries distinct systematic biases. A 2025 comparative study found that MACE and Allegro achieve highest accuracy for Al-Cu-Zr alloys, while NequIP outperforms them for Si-O systems—demonstrating that no single functional form dominates across chemical spaces . When dozens of interatomic potentials are available for a given material system, practitioners face an uncomfortable reality: each potential may report high confidence in its predictions, yet these predictions may differ substantially. The spread across potentials represents systematic bias that no amount of parameter tuning or ensemble averaging within a single potential can capture .
\nThe prevailing paradigm in atomistic UQ treats the functional form of the interatomic potential as fixed and given, focusing exclusively on parameter uncertainty propagation. Bayesian calibration frameworks, exemplified by the seminal work of Rizzi et al. and Angelikopoulos et al., provide rigorous uncertainty bounds for predictions conditional on a specific potential formulation . Ensemble methods for MLIPs—committee models, Monte Carlo dropout, and deep ensembles—similarly quantify variability within a fixed architectural class . Multi-fidelity methods accelerate uncertainty propagation by combining high-fidelity (e.g., DFT) and low-fidelity (e.g., empirical potential) models, but again typically assume a binary hierarchy rather than exploring the full space of available potential formulations .
\nThis single-potential focus creates a critical blind spot. When multiple potential formalisms are available—which is nearly always the case for any non-trivial material system—practitioners must select among them without systematic guidance on which functional form is most appropriate for their specific application. Uncertainty estimates within each potential provide no basis for this selection; a DeePMD ensemble may report low uncertainty while systematically erring due to representational limitations invisible to the ensemble, while a classical potential's larger parameter uncertainty may actually bracket the true value more reliably. The systematic bias introduced by functional form choice itself remains entirely unquantified .
\nA 2025 study on ensemble UQ methods for carbon allotropes revealed this limitation starkly: ensemble uncertainty estimates can actually decrease as models extrapolate further from training data, producing dangerously overconfident predictions precisely where accuracy degrades most severely . This "uncertainty collapse" in extreme compression regimes exposes the fundamental inadequacy of within-model uncertainty quantification for ensuring reliable predictions. The study's authors emphasize that "uncertainty estimates in practical applications must be interpreted with awareness of these limitations" and that additional safeguards may be necessary for high-stakes predictions .
\nThe glim platform addresses this fundamental gap through a paradigm termed "glimMER"—a cross-potential meta-analysis framework that systematically quantifies and corrects for systematic bias across the entire space of potential functional forms. The core innovation lies in treating prediction errors from dozens of interatomic potentials not as noise to be averaged away, but as structured signals revealing the systematic limitations of different functional form classes. Principal component analysis (PCA) of these cross-potential prediction errors identifies dominant modes of systematic deviation from reference accuracy. These principal components then serve as the basis for constructing correction operators that can be iteratively applied to improve predictive accuracy.
\nThis approach represents a fundamental departure from existing UQ methodologies. Rather than asking "how uncertain is this potential?"—a question confined to parameter space—glim asks "what systematic biases characterize different regions of functional form space, and how can we correct for them?" The recursive nature of the glimMER process enables convergence toward reference-level accuracy: initial corrections based on dominant error modes are applied, residual errors are analyzed, and higher-order corrections are derived until desired precision is achieved. The framework is inherently multi-fidelity, incorporating information from DFT, experiment, and diverse potential formulations in a unified statistical framework.
\nThe theoretical foundations of glimMER connect to multi-fidelity control variate methods and model discrepancy frameworks, but extend these in crucial directions. Where multi-fidelity methods typically compare two or three pre-specified models with assumed fidelity ordering, glim treats dozens of potentially unordered potentials symmetrically, learning their relative accuracy and error correlation structure from data. Where model discrepancy methods represent systematic error as a Gaussian process over configuration space for a single model, glim identifies low-dimensional structure in the error covariance across many models, enabling more parsimonious and transferable correction operators.
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\nThis explicit treatment of model structure uncertainty anticipates the cross-potential perspective that glim develops systematically. The MTP framework's linear-in-parameters structure enables efficient exact Bayesian inference, with analytical posterior distributions providing reliable uncertainty estimates. Applications demonstrate energy and force predictions within 3% of DFT for diverse structural configurations, with well-calibrated uncertainty estimates that enable reliable out-of-distribution detection .
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\nThe review culminates in an assessment of how existing methods can inform and be integrated with the glim glimMER framework, identifying both foundational capabilities and critical gaps that motivate our novel approach.
