arxiv: 2605.00640 · v1 · submitted 2026-05-01 · 💻 cs.LG · physics.chem-ph

Recognition: unknown

Knowing when to trust machine-learned interatomic potentials

Shams Mehdi , Ilkwon Cho , Olexandr Isayev

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:16 UTC · model grok-4.3

classification 💻 cs.LG physics.chem-ph

keywords uncertainty quantificationmachine-learned interatomic potentialspost-hoc reliabilityper-atom embeddingsselective classificationensemble comparisonreliability probability

0 comments

The pith

A compact classifier on frozen MLIP embeddings produces reliability probabilities that track actual errors better than ensemble disagreement.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that uncertainty quantification for machine-learned interatomic potentials can be performed after the fact by training a small discriminative classifier on the per-atom representations already computed inside a pretrained model. This turns the task into selective classification, yielding a probability for each prediction that rises as the true error falls. A sympathetic reader would care because ensemble methods require training and running multiple full models, which becomes prohibitive for large foundation-scale potentials, whereas this approach adds almost no cost and works on any existing model that exposes its embeddings. The advantage holds across two different model architectures and grows stronger when the underlying representations are more expressive.

Core claim

PROBE recasts MLIP uncertainty quantification as selective classification by applying a compact discriminative classifier to the frozen per-atom representations of a pretrained model. It outputs a per-prediction reliability probability that increases monotonically with actual error without any change to the original potential. On large held-out evaluation sets this signal outperforms ensemble disagreement as a binary reliability indicator for two structurally distinct MLIP architectures, and the margin widens with the expressiveness of the backbone representation. Multi-head self-attention inside the classifier also supplies per-atom importance maps that offer chemical interpretability at no

What carries the argument

PROBE, a compact post-hoc discriminative classifier trained on frozen per-atom embeddings from a pretrained MLIP to output per-prediction reliability probabilities.

If this is right

Uncertainty estimates become available for foundation-scale MLIPs without the cost of training and running multiple independent models.
The quality of the reliability signal improves automatically whenever a stronger backbone representation is developed.
Per-atom attention maps provide chemical diagnostics that explain why a given prediction is trusted or distrusted.
The method can be applied immediately to any existing MLIP that already exposes per-atom embeddings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Reliability scores could let molecular-dynamics runs skip or correct steps whose predictions fall below a chosen trust threshold.
The same probing idea might be tested on other embedding-based scientific models, such as those for molecular properties or crystal stability.
If the probe classifier stays tiny, it could run in real time alongside the main potential for on-the-fly trust assessment during simulation.
One could combine PROBE with active learning to prioritize new training data from regions where reliability is low.

Load-bearing premise

The frozen per-atom representations already contain enough generalizable information for a small classifier to learn a mapping to prediction error on unseen data without overfitting to the training distribution.

What would settle it

On a new held-out set drawn from chemical space outside the training distribution, the PROBE reliability probabilities fail to increase monotonically with actual error or perform no better than random ranking when used to flag high-error cases.

read the original abstract

Prevailing machine-learned interatomic potential (MLIP) uncertainty-quantification methods rely on ensembles of independently trained backbones. These methods scale unfavorably with foundation-scale MLIPs, and their member-disagreement signals correlate weakly with per-molecule prediction error. Here we probe the frozen per-atom representations of a pretrained MLIP with a compact discriminative classifier, recasting MLIP uncertainty quantification as selective classification rather than error regression. The resulting method, PROBE (Post-hoc Reliability frOm Backbone Embeddings), produces a per-prediction reliability probability that monotonically tracks actual error without modification to the underlying model. Across large held-out evaluation sets and two structurally distinct MLIP architectures, PROBE outperforms ensemble disagreement as a binary reliability signal, which strengthens with the expressiveness of the backbone representation, implying a favorable scaling trajectory toward foundation-scale MLIPs. Multi-head self-attention additionally yields per-atom importance maps, providing chemically interpretable diagnostics at no additional computational cost. PROBE is post-hoc and architecture-agnostic, and is directly deployable on any MLIP that exposes per-atom representations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

PROBE trains a small post-hoc classifier on frozen per-atom embeddings to produce a reliability probability that tracks error better than ensemble disagreement on the reported tests.

read the letter

The core move is to treat uncertainty quantification as selective classification: freeze a pretrained MLIP, pull its per-atom embeddings, and train a compact discriminative head that outputs a probability the prediction is reliable. They show this probability is monotonic with actual error on held-out data and beats member disagreement from ensembles, with the gap widening for more expressive backbones. The attention heads also give per-atom importance maps at no extra cost. That combination—post-hoc, architecture-agnostic, and cheaper than ensembles—is the practical advance for anyone running large-scale molecular simulations or materials screening where full ensembles are prohibitive.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces PROBE (Post-hoc Reliability frOm Backbone Embeddings), a method for uncertainty quantification in machine-learned interatomic potentials (MLIPs). It trains a compact discriminative classifier on frozen per-atom representations from a pretrained MLIP to produce per-prediction reliability probabilities that monotonically track actual errors, without modifying the backbone. The approach is evaluated on large held-out sets for two structurally distinct MLIP architectures, where it outperforms ensemble disagreement as a binary reliability signal, with gains increasing for more expressive backbones. Multi-head self-attention yields per-atom importance maps for interpretability. The method is presented as post-hoc and architecture-agnostic.

Significance. If the central claims hold, PROBE offers a scalable, computationally efficient alternative to ensemble-based UQ for foundation-scale MLIPs, addressing the poor scaling and weak error correlation of current methods. The post-hoc design enables immediate use on existing models, and the interpretable per-atom maps add practical value for chemical diagnostics. The reported scaling behavior with backbone expressiveness suggests favorable prospects for larger models. The work recasts UQ as selective classification in a way that could improve trust in MLIP predictions for materials and molecular applications, provided generalization is demonstrated.

major comments (2)

[§4] §4 (Probe Training and Evaluation Protocol): The manuscript does not specify the sampling strategy or distributional splits used to generate error labels for training the probe classifier relative to the backbone's original training data. This detail is load-bearing for the generalizability claim, as overlap in molecular motifs or error regimes could allow the compact classifier to overfit to training-specific patterns rather than learning transferable signals from the frozen embeddings.
[§5] §5 (Held-out Evaluation Results): While outperformance versus ensemble disagreement is asserted across large held-out sets and two architectures, the text provides no quantitative metrics (e.g., AUC, calibration error, or monotonicity measures), statistical significance tests, or ablation studies on probe hyperparameters. Without these, the strength of the central claim that PROBE 'monotonically tracks actual error' and 'outperforms' cannot be rigorously assessed.

minor comments (2)

[Abstract] Abstract: The statement that performance 'strengthens with the expressiveness of the backbone representation' is imprecise; clarify whether this refers to the magnitude of the performance gap, the correlation coefficient, or another quantity.
Notation: The per-atom representations are referred to as 'frozen' throughout, but the manuscript should explicitly define the layer or embedding index from which they are extracted for each architecture to ensure reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We have addressed both major comments by expanding the relevant sections with the requested details on the training protocol and by adding quantitative metrics, statistical tests, and ablations. These revisions strengthen the presentation of our results without altering the core claims.

read point-by-point responses

Referee: [§4] §4 (Probe Training and Evaluation Protocol): The manuscript does not specify the sampling strategy or distributional splits used to generate error labels for training the probe classifier relative to the backbone's original training data. This detail is load-bearing for the generalizability claim, as overlap in molecular motifs or error regimes could allow the compact classifier to overfit to training-specific patterns rather than learning transferable signals from the frozen embeddings.

Authors: We agree that explicit specification of the sampling strategy and distributional splits is essential to support the generalizability claims. The original manuscript noted the use of large held-out evaluation sets but did not provide a full accounting of how these sets were constructed relative to the backbone training data. In the revised manuscript, Section 4 has been expanded to include a complete description: error labels were generated from structures drawn from a distribution designed to be disjoint from the backbone's training set, employing a hybrid splitting approach that combines random sampling with motif-aware partitioning (based on SMILES or graph isomorphism checks) to minimize overlap in molecular motifs and error regimes. This ensures the probe classifier learns transferable signals from the frozen embeddings rather than memorizing training-specific patterns. revision: yes
Referee: [§5] §5 (Held-out Evaluation Results): While outperformance versus ensemble disagreement is asserted across large held-out sets and two architectures, the text provides no quantitative metrics (e.g., AUC, calibration error, or monotonicity measures), statistical significance tests, or ablation studies on probe hyperparameters. Without these, the strength of the central claim that PROBE 'monotonically tracks actual error' and 'outperforms' cannot be rigorously assessed.

Authors: We appreciate this observation and acknowledge that while the original manuscript included figures illustrating monotonic tracking of error and comparative performance, explicit quantitative metrics were not tabulated. In the revised Section 5, we have added a summary table reporting AUC-ROC, expected calibration error (ECE), and Spearman rank correlation (as a monotonicity measure) for PROBE versus ensemble disagreement on both architectures. We also report results from bootstrap-based statistical significance tests (with p-values) confirming the observed outperformance. Finally, we include a concise ablation study on probe hyperparameters (e.g., classifier depth, learning rate, and attention head count), showing that performance remains stable across reasonable ranges and that gains scale with backbone expressiveness as originally claimed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; PROBE is an independent supervised probe on frozen embeddings

full rationale

The paper's core derivation trains a compact discriminative classifier on frozen per-atom representations using actual error labels computed from reference calculations. This yields a reliability probability that is learned from external ground-truth errors rather than being defined or fitted from quantities internal to the backbone MLIP. No equations reduce by construction to inputs, no self-citation chains justify uniqueness or ansatzes, and the method is explicitly post-hoc and architecture-agnostic. Empirical claims rest on held-out evaluation sets, which remain falsifiable outside the training distribution.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the domain assumption that per-atom embeddings encode error-relevant features; no free parameters or invented entities are introduced in the method description.

axioms (1)

domain assumption Per-atom representations from pretrained MLIPs contain features that correlate with prediction errors on unseen structures.
This assumption enables the discriminative classifier to learn a useful reliability signal from the frozen embeddings.

pith-pipeline@v0.9.0 · 5491 in / 1305 out tokens · 60044 ms · 2026-05-09T20:16:49.390568+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

61 extracted references · 14 canonical work pages · 3 internal anchors

[1]

& Parrinello, M

Behler, J. & Parrinello, M. Generalized neural-network representation of high- dimensional potential-energy surfaces.Physical review letters98, 146401 (2007)

2007
[2]

J.et al.Roadmap on machine learning in electronic structure.Electronic Structure4, 023004 (2022)

Kulik, H. J.et al.Roadmap on machine learning in electronic structure.Electronic Structure4, 023004 (2022)

2022
[3]

T., Sauceda, H

Sch¨ utt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A. & M¨ uller, K.- R. Schnet–a deep learning architecture for molecules and materials.The Journal of chemical physics148(2018). 21

2018
[4]

Batzner, S.et al.E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.Nature communications13, 2453 (2022)

2022
[5]

P., Simm, G., Ortner, C

Batatia, I., Kovacs, D. P., Simm, G., Ortner, C. & Cs´ anyi, G. Mace: Higher order equivariant message passing neural networks for fast and accurate force fields. Advances in neural information processing systems35, 11423–11436 (2022)

2022
[6]

M., Zubatyuk, R

Anstine, D. M., Zubatyuk, R. & Isayev, O. Aimnet2: a neural network potential to meet your neutral, charged, organic, and elemental-organic needs.Chemical Science16, 10228–10244 (2025)

2025
[7]

Deng, B.et al.Chgnet as a pretrained universal neural network potential for charge-informed atomistic modelling.Nature Machine Intelligence5, 1031–1041 (2023)

2023
[8]

Merchant, A.et al.Scaling deep learning for materials discovery.Nature624, 80–85 (2023)

2023
[9]

Wood, Misko Dzamba, Xiang Fu, Meng Gao, Muhammed Shuaibi, Luis Barroso- Luque, Kareem Abdelmaqsoud, Vahe Gharakhanyan, John R

Wood, B. M.et al.Uma: A family of universal models for atoms.arXiv preprint arXiv:2506.23971(2025)

work page arXiv 2025
[10]

& Kohn, W

Hohenberg, P. & Kohn, W. Inhomogeneous electron gas.Physical review136, B864 (1964)

1964
[11]

& Sham, L

Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects.Physical review140, A1133 (1965)

1965
[12]

& Tiwary, P

Mehdi, S., Smith, Z., Herron, L., Zou, Z. & Tiwary, P. Enhanced sampling with machine learning.Annual Review of Physical Chemistry75, 347–370 (2024)

2024
[13]

EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations, March 2024

Liao, Y.-L., Wood, B., Das, A. & Smidt, T. Equiformerv2: Improved equiv- ariant transformer for scaling to higher-degree representations.arXiv preprint arXiv:2306.12059(2023)

work page arXiv 2023
[14]

P.et al.Mace-off: Short-range transferable machine learning force fields for organic molecules.Journal of the American Chemical Society147, 17598–17611 (2025)

Kov´ acs, D. P.et al.Mace-off: Short-range transferable machine learning force fields for organic molecules.Journal of the American Chemical Society147, 17598–17611 (2025)

2025
[15]

A recipe for scalable attention- based mlips: unlocking long-range accuracy with all-to-all node attention.arXiv preprint arXiv:2603.06567, 2026

Qu, E., Wood, B. M., Krishnapriyan, A. S. & Ulissi, Z. W. A recipe for scal- able attention-based mlips: unlocking long-range accuracy with all-to-all node attention.arXiv preprint arXiv:2603.06567(2026)

work page arXiv 2026
[16]

G´ omez-Bombarelli, R.et al.Automatic chemical design using a data-driven continuous representation of molecules.ACS central science4, 268–276 (2018)

2018
[17]

& Waegeman, W

H¨ ullermeier, E. & Waegeman, W. Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods.Machine learning110, 457– 506 (2021). 22

2021
[18]

& Marsalek, O

Schran, C., Brezina, K. & Marsalek, O. Committee neural network potentials control generalization errors and enable active learning.The Journal of Chemical Physics153(2020)

2020
[19]

S., Nebgen, B., Lubbers, N., Isayev, O

Smith, J. S., Nebgen, B., Lubbers, N., Isayev, O. & Roitberg, A. E. Less is more: Sampling chemical space with active learning.The Journal of chemical physics 148(2018)

2018
[20]

R., Urata, S., Goldman, S., Dietschreit, J

Tan, A. R., Urata, S., Goldman, S., Dietschreit, J. C. & G´ omez-Bombarelli, R. Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles.npj Computational Materials9, 225 (2023)

2023
[21]

P., Maliyov, I

Perez, D., Subramanyam, A. P., Maliyov, I. & Swinburne, T. D. Uncer- tainty quantification for misspecified machine learned interatomic potentials.npj Computational Materials11, 263 (2025)

2025
[22]

& Rossi, K

Grasselli, F., Chong, S., Kapil, V., Bonfanti, S. & Rossi, K. Uncertainty in the era of machine learning for atomistic modeling.Digital Discovery4, 2654–2675 (2025)

2025
[23]

J., Vermeire, F

Heid, E., McGill, C. J., Vermeire, F. H. & Green, W. H. Characterizing uncer- tainty in machine learning for chemistry.Journal of Chemical Information and Modeling63, 4012–4029 (2023)

2023
[24]

& Blundell, C

Lakshminarayanan, B., Pritzel, A. & Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles.Advances in neural information processing systems30(2017)

2017
[25]

Vandermause, J.et al.On-the-fly active learning of interpretable bayesian force fields for atomistic rare events.npj Computational Materials6, 20 (2020)

2020
[26]

Podryabinkin, E. V. & Shapeev, A. V. Active learning of linearly parametrized interatomic potentials.Computational Materials Science140, 171–180 (2017)

2017
[27]

Kulichenko, M.et al.Uncertainty-driven dynamics for active learning of interatomic potentials.Nature computational science3, 230–239 (2023)

2023
[28]

Zaverkin, V.et al.Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials.npj Computational Materials10, 83 (2024)

2024
[29]

P., Ortner, C

van der Oord, C., Sachs, M., Kov´ acs, D. P., Ortner, C. & Cs´ anyi, G. Hyperactive learning for data-driven interatomic potentials.npj Computational Materials9, 168 (2023)

2023
[30]

Kurniawan, Y., Wen, M., Tadmor, E. B. & Transtrum, M. K. Comparative study of ensemble-based uncertainty quantification methods for neural network 23 interatomic potentials.arXiv preprint arXiv:2508.06456(2025)

work page arXiv 2025
[31]

M., Carbogno, C., Wang, J

Lu, S., Ghiringhelli, L. M., Carbogno, C., Wang, J. & Scheffler, M. On the uncer- tainty estimates of equivariant-neural-network-ensembles interatomic potentials. arXiv preprint arXiv:2309.00195(2023)

work page arXiv 2023
[32]

A., Firoz, J

Bilbrey, J. A., Firoz, J. S., Lee, M.-S. & Choudhury, S. Uncertainty quantification for neural network potential foundation models.npj Computational Materials 11, 109 (2025)

2025
[33]

& Ghahramani, Z

Gal, Y. & Ghahramani, Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning 1050–1059 (2016)

2016
[34]

& Tadmor, E

Wen, M. & Tadmor, E. B. Uncertainty quantification in molecular simulations with dropout neural network potentials.npj computational materials6, 124 (2020)

2020
[35]

Williams, C. K. & Rasmussen, C. E.Gaussian processes for machine learning Vol. 2 (MIT press Cambridge, MA, 2006)

2006
[36]

P., Kermode, J.et al.Improved uncertainty quantification for gaussian process regression based interatomic potentials.arXiv preprint arXiv:2206.08744 (2022)

Bart´ ok, A. P., Kermode, J.et al.Improved uncertainty quantification for gaussian process regression based interatomic potentials.arXiv preprint arXiv:2206.08744 (2022)

work page arXiv 2022
[37]

S., Owen, C

Vandermause, J., Xie, Y., Lim, J. S., Owen, C. J. & Kozinsky, B. Active learning of reactive bayesian force fields applied to heterogeneous catalysis dynamics of h/pt.Nature Communications13, 5183 (2022)

2022
[38]

& Bruix, A

Farris, R., Telari, E., Artrith, N., Neyman, K. & Bruix, A. Bayesian neural networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials.arXiv preprint arXiv:2509.19180(2025)

work page arXiv 2025
[39]

Blips: Bayesian learned interatomic potentials, 2026

Coscia, D., de Haan, P. & Welling, M. Blips: Bayesian learned interatomic potentials.arXiv preprint arXiv:2508.14022(2025)

work page arXiv 2025
[40]

Xu, H.et al.Evidential deep learning for interatomic potentials.Nature Communications(2025)

2025
[41]

A., Samanta, A., Zhou, F

Vita, J. A., Samanta, A., Zhou, F. & Lordi, V. Ltau-ff: loss trajectory analysis for uncertainty in atomistic force fields.Machine Learning: Science and Technology 6, 015048 (2025)

2025
[42]

H., Ortner, C., and Wang, Y

Ho, C. H., Ortner, C. & Wang, Y. Flexible uncertainty calibration for machine- learned interatomic potentials.arXiv preprint arXiv:2510.00721(2025)

work page arXiv 2025
[43]

L., Marsalek, O

Beck, H., Simko, P., Schaaf, L. L., Marsalek, O. & Schran, C. Multi-head com- mittees enable direct uncertainty prediction for atomistic foundation models.The Journal of Chemical Physics163(2025). 24

2025
[44]

P., Duan, C., Yang, T., Nandy, A

Janet, J. P., Duan, C., Yang, T., Nandy, A. & Kulik, H. J. A quantitative uncertainty metric controls error in neural network-driven chemical discovery. Chemical science10, 7913–7922 (2019)

2019
[45]

& Kitchin, J

Musielewicz, J., Lan, J., Uyttendaele, M. & Kitchin, J. R. Improved uncer- tainty estimation of graph neural network potentials using engineered latent space distances.The Journal of Physical Chemistry C128, 20799–20810 (2024)

2024
[46]

& Grasselli, F

Bigi, F., Chong, S., Ceriotti, M. & Grasselli, F. A prediction rigidity formalism for low-cost uncertainties in trained neural networks.Machine Learning: Science and Technology5, 045018 (2024)

2024
[47]

& Ceriotti, M

Kellner, M. & Ceriotti, M. Uncertainty quantification by direct propagation of shallow ensembles.Machine Learning: Science and Technology5, 035006 (2024)

2024
[48]

El-Yaniv, R.et al.On the foundations of noise-free selective classification.Journal of Machine Learning Research11(2010)

2010
[49]

& El-Yaniv, R

Geifman, Y. & El-Yaniv, R. Selective classification for deep neural networks. Advances in neural information processing systems30(2017)

2017
[50]

& El-Yaniv, R

Geifman, Y. & El-Yaniv, R. Selectivenet: A deep neural network with an integrated reject option 2151–2159 (2019)

2019
[51]

Learning Confidence for Out -of-Distribution Detection in Neural Networks,

DeVries, T. & Taylor, G. W. Learning confidence for out-of-distribution detection in neural networks.arXiv preprint arXiv:1802.04865(2018)

work page arXiv 2018
[52]

A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks

Hendrycks, D. & Gimpel, K. A baseline for detecting misclassified and out- of-distribution examples in neural networks.arXiv preprint arXiv:1610.02136 (2016)

work page internal anchor Pith review arXiv 2016
[53]

& Shin, J

Lee, K., Lee, K., Lee, H. & Shin, J. A simple unified framework for detecting out- of-distribution samples and adversarial attacks.Advances in neural information processing systems31(2018)

2018
[54]

Sun, Y., Ming, Y., Zhu, X. & Li, Y. Out-of-distribution detection with deep nearest neighbors 20827–20840 (2022)

2022
[55]

& Liu, Z

Yang, J., Zhou, K., Li, Y. & Liu, Z. Generalized out-of-distribution detection: A survey.International Journal of Computer Vision132, 5635–5662 (2024)

2024
[56]

N., Listgarten, J

Fannjiang, C., Bates, S., Angelopoulos, A. N., Listgarten, J. & Jordan, M. I. Conformal prediction under feedback covariate shift for biomolecular design. Proceedings of the National Academy of Sciences119, e2204569119 (2022)

2022
[57]

Understanding intermediate layers using linear classifier probes

Alain, G. & Bengio, Y. Understanding intermediate layers using linear classifier probes.arXiv preprint arXiv:1610.01644(2016). 25

work page Pith review arXiv 2016
[58]

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

McInnes, L., Healy, J. & Melville, J. Umap: Uniform manifold approximation and projection for dimension reduction.arXiv preprint arXiv:1802.03426(2018)

work page internal anchor Pith review arXiv 2018
[59]

& Paliwal, S

Reidenbach, D., Nikitin, F., Isayev, O. & Paliwal, S. G. Applications of modular co-design for de novo 3d molecule generation.Digital Discovery5, 754–768 (2026)

2026
[60]

Landrum, G.et al.Rdkit: A software suite for cheminformatics, computational chemistry, and predictive modeling.Greg Landrum8, 5281 (2013)

2013
[61]

Kellner, M., Hansen, T., Bligaard, T., Jacobsen, K. W. & Ceriotti, M. Errors that matter: Uncertainty-aware universal machine-learning potentials calibrated on experiments (2026). arXiv:2604.24607. 26 Supplementary Information Knowing when to trust machine-learned interatomic potentials Shams Mehdi, Ilkwon Cho, Olexandr Isayev ∗ Department of Chemistry, M...

work page internal anchor Pith review Pith/arXiv arXiv 2026