pith. machine review for the scientific record. sign in

arxiv: 2605.13788 · v1 · submitted 2026-05-13 · 💻 cs.LG

Recognition: unknown

Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs

Eszter Varga-Umbrich , Zachary Weller-Davies , Paul Duckworth , Jules Tilly , Olivier Peltre , Shikha Surana
Authors on Pith no claims yet

Pith reviewed 2026-05-14 19:07 UTC · model grok-4.3

classification 💻 cs.LG
keywords active learningneural tangent kernelmachine learning interatomic potentialsforce predictionscalable acquisitiondistribution robustnessOC20 dataset
0
0 comments X

The pith

Mixed parameter-coordinate derivatives of the NTK yield natural similarity metrics for force-aware active learning in MLIPs.

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

The paper shows how to make active learning practical for machine learning interatomic potentials by solving three problems at once: screening hundreds of thousands of candidate structures without building huge kernel matrices, using both energy and force labels during selection, and staying reliable even when the pool of candidates differs from the target data. It does this with a chunked posterior-variance method that only ever materializes small blocks of the feature-space kernel, plus an extension of the Neural Tangent Kernel that incorporates forces through mixed derivatives with respect to model parameters and atomic coordinates. On the OC20 dataset the joint energy-force version records the lowest energy and force errors across every reported metric and split, while on T1x, PMechDB and RGD it matches or beats committee baselines at far lower cost and shows less variance under controlled distribution shift.

Core claim

We extend the Neural Tangent Kernel to a force-aware setting via mixed parameter-coordinate derivatives, yielding a force NTK and a joint energy-force NTK that provide natural similarity metrics for vector-field prediction. Paired with a linearly scaling acquisition framework based on chunked feature-space posterior-variance shortlisting, the method screens approximately 200k structures in hours, achieves the lowest energy and force MAE and RMSE on OC20, remains competitive on T1x/PMechDB/RGD, and exhibits lower variance than committee methods when candidate pools are shifted relative to the target distribution.

What carries the argument

The joint energy-force NTK formed by mixed derivatives of the NTK with respect to parameters and atomic coordinates; it supplies a similarity metric for both scalar energies and vector forces without extra fitting.

If this is right

  • A single pretrained MLIP can drive the entire active-learning loop without maintaining an ensemble.
  • Screening pools of 200k structures becomes feasible on modest hardware because only small kernel blocks are ever formed.
  • Force-aware selection improves both energy and force accuracy on datasets where forces dominate the learning signal.
  • Acquisition remains stable when the unlabeled pool is drawn from a different distribution than the target.

Where Pith is reading between the lines

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

  • The same mixed-derivative construction could supply uncertainty estimates for any vector or tensor output in physics-informed models.
  • Because the method re-uses a frozen pretrained network as a feature extractor, it lowers the barrier to applying active learning to large foundation-model fine-tuning campaigns.
  • The chunked posterior-variance approach may transfer directly to other kernel-based acquisition strategies that currently materialise full candidate kernels.

Load-bearing premise

The mixed derivatives of the NTK produce similarity scores that correctly rank uncertainty in force predictions for structures outside the training distribution.

What would settle it

An experiment on a held-out test set in which force-aware NTK acquisition selects batches whose addition does not reduce force RMSE more than energy-only NTK or random selection.

Figures

Figures reproduced from arXiv: 2605.13788 by Eszter Varga-Umbrich, Jules Tilly, Olivier Peltre, Paul Duckworth, Shikha Surana, Zachary Weller-Davies.

Figure 1
Figure 1. Figure 1: OC20 final-round test errors on val_is (ID) and the mean of the three out-of-distribution splits val_oos_ads, val_oos_bulk, and val_oos_ads_bulk. The joint energy–force NTK achieves the lowest energy and force errors across all panels. We consider active learning on a randomly selected 200k subset of OC20 Chanussot et al. [2021]. To handle the pool size we use feature-space PV to shortlist candidates, foll… view at source ↗
Figure 2
Figure 2. Figure 2: Cost, accuracy, and memory scaling of feature-space acquisition on OC20. (a,b) Mean [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Energy RMSE learning curves (meV) for the methods presented in the main text. [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Energy MAE learning curves (meV) for the methods presented in the main text. [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Force RMSE learning curves (meV/Å) for the methods presented in the main text. [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Force MAE learning curves (meV/Å) for the methods presented in the main text. [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Inter-reaction bias. Left: energy RMSE AUC (meV [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Intra-reaction (frame) bias. Left: energy RMSE AUC (meV [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Global kernel matrices on a five-reaction T1x subset. Structures are sorted by reaction [PITH_FULL_IMAGE:figures/full_fig_p030_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: OC20 test error vs. training-set size on the [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: OC20 final-round test errors resolved by validation split ( [PITH_FULL_IMAGE:figures/full_fig_p031_11.png] view at source ↗
read the original abstract