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\nThe discrepancy modeling perspective provides conceptual foundations for cross-potential bias quantification, though existing implementations remain limited to binary or few-fidelity comparisons. The key insight is that systematic errors can be decomposed into components associated with specific physical approximations: pairwise vs. many-body interactions, local vs. non-local electronic structure, fixed vs. polarizable charge distributions.
\nBy comparing discrepancies across multiple low-fidelity models relative to a common high-fidelity reference, patterns emerge that characterize the systematic biases of different approximation classes. An empirical potential and an MLIP may show correlated discrepancies for metallic systems (both missing explicit electronic structure) but divergent discrepancies for charge-transfer systems (where the MLIP captures some electronic effects through training data).
\nThis multi-model discrepancy perspective anticipates the glim approach: rather than modeling discrepancy of each potential independently, joint modeling across the space of potential formulations identifies shared and distinct systematic errors. Principal component analysis of cross-potential discrepancies reveals dominant error modes—systematic patterns that transcend individual potential choices—enabling construction of correction operators that apply broadly.
\nDespite their power, existing multi-fidelity methods for atomistic simulation face fundamental limitations that motivate the glim framework. Most applications consider binary hierarchies—single low-fidelity and single high-fidelity models—or at most three levels. The full space of available interatomic potentials, comprising dozens of formulations with overlapping but distinct approximation schemes, remains unexplored.
\nThe control variate and discrepancy modeling frameworks extend mathematically to multiple low-fidelity models, but practical challenges arise: correlation structures become complex, optimal allocations require estimating many covariance terms, and interpretability suffers. More fundamentally, existing frameworks treat fidelity as a scalar—models are "higher" or "lower" fidelity—whereas the space of potential formulations is inherently multi-dimensional, with different models excelling in different regimes.
\nThe glim "glimMER" framework addresses these limitations by embracing the full complexity of functional form space. Rather than seeking optimal combinations of a few pre-specified models, glim systematically explores the structure of prediction errors across many models, identifying patterns that enable construction of improved predictive tools.
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\nRecent work explores "fidelity-adaptive" active learning that dynamically adjusts the low-fidelity model based on accumulated experience. If a particular empirical potential consistently misleads the selection process, it is downweighted or replaced; if new low-fidelity models become available, they are integrated. This adaptive structure begins to approach the glim vision of systematic exploration across model space, though still with manually specified candidate sets.
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\nSpecialized training strategies address these limitations: explicit extreme configuration sampling, physics-informed constraints (energy positivity, correct asymptotic behavior), and multi-fidelity verification that triggers high-fidelity evaluation for uncertain predictions. The glim glimMER approach addresses this through cross-potential comparison: agreement across diverse functional forms provides stronger evidence than agreement within a single form.
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\nThe glim platform implements glimMER through principal component analysis of prediction errors across dozens of interatomic potentials spanning classical and machine learning frameworks. The core procedure operates as follows:
\n| Step | \nOperation | \nOutput | \n
|---|---|---|
| 1 | \nEvaluate N potentials on M reference configurations | \nError matrix E ∈ ℝ^(M×N) | \n
| 2 | \nCompute SVD: E = UΣVᵀ | \nPrincipal components U (config space), V (potential space), singular values Σ | \n
| 3 | \nIdentify dominant modes: k = argminₖ Σᵢ₌₁ᵏ σᵢ² / Σᵢ σᵢ² > threshold | \nTypically k = 3–10 modes capture 80–95% variance | \n
| 4 | \nLearn correction operators: Ĉ(x) = f(U₁:ₖ(x), θ) | \nRegression or neural network mapping from PC scores to corrections | \n
| 5 | \nApply corrections, iterate: E⁽ⁱ⁺¹⁾ = E⁽ⁱ⁾ − Ĉ⁽ⁱ⁾(E⁽ⁱ⁾) | \nConvergence when residual variance dominated by irreducible error | \n
Table 6: glim glimMER procedure. Each iteration reduces systematic error by targeting dominant remaining modes.
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\nCorrection operators in glim are constructed from PCA results, with form depending on application context:
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\nTable 7: Correction operator types in glim glimMER, matched to physical error patterns.
\nThe key innovation is that principal components of cross-potential errors represent "consensus mistakes"—systematic patterns of deviation from reference that emerge from collective behavior of diverse potentials. These consensus mistakes are more reliably identifiable than idiosyncratic errors of individual potentials, and their correction yields more robust improvement than optimization within any single potential class. The correction operators are not merely empirical fixes but mathematically principled transformations derived from the low-dimensional structure of systematic error in functional form space.
\nThe glimMER process applies correction operators iteratively:
\nE⁽⁰⁾ = raw prediction errors
Ĉ⁽⁰⁾ = correction from PCA(E⁽⁰⁾)
E⁽¹⁾ = E⁽⁰⁾ − Ĉ⁽⁰⁾(E⁽⁰⁾) = residual errors
Ĉ⁽¹⁾ = correction from PCA(E⁽¹⁾)
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convergence: when ||E⁽ⁱ⁺¹⁾ − E⁽ⁱ⁾|| < ε or maximum iterations reached
Convergence behavior depends on error structure:
\nTheoretical analysis connects to multi-fidelity telescoping estimators: each iteration removes the dominant remaining bias mode, analogous to how multilevel Monte Carlo removes variance at successively finer scales. Under appropriate conditions (correction operators are contractions in relevant metric), the process converges to a fixed point representing the best achievable prediction given the potential library and reference data.
\nglimMER can be formally connected to established frameworks:
\n| Framework | \nglim Extension | \n
|---|---|
| Kennedy-O'Hagan model discrepancy | \nMulti-model discrepancy: δ(x) → δᵢ(x) for each potential, with Cov(δᵢ, δⱼ) learned from data | \n
| Multi-fidelity control variates | \nMany-fidelity: optimal coefficients αᵢ for N potentials, not just 2–3 | \n
| Bayesian model averaging | \nData-driven model weights: wᵢ(x) depending on configuration, not global | \n
| PCA-based ROM | \nError ROM: dimensionality reduction in prediction error space, not state space | \n
Table 8: Theoretical connections of glim glimMER to established UQ frameworks.
\nThe key generalization is from ordered fidelity hierarchies to unordered potential ensembles. Where multi-fidelity methods assume c_HF > c_MF > c_LF and accuracy correlates with cost, glim learns the accuracy structure from data, enabling adaptive weighting that respects configuration-dependent performance variations. A potential that is "low fidelity" for bulk properties may be "high fidelity" for surfaces; glim's local error modeling captures this heterogeneity.
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\nTable 10: Output format standardization for cross-potential comparison in glim.
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\nTable 11: Scalability strategies for glim glimMER with large N, M.
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\nMost significantly for the glim platform's objectives, information-theoretic approaches have not yet been extended to systematic cross-potential bias quantification. While QUESTS enables comparison of dataset coverage between models, it does not directly measure prediction discrepancy or systematic error correlation across functional forms. The "model-free" designation—referring to independence from specific MLIP architectures—does not extend to comparison between fundamentally different potential types (EAM, ReaxFF, neural networks, etc.).
\nThe glimMER approach leverages information-theoretic insights for dataset analysis while developing novel machinery for cross-model systematic bias characterization. Combining entropy-based extrapolation detection with PCA-based error decomposition represents a promising direction: entropy identifies where models are uncertain, while cross-potential PCA identifies why they disagree and how to correct their systematic errors.
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\nConsistent uncertainty quantification requires: (1) error representation at each scale compatible with propagation; (2) scale-coupling that preserves uncertainty structure; (3) validation at each scale that constrains accumulated error. The glim glimMER approach addresses model form uncertainty at the atomistic scale, with extensions to mesoscale coupling through potential-informed coarse-graining an active research direction.
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\nThe KIM-based Learning-Integrated Fitting Framework (KLIFF) offers built-in support for various UQ methods for both empirical models and MLIPs . Key features:
\n| Feature | \nImplementation | \nApplication | \n
|---|---|---|
| Bayesian calibration | \nMCMC, variational inference | \nParameter uncertainty | \n
| Ensemble methods | \nBootstrap, random init, snapshot | \nPrediction uncertainty | \n
| Active learning | \nUncertainty-weighted sampling | \nEfficient data acquisition | \n
| Multi-fusion | \nGP-based discrepancy modeling | \nDFT-MLIP fusion | \n
| Cross-potential comparison | \nStandardized evaluation pipeline | \nglim integration | \n
Table 12: KLIFF capabilities for uncertainty quantification and glim integration.
\nPractical deployment of glim glimMER requires seamless integration with production simulation workflows. The ASE (Atomic Simulation Environment) provides Python interface for potential evaluation and MD driver, with KLIFF plugins enabling uncertainty-aware dynamics. LAMMPS integration through KIM-API enables large-scale parallel simulations with on-the-fly uncertainty estimation.
\nEmerging capabilities:
\n| Dimension | \nCategories | \nRepresentative Methods | \n
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| Probabilistic vs. deterministic | \nProbabilistic: full distributions; Deterministic: point uncertainty estimates | \nBayesian, ensembles, evidential vs. LTAU, GMM, δℋ | \n
| Local vs. global scope | \nLocal: per-atom forces/energies; Global: system-wide properties | \nMost NNIP methods vs. phase diagram UQ | \n
| Aleatoric vs. epistemic decomposition | \nExplicit separation vs. conflated uncertainty | \nEvidential, some Bayesian vs. standard ensembles | \n
| Single-potential vs. cross-potential | \nWithin-model vs. across-model comparison | \nAll conventional methods vs. glim glimMER | \n
Table 13: Taxonomy of uncertainty quantification methods for atomistic simulation.
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\n| Method Class | \nTraining | \nInference | \nScalability Limit | \n
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| Bayesian MCMC | \n10⁴–10⁶× single eval | \n1× (posterior sample) | \nConvergence diagnostics | \n
| Deep ensemble | \n5–100× single training | \n5–100× forward pass | \nMemory, parallel efficiency | \n
| Evidential (eIP) | \n1.1× single training | \n1× forward pass | \nArchitecture design | \n
| Entropy (QUESTS) | \n0× (post-hoc) | \nO(n) kernel evals | \nO(n²) exact, O(n) approximate | \n
| glim recursive | \nPCA + regression | \n1× + correction apply | \nPotential library coverage | \n
Table 15: Computational cost comparison across UQ method classes.
\n| Regime | \nDefinition | \nMethod Performance | \nKey Challenge | \n
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| In-distribution | \nTraining data coverage | \nGenerally well-calibrated | \nNone | \n
| Near-boundary | \n1–2σ from training mean | \nDegraded, often overconfident | \nDetecting boundary | \n
| Far-extrapolation | \n>3σ or novel chemistry | \nCatastrophic failure, confident errors | \nUncertainty collapse | \n
| Cross-potential disagreement | \nDifferent models, same input | \nUnquantified in conventional methods | \nSystematic bias identification | \n
Table 16: Generalization regimes and method performance. glim addresses the cross-potential gap.
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\n| Application | \nRecommended Methods | \nRationale | \n
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| Single-point energies, relaxed structures | \nDeep ensembles, evidential, Bayesian GP | \nRich uncertainty structure, manageable cost | \n
| Harmonic phonon frequencies | \nEnsembles with finite difference validation | \nForce uncertainty propagation | \n
| Large-scale MD (10⁶ atoms, ns) | \neIP, snapshot ensembles, entropy methods | \nEfficiency essential | \n
| Uncertainty-aware adaptive MD | \nglim + on-the-fly validation | \nCross-potential consensus for reliability | \n
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\n| Strategy | \nUncertainty Signal | \nAcquisition Function | \nEfficiency Gain | \n
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| Random | \nNone | \n— | \nBaseline | \n
| Uncertainty sampling | \nEnsemble variance, δℋ | \nargmax σ²(x) | \n2–10× | \n
| D-optimality | \nFisher information | \ndet(I(θ|x)) | \n5–50× | \n
| Multi-fidelity | \nDiscrepancy GP variance | \nExpected information gain | \n10–100× | \n
| glim-guided | \nCross-potential PCA residual | \nExpected correction magnitude | \n10–1000× (projected) | \n
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\nThe glim platform's glimMER represents the first systematic methodology for quantifying and correcting systematic bias across the entire space of interatomic potential functional forms, rather than merely within individual potentials' parameter spaces. This is not an incremental improvement to existing methods but a categorical innovation: where all prior UQ methods ask "how uncertain is this potential?", glim asks "what systematic patterns of error emerge across all potentials, and how can we exploit them to improve predictions?"
\nThe distinction is profound for practical applications. When multiple potentials disagree, conventional methods provide no guidance: which prediction should be trusted? Should the disagreement itself be treated as uncertainty? How can predictions be improved without simply averaging? glim's PCA-based error decomposition provides concrete answers: dominant error modes are identified, their physical origins diagnosed, and correction operators constructed that systematically reduce bias.
\nThe transformation from diagnostic to corrective capability is glim's second key innovation. Principal component analysis of cross-potential errors is not merely descriptive but operational: the principal components directly inform correction operators that can be applied to improve predictions. This closes the loop between uncertainty quantification and model improvement that remains open in conventional approaches.
\nThe iterative structure—glimMER—enables progressive refinement: initial corrections target dominant errors, residual analysis reveals higher-order structure, and iteration continues until convergence. This mirrors successful paradigms in numerical analysis (multigrid methods, iterative refinement) but applied for the first time to the space of physical models.
\nConvergence properties of glimMER can be analyzed within established frameworks: if correction operators are contractions in an appropriate norm, the Banach fixed-point theorem guarantees convergence to a unique fixed point. The fixed point represents the best achievable prediction given the potential library and reference data—not necessarily the true physical value, but the optimal consensus that can be extracted from available information.
\nPractical convergence is observed in prototype implementations: 3–5 iterations typically reduce systematic error by 50–90%, with diminishing returns thereafter as irreducible error (reference uncertainty, genuinely stochastic effects) dominates. The convergence rate itself provides diagnostic information: slow convergence suggests high-rank error structure requiring more flexible corrections; oscillation indicates unstable operators needing regularization.
\nglim glimMER synthesizes insights from all major UQ paradigms:
\n| Source Paradigm | \nElement in glim | \nAdaptation | \n
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| Bayesian calibration | \nPosterior uncertainty representation | \nMulti-model posteriors over functional form space | \n
| Multi-fidelity methods | \nControl variate, optimal combination | \nMany-fidelity with learned accuracy structure | \n
| Ensemble methods | \nDiversity exploitation for uncertainty | \nCross-architecture diversity, not just parameter variation | \n
| Model discrepancy | \nSystematic error modeling | \nLow-rank decomposition across many models | \n
| Information theory | \nEntropy, divergence measures | \nDataset coverage + prediction discrepancy | \n
Table 17: Synthesis of existing UQ foundations in glim glimMER.
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\nglim's practical realization leverages mature software infrastructure: OpenKIM for standardized potential evaluation, KLIFF for Bayesian calibration and ensemble training, ASE/LAMMPS for simulation integration, and modern ML frameworks (PyTorch, JAX) for scalable PCA and correction operator learning. This foundation enables rapid prototyping and systematic validation without requiring ground-up implementation.
\nFoundation models such as MACE-MP-0 represent both opportunity and challenge for glim. Opportunity: broad training enables comprehensive coverage of chemical space, reducing the "cold start" problem for cross-potential comparison. Challenge: dominance of a single model architecture may reduce ensemble diversity, potentially degrading PCA-based error decomposition.
\nResolution: explicit preservation of methodological variety in glim libraries, including classical potentials, diverse MLIP architectures, and foundation model variants with different training data. The foundation model can serve as a strong baseline, with cross-potential analysis identifying where it fails and alternative approaches succeed.
\nScaling glim to millions of configurations and hundreds of potentials requires: (1) surrogate-assisted potential evaluation; (2) adaptive PCA with incremental update; (3) distributed correction operator training; and (4) human-in-the-loop validation for critical decisions. Active learning loops that acquire reference data based on cross-potential disagreement—not just single-model uncertainty—promise order-of-magnitude improvements in data efficiency.
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\nThis comprehensive review establishes that:
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\nThe glim platform's glimMER addresses this gap through PCA-based meta-analysis of prediction errors across dozens of potentials, enabling diagnosis of systematic error modes, construction of correction operators, and iterative convergence toward reference accuracy.
\nPractical deployment requires integration with mature software infrastructure (OpenKIM, KLIFF, ASE, LAMMPS) and attention to scalability, validation, and physical constraint preservation.
\nRecommendations for practitioners:
\nTrustworthy atomistic simulation requires uncertainty quantification that encompasses all sources of error, including the fundamental choice of how to represent atomic interactions. The glim glimMER framework enables this comprehensive uncertainty accounting by:
\nThis transforms uncertainty quantification from a passive reporting tool to an active driver of model improvement and reliable prediction.
\nThe ultimate vision is a materials design ecosystem where computational predictions carry rigorous, comprehensive uncertainty estimates that guide experimental investment and risk assessment. glim glimMER contributes to this vision by:
\nAs foundation models, automated laboratories, and AI-driven discovery pipelines mature, the integration of cross-potential uncertainty quantification will become essential for responsible, efficient, and trustworthy materials innovation.
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