Active learning for machine-learning interatomic potentials (MLIPs) must address several challenges to be practical: scaling to large candidate pools, leveraging energy-force supervision, and maintaining robustness when candidate pools are biased relative to the target distribution. In this work, we jointly address these challenges. We first introduce a linearly scaling acquisition framework based on chunked feature-space posterior-variance shortlisting. By avoiding materialisation of the candidate and train set kernels, this approach enables screening of ~200k structures within hours and applies broadly to acquisition strategies that score candidates based on molecular similarity metrics. We then extend the Neural Tangent Kernel (NTK) to a force-aware setting via mixed parameter-coordinate derivatives, yielding a force NTK and a joint energy-force NTK that provide natural similarity metrics for vector-field prediction. We demonstrate the effectiveness of the joint energy-force NTK on the OC20 dataset, where force-aware acquisition is crucial: it achieves the lowest energy and force MAE and RMSE across all metrics and distribution splits. Across T1x, PMechDB, and RGD benchmarks, our force NTK methods remain competitive with established baselines while being significantly more efficient than committee-based approaches. Under a controlled candidate-pool shift case study on T1x, acquisition based on pretrained MLIP embeddings and NTKs remains robust, whereas committee-based methods exhibit higher variance. Overall, these results show that a single pretrained MLIP can enable scalable, force-aware, and distribution-robust active learning for foundation-model fine-tuning.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a linearly scaling acquisition framework for active learning of MLIPs based on chunked feature-space posterior-variance shortlisting that avoids materializing full kernels, enabling screening of ~200k structures. It extends the NTK to force-aware settings via mixed parameter-coordinate derivatives, defining a force NTK and joint energy-force NTK as natural similarity metrics for vector-field prediction in pretrained models without extra fitting. On OC20 the joint NTK yields the lowest energy and force MAE/RMSE across metrics and splits; on T1x/PMechDB/RGD it remains competitive with baselines while being more efficient than committees; under controlled distribution shift on T1x the NTK methods show greater robustness than committees.

Significance. If the force NTK construction is shown to reliably capture force-field similarity, the work supplies a practical, single-model, committee-free route to scalable and distribution-robust active learning for foundation-model fine-tuning of MLIPs. The linear scaling and explicit handling of force supervision address two central practical bottlenecks in the field.

major comments (3)
  1. [§3.2 (force NTK definition)] The central claim that mixed parameter-coordinate derivatives of the NTK supply effective natural similarity metrics for force prediction (without additional fitting or validation) is load-bearing for the OC20 superiority and robustness results, yet no correlation analysis between the derived kernel values and actual force errors or uncertainty estimates is reported.
  2. [§4 (experiments)] The abstract and results sections report lowest MAE/RMSE on OC20 and competitiveness elsewhere, but provide no details on baseline implementations, number of independent runs, statistical significance tests, or hyperparameter controls; these omissions leave open the possibility that observed gains arise from implementation specifics rather than the NTK construction itself.
  3. [§4.3] In the T1x distribution-shift case study, the claim that committee methods exhibit higher variance while NTK methods remain robust is stated qualitatively; quantitative variance or standard-error values across repeated trials are needed to substantiate the robustness advantage.
minor comments (2)
  1. [Abstract] The phrase 'significantly more efficient' in the abstract should be accompanied by concrete wall-clock or scaling numbers relative to the committee baselines.
  2. [§3.2] Notation for the mixed derivatives in the force NTK should be introduced with an explicit equation reference to avoid ambiguity when the joint energy-force kernel is later defined.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive feedback and positive assessment of the significance of our work. We address each major comment point by point below, with planned revisions where appropriate to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3.2 (force NTK definition)] The central claim that mixed parameter-coordinate derivatives of the NTK supply effective natural similarity metrics for force prediction (without additional fitting or validation) is load-bearing for the OC20 superiority and robustness results, yet no correlation analysis between the derived kernel values and actual force errors or uncertainty estimates is reported.

    Authors: We agree that a direct correlation analysis between force NTK values and observed force errors would provide valuable supporting evidence for the interpretation of the joint NTK as a natural similarity metric. While the OC20 results (lowest MAE/RMSE across metrics) and T1x robustness already offer empirical validation of the construction, we will add a supplementary correlation plot and analysis in the revised manuscript to directly address this point. revision: yes

  2. Referee: [§4 (experiments)] The abstract and results sections report lowest MAE/RMSE on OC20 and competitiveness elsewhere, but provide no details on baseline implementations, number of independent runs, statistical significance tests, or hyperparameter controls; these omissions leave open the possibility that observed gains arise from implementation specifics rather than the NTK construction itself.

    Authors: We acknowledge the need for greater experimental transparency. In the revised manuscript we will expand §4 to include: (i) precise descriptions of all baseline implementations (including committee sizes and training protocols), (ii) the number of independent runs performed for each method, (iii) results of statistical significance tests (e.g., paired t-tests with p-values), and (iv) a consolidated table of hyperparameter settings to ensure the reported gains can be attributed to the NTK construction rather than implementation details. revision: yes

  3. Referee: [§4.3] In the T1x distribution-shift case study, the claim that committee methods exhibit higher variance while NTK methods remain robust is stated qualitatively; quantitative variance or standard-error values across repeated trials are needed to substantiate the robustness advantage.

    Authors: We concur that quantitative measures are required to substantiate the robustness claim. We will revise §4.3 to report standard deviations or standard errors across repeated trials for both NTK and committee methods, and will add error bars to the relevant figures so that the variance comparison is presented quantitatively rather than qualitatively. revision: yes

Circularity Check

0 steps flagged

No circularity: force NTK derived via standard mixed derivatives on NTK definition

full rationale

The paper's central construction applies mixed parameter-coordinate derivatives directly to the standard Neural Tangent Kernel definition to obtain the force NTK and joint energy-force NTK. This is a mathematical extension independent of any fitted parameters, empirical predictions, or self-citations within the work. The chunked variance shortlisting is a computational scaling method that does not reduce to the kernel values by construction. Empirical results on OC20, T1x, etc., function as external validation rather than inputs to the derivation. No load-bearing steps match the enumerated circularity patterns; the derivation chain is self-contained against the NTK literature.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Based solely on abstract; the work relies on standard NTK properties and introduces new kernel variants without specifying fitted parameters or new entities beyond the described extensions.

axioms (1)
  • domain assumption Neural Tangent Kernel regime applies to the architectures of the pretrained MLIPs
    Invoked to justify using NTK as a similarity metric for acquisition in the force-aware setting.
invented entities (1)
  • force NTK no independent evidence
    purpose: Similarity metric for vector-field force predictions
    Defined through mixed parameter-coordinate derivatives of the standard NTK.

pith-pipeline@v0.9.0 · 5596 in / 1297 out tokens · 53195 ms · 2026-05-14T19:07:33.136069+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

123 extracted references · 123 canonical work pages · 1 internal anchor

  1. [1]

    Anstine, Roman Zubatyuk, and Olexandr Isayev

    Dylan M. Anstine, Roman Zubatyuk, and Olexandr Isayev. Data generation for machine learning interatomic potentials and beyond. Chemical Reviews, 2025. doi:10.1021/acs.chemrev.4c00572

    work page doi:10.1021/acs.chemrev.4c00572 2025

  2. [2]

    Bartók, Risi Kondor, and Gábor Csányi

    Albert P. Bartók, Risi Kondor, and Gábor Csányi. On representing chemical environments. Physical Review B, 87 0 (18): 0 184115, 2013. doi:10.1103/PhysRevB.87.184115

    work page doi:10.1103/physrevb.87.184115 2013

  3. [3]

    arXiv preprint arXiv:2401.00096 , year=

    Ilyes Batatia, Philipp Benner, Yuan Chiang, Alin M. Elena, Dávid P. Kovács, Janosh Riebesell, Xavier R. Advincula, Mark Asta, Matthew Avaylon, et al. A foundation model for atomistic materials chemistry, 2023 a . URL https://arxiv.org/abs/2401.00096

    work page arXiv 2023

  4. [4]

    Ilyes Batatia, Dávid Péter Kovács, Gregor N. C. Simm, Christoph Ortner, and Gábor Csányi. Mace: Higher order equivariant message passing neural networks for fast and accurate force fields, 2023 b . URL https://arxiv.org/abs/2206.07697

    work page arXiv 2023

  5. [5]

    Andreas Bender, Nadine Schneider, Marwin Segler, W

    Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P. Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E. Smidt, and Boris Kozinsky. E(3) -equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature Communications, 13: 0 2453, 2022. doi:10.1038/s41467-022-29939-5

    work page doi:10.1038/s41467-022-29939-5 2022

  6. [6]

    Schaaf, Ondrej Marsalek, and Christoph Schran

    Hubert Beck, Pavol Simko, Lars L. Schaaf, Ondrej Marsalek, and Christoph Schran. Multi-head committees enable direct uncertainty prediction for atomistic foundation models. The Journal of Chemical Physics, 163 0 (23): 0 234103, 2025. doi:10.1063/5.0288994

    work page doi:10.1063/5.0288994 2025

  7. [7]

    Generalized Neural-Network Representation of High- Dimensional Potential-Energy Surfaces.Physical Review Letters, 98(14):146401, April 2007

    Jörg Behler and Michele Parrinello. Generalized neural-network representation of high-dimensional potential-energy surfaces. Physical Review Letters, 98 0 (14): 0 146401, 2007. doi:10.1103/PhysRevLett.98.146401

    work page doi:10.1103/physrevlett.98.146401 2007

  8. [8]

    JAX : composable transformations of P ython+ N um P y programs, 2018

    James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Yash Katariya, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake Vander P las, Skye Wanderman- M ilne, and Qiao Zhang. JAX : composable transformations of P ython+ N um P y programs, 2018. URL http://github.com/jax-ml/jax

    work page 2018

  9. [9]

    Machine learning interatomic potentials: library for efficient training, model development and simulation of molecular systems, 2025

    Christoph Brunken, Olivier Peltre, Heloise Chomet, Lucien Walewski, Manus McAuliffe, Valentin Heyraud, Solal Attias, Martin Maarand, Yessine Khanfir, Edan Toledo, Fabio Falcioni, Marie Bluntzer, Silvia Acosta-Gutiérrez, and Jules Tilly. Machine learning interatomic potentials: library for efficient training, model development and simulation of molecular s...

    work page arXiv 2025

  10. [11]

    Blips: Bayesian learned interatomic potentials, 2026

    Dario Coscia, Pim de Haan, and Max Welling. Blips: Bayesian learned interatomic potentials, 2026. URL https://arxiv.org/abs/2508.14022

    work page arXiv 2026

  11. [12]

    Online test-time adaptation for better generalization of interatomic potentials to out-of-distribution data

    Taoyong Cui, Chenyu Tang, Dongzhan Zhou, Longtao Wang, Yu Zheng, Yu Wang, Liang Wang, Weizhi Yang, Lei Bai, and Wanli Ouyang. Online test-time adaptation for better generalization of interatomic potentials to out-of-distribution data. Nature Communications, 16: 0 1891, 2025. doi:10.1038/s41467-025-57101-4

    work page doi:10.1038/s41467-025-57101-4 2025

  12. [13]

    Bartók, Gábor Csányi, and Michele Ceriotti

    Sandip De, Albert P. Bartók, Gábor Csányi, and Michele Ceriotti. Machine learning unifies the modeling of materials and molecules. Science Advances, 3 0 (12): 0 e1701816, 2017. doi:10.1126/sciadv.1701816

    work page doi:10.1126/sciadv.1701816 2017

  13. [14]

    Bartel, and Gerbrand Ceder

    Bowen Deng, Peichen Zhong, KyuJung Jun, Janosh Riebesell, Kevin Han, Christopher J. Bartel, and Gerbrand Ceder. CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nature Machine Intelligence, 5: 0 1031--1041, 2023. doi:10.1038/s42256-023-00716-3

    work page doi:10.1038/s42256-023-00716-3 2023

  14. [15]

    Persson, and Gerbrand Ceder

    Bowen Deng, Yunyeong Choi, Peichen Zhong, Janosh Riebesell, Shashwat Anand, Zhuoying Li, KyuJung Jun, Kristin A. Persson, and Gerbrand Ceder. Systematic softening in universal machine learning interatomic potentials. npj Computational Materials, 11: 0 9, 2025. doi:10.1038/s41524-024-01500-6

    work page doi:10.1038/s41524-024-01500-6 2025

  15. [19]

    Lauri Himanen, Marc O. J. J \"a ger, Eiaki V. Morooka, Filippo Federici Canova, Yashasvi S. Ranawat, David Z. Gao, Patrick Rinke, and Adam S. Foster. DScribe: Library of descriptors for machine learning in materials science . Computer Physics Communications, 247: 0 106949, 2020. ISSN 0010-4655. doi:10.1016/j.cpc.2019.106949. URL https://doi.org/10.1016/j....

    work page doi:10.1016/j.cpc.2019.106949 2020

  16. [20]

    A framework and benchmark for deep batch active learning for regression

    David Holzmüller, Viktor Zaverkin, Johannes Kästner, and Ingo Steinwart. A framework and benchmark for deep batch active learning for regression. Journal of Machine Learning Research, 24 0 (164): 0 1--81, 2023. URL https://www.jmlr.org/papers/v24/22-0937.html

    work page 2023

  17. [23]

    Neural tangent kernel: Convergence and generalization in neural networks

    Arthur Jacot, Franck Gabriel, and Clément Hongler. Neural tangent kernel: Convergence and generalization in neural networks. In Advances in Neural Information Processing Systems, 2018. URL https://arxiv.org/abs/1806.07572

    work page arXiv 2018

  18. [24]

    On-the-fly machine learning force field generation: Application to melting points

    Ryosuke Jinnouchi, Ferenc Karsai, and Georg Kresse. On-the-fly machine learning force field generation: Application to melting points. Physical Review B, 100 0 (1): 0 014105, 2019. doi:10.1103/PhysRevB.100.014105

    work page doi:10.1103/physrevb.100.014105 2019

  19. [27]

    Uncertainty quantification by direct propagation of shallow ensembles

    Matthias Kellner and Michele Ceriotti. Uncertainty quantification by direct propagation of shallow ensembles. Machine Learning: Science and Technology, 5 0 (3): 0 035006, 2024. doi:10.1088/2632-2153/ad594a

    work page doi:10.1088/2632-2153/ad594a 2024

  20. [28]

    Enhanced representation-based sampling for the efficient generation of data sets for machine-learned interatomic potentials

    Matthias Kellner and Michele Ceriotti. Enhanced representation-based sampling for the efficient generation of data sets for machine-learned interatomic potentials. Journal of Chemical Theory and Computation, 2025. doi:10.1021/acs.jctc.5c01767

    work page doi:10.1021/acs.jctc.5c01767 2025

  21. [29]

    Smith, and Benjamin Nebgen

    Maksim Kulichenko, Kipton Barros, Nicholas Lubbers, Ying Wai Li, Richard Messerly, Sergei Tretiak, Justin S. Smith, and Benjamin Nebgen. Uncertainty-driven dynamics for active learning of interatomic potentials. Nature Computational Science, 3: 0 230--239, 2023. doi:10.1038/s43588-023-00406-5

    work page doi:10.1038/s43588-023-00406-5 2023

  22. [30]

    How accurate are dft forces? unexpectedly large uncertainties in molecular datasets, 2025

    Domantas Kuryla, Fabian Berger, Gábor Csányi, and Angelos Michaelides. How accurate are dft forces? unexpectedly large uncertainties in molecular datasets, 2025. URL https://arxiv.org/abs/2510.19774

    work page arXiv 2025

  23. [33]

    Levine, Muhammad Shuaibi, Evan W

    Daniel S. Levine, Muhammed Shuaibi, Evan Walter Clark Spotte-Smith, Michael G. Taylor, Muhammad R. Hasyim, Kyle Michel, Ilyes Batatia, Gábor Csányi, Misko Dzamba, Peter Eastman, Nathan C. Frey, Xiang Fu, Vahe Gharakhanyan, Aditi S. Krishnapriyan, Joshua A. Rackers, Sanjeev Raja, Ammar Rizvi, Andrew S. Rosen, Zachary Ulissi, Santiago Vargas, C. Lawrence Zi...

    work page arXiv 2025

  24. [34]

    A critical review of machine learning interatomic potentials and hamiltonian

    Yifan Li, Xiuying Zhang, Mingkang Liu, and Lei Shen. A critical review of machine learning interatomic potentials and hamiltonian. Journal of Materials Informatics, 5 0 (4), 2025. ISSN 2770-372X. doi:10.20517/jmi.2025.17. URL https://www.oaepublish.com/articles/jmi.2025.17

    work page doi:10.20517/jmi.2025.17 2025

  25. [36]

    arXiv preprint arXiv:2504.06231 , year=

    Mark Neumann, James Gin, Benjamin Rhodes, Steven Bennett, Zhiyi Li, Hitarth Choubisa, Arthur Hussey, and Jonathan Godwin. Orb-v3: atomistic simulation at scale, 2025. URL https://arxiv.org/abs/2504.06231

    work page arXiv 2025

  26. [39]

    Peterson, Rune Christensen, and Alireza Khorshidi

    Andrew A. Peterson, Rune Christensen, and Alireza Khorshidi. Addressing uncertainty in atomistic machine learning. Physical Chemistry Chemical Physics, 19: 0 10978--10985, 2017. doi:10.1039/C7CP00375G

    work page doi:10.1039/c7cp00375g 2017

  27. [40]

    Podryabinkin and Alexander V

    Evgeny V. Podryabinkin and Alexander V. Shapeev. Active learning of linearly parametrized interatomic potentials. Computational Materials Science, 140: 0 171--180, 2017. doi:10.1016/j.commatsci.2017.08.031

    work page doi:10.1016/j.commatsci.2017.08.031 2017

  28. [43]

    Extended-connectivity fingerprints

    David Rogers and Mathew Hahn. Extended-connectivity fingerprints. Journal of Chemical Information and Modeling, 50 0 (5): 0 742--754, 2010. doi:10.1021/ci100050t

    work page doi:10.1021/ci100050t 2010

  29. [44]

    Levine, Zachary Ulissi, C

    Sushree Jagriti Sahoo, Mikael Maraschin, Daniel S. Levine, Zachary Ulissi, C. Lawrence Zitnick, Joel B Varley, Joseph A. Gauthier, Nitish Govindarajan, and Muhammed Shuaibi. The open catalyst 2025 (oc25) dataset and models for solid-liquid interfaces, 2025. URL https://arxiv.org/abs/2509.17862

    work page arXiv 2025

  30. [45]

    Committee neural network potentials control generalization errors and enable active learning

    Christoph Schran, Krystof Brezina, and Ondrej Marsalek. Committee neural network potentials control generalization errors and enable active learning. The Journal of Chemical Physics, 153 0 (10): 0 104105, 2020. doi:10.1063/5.0016004

    work page doi:10.1063/5.0016004 2020

  31. [47]

    Schütt, Huziel E

    Kristof T. Schütt, Huziel E. Sauceda, Pieter-Jan Kindermans, Alexandre Tkatchenko, and Klaus-Robert Müller. SchNet -- a deep learning architecture for molecules and materials. The Journal of Chemical Physics, 148 0 (24): 0 241722, 2018. doi:10.1063/1.5019779

    work page doi:10.1063/1.5019779 2018

  32. [49]

    Smith, Ben Nebgen, Nicholas Lubbers, Olexandr Isayev, and Adrian E

    Justin S. Smith, Ben Nebgen, Nicholas Lubbers, Olexandr Isayev, and Adrian E. Roitberg. Less is more: Sampling chemical space with active learning. The Journal of Chemical Physics, 148 0 (24): 0 241733, 2018. doi:10.1063/1.5023802

    work page doi:10.1063/1.5023802 2018

  33. [51]

    Torrisi, Simon Batzner, Yu Xie, Lixin Sun, Alexie M

    Jonathan Vandermause, Steven B. Torrisi, Simon Batzner, Yu Xie, Lixin Sun, Alexie M. Kolpak, and Boris Kozinsky. On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events. npj Computational Materials, 6: 0 20, 2020. doi:10.1038/s41524-020-0283-z

    work page doi:10.1038/s41524-020-0283-z 2020

  34. [52]

    Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs

    Eszter Varga-Umbrich, Shikha Surana, Paul Duckworth, Jules Tilly, Olivier Peltre, and Zachary Weller-Davies. Pretrained model representations as acquisition signals for active learning of mlips, 2026. URL https://arxiv.org/abs/2605.03964

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  35. [54]

    Uma: A family of universal models for atoms.arXiv preprint arXiv:2506.23971, 2025

    Brandon M. Wood, Misko Dzamba, Xiang Fu, Meng Gao, Muhammed Shuaibi, Luis Barroso-Luque, Kareem Abdelmaqsoud, Vahe Gharakhanyan, John R. Kitchin, Daniel S. Levine, Kyle Michel, Anuroop Sriram, Taco Cohen, Abhishek Das, Ammar Rizvi, Sushree Jagriti Sahoo, Zachary W. Ulissi, and C. Lawrence Zitnick. Uma: A family of universal models for atoms, 2026. URL htt...

    work page arXiv 2026

  36. [55]

    Exploring chemical and conformational spaces by batch mode deep active learning

    Viktor Zaverkin, David Holzmüller, Ingo Steinwart, and Johannes Kästner. Exploring chemical and conformational spaces by batch mode deep active learning. Digital Discovery, 1: 0 605--620, 2022. doi:10.1039/D2DD00034B

    work page doi:10.1039/d2dd00034b 2022

  37. [56]

    Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials

    Viktor Zaverkin, David Holzmüller, Henrik Christiansen, Federico Errica, Francesco Alesiani, Makoto Takamoto, Mathias Niepert, and Johannes Kästner. Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials. npj Computational Materials, 10: 0 83, 2024. doi:10.1038/s41524-024-01254-1

    work page doi:10.1038/s41524-024-01254-1 2024

  38. [57]

    Active learning meets metadynamics: automated workflow for reactive machine learning interatomic potentials

    Viktor Zaverkin, David Holzmüller, and Johannes Kästner. Active learning meets metadynamics: automated workflow for reactive machine learning interatomic potentials. Digital Discovery, 2026. doi:10.1039/D5DD00261C

    work page doi:10.1039/d5dd00261c 2026

  39. [58]

    Active learning of uniformly accurate interatomic potentials for materials simulation

    Linfeng Zhang, De-Ye Lin, Han Wang, Roberto Car, and Weinan E. Active learning of uniformly accurate interatomic potentials for materials simulation. Physical Review Materials, 3 0 (2): 0 023804, 2019. doi:10.1103/PhysRevMaterials.3.023804

    work page doi:10.1103/physrevmaterials.3.023804 2019

  40. [60]

    Data curation for machine learning interatomic potentials by determinantal point processes, 2026

    Joanna Zou and Youssef Marzouk. Data curation for machine learning interatomic potentials by determinantal point processes, 2026. URL https://arxiv.org/abs/2603.22160

    work page arXiv 2026

  41. [61]

    and Becke, A

    Kohn, W. and Becke, A. D. and Parr, R. G. , title =. The Journal of Physical Chemistry , year =. doi:10.1021/jp960669l , url =

    work page doi:10.1021/jp960669l

  42. [62]

    2023 , eprint=

    MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields , author=. 2023 , eprint=

    work page 2023

  43. [63]

    2025 , eprint=

    Machine Learning Interatomic Potentials: library for efficient training, model development and simulation of molecular systems , author=. 2025 , eprint=

    work page 2025

  44. [64]

    Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations , journal =

    Guanjie Wang and Changrui Wang and Xuanguang Zhang and Zefeng Li and Jian Zhou and Zhimei Sun , keywords =. Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations , journal =. 2024 , issn =. doi:https://doi.org/10.1016/j.isci.2024.109673 , url =

    work page doi:10.1016/j.isci.2024.109673 2024

  45. [65]

    Quality of uncertainty estimates from neural network potential ensembles , volume=

    Kahle, Leonid and Zipoli, Federico , year=. Quality of uncertainty estimates from neural network potential ensembles , volume=. Physical Review E , publisher=. doi:10.1103/physreve.105.015311 , number=

    work page doi:10.1103/physreve.105.015311

  46. [66]

    Journal of Materials Informatics , VOLUME =

    Yifan Li and Xiuying Zhang and Mingkang Liu and Lei Shen , TITLE =. Journal of Materials Informatics , VOLUME =. 2025 , NUMBER =

    work page 2025

  47. [67]

    Jacobs, Ryan and Morgan, Dane and Attarian, Siamak and Meng, Jun and Shen, Chen and Wu, Zhenghao and Xie, Clare Yijia and Yang, Julia H. and Artrith, Nongnuch and Blaiszik, Ben and Ceder, Gerbrand and Choudhary, Kamal and Csanyi, Gabor and Cubuk, Ekin Dogus and Deng, Bowen and Drautz, Ralf and Fu, Xiang and Godwin, Jonathan and Honavar, Vasant and Isayev,...

    work page doi:10.1016/j.cossms.2025.101214 2025

  48. [68]

    Physical Review Letters , volume=

    Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons , author=. Physical Review Letters , volume=. 2010 , doi=

    work page 2010

  49. [69]

    Physical Review Letters , volume=

    Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics , author=. Physical Review Letters , volume=. 2018 , doi=

    work page 2018

  50. [70]

    and Sauceda, Huziel E

    Schütt, Kristof T. and Sauceda, Huziel E. and Kindermans, Pieter-Jan and Tkatchenko, Alexandre and Müller, Klaus-Robert , journal=. 2018 , doi=

    work page 2018

  51. [71]

    Physical Review B , volume=

    Atomic cluster expansion for accurate and transferable interatomic potentials , author=. Physical Review B , volume=. 2019 , doi=

    work page 2019

  52. [72]

    and Kornbluth, Mordechai and Molinari, Nicola and Smidt, Tess E

    Batzner, Simon and Musaelian, Albert and Sun, Lixin and Geiger, Mario and Mailoa, Jonathan P. and Kornbluth, Mordechai and Molinari, Nicola and Smidt, Tess E. and Kozinsky, Boris , journal=. 2022 , doi=

    work page 2022

  53. [73]

    Nature Communications , volume=

    Learning local equivariant representations for large-scale atomistic dynamics , author=. Nature Communications , volume=. 2023 , doi=

    work page 2023

  54. [74]

    2026 , eprint=

    UMA: A Family of Universal Models for Atoms , author=. 2026 , eprint=

    work page 2026

  55. [75]

    PET-MAD as a lightweight universal interatomic potential for advanced materials modeling.Nature Communications, 16(1):10653, November 2025

    Mazitov, Arslan and Bigi, Filippo and Kellner, Matthias and Pegolo, Paolo and Tisi, Davide and Fraux, Guillaume and Pozdnyakov, Sergey and Loche, Philip and Ceriotti, Michele , title =. Nature Communications , year =. doi:10.1038/s41467-025-65662-7 , url =

    work page doi:10.1038/s41467-025-65662-7

  56. [76]

    Physical Review Letters , volume=

    Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces , author=. Physical Review Letters , volume=. 2007 , doi=

    work page 2007

  57. [77]

    Physical Review B , volume=

    On representing chemical environments , author=. Physical Review B , volume=. 2013 , doi=

    work page 2013

  58. [78]

    Science Advances , volume=

    Machine learning unifies the modeling of materials and molecules , author=. Science Advances , volume=. 2017 , doi=

    work page 2017

  59. [79]

    Journal of Chemical Information and Modeling , volume=

    Extended-Connectivity Fingerprints , author=. Journal of Chemical Information and Modeling , volume=. 2010 , doi=

    work page 2010

  60. [80]

    Chemical Reviews , year=

    Data Generation for Machine Learning Interatomic Potentials and Beyond , author=. Chemical Reviews , year=

    work page

  61. [81]

    The Journal of Chemical Physics , volume=

    Less is more: Sampling chemical space with active learning , author=. The Journal of Chemical Physics , volume=. 2018 , doi=

    work page 2018

  62. [82]

    Computational Materials Science , volume=

    Active learning of linearly parametrized interatomic potentials , author=. Computational Materials Science , volume=. 2017 , doi=

    work page 2017

  63. [83]

    Physical Review B , volume=

    On-the-fly machine learning force field generation: Application to melting points , author=. Physical Review B , volume=. 2019 , doi=

    work page 2019

  64. [84]

    and Batzner, Simon and Xie, Yu and Sun, Lixin and Kolpak, Alexie M

    Vandermause, Jonathan and Torrisi, Steven B. and Batzner, Simon and Xie, Yu and Sun, Lixin and Kolpak, Alexie M. and Kozinsky, Boris , journal=. On-the-fly active learning of interpretable. 2020 , doi=

    work page 2020

  65. [85]

    Physical Review Materials , volume=

    Active learning of uniformly accurate interatomic potentials for materials simulation , author=. Physical Review Materials , volume=. 2019 , doi=

    work page 2019

  66. [86]

    A comprehensive benchmark of active learning strategies with AutoML for small-sample regression in materials science , volume =

    Bi, Jinghou and Xu, Yuanhao and Conrad, Felix and Wiemer, Hajo and Ihlenfeldt, Steffen , year =. A comprehensive benchmark of active learning strategies with AutoML for small-sample regression in materials science , volume =. Scientific Reports , publisher =. doi:10.1038/s41598-025-24613-4 , number =

    work page doi:10.1038/s41598-025-24613-4

  67. [87]

    Nature Computational Science , volume=

    Uncertainty-driven dynamics for active learning of interatomic potentials , author=. Nature Computational Science , volume=. 2023 , doi=

    work page 2023

  68. [88]

    npj Computational Materials , volume=

    De novo exploration and self-guided learning of potential-energy surfaces , author=. npj Computational Materials , volume=. 2019 , doi=

    work page 2019

  69. [89]

    The Journal of Chemical Physics , volume=

    An entropy-maximization approach to automated training set generation for interatomic potentials , author=. The Journal of Chemical Physics , volume=. 2020 , doi=

    work page 2020

  70. [90]

    Digital Discovery , year=

    Active learning meets metadynamics: automated workflow for reactive machine learning interatomic potentials , author=. Digital Discovery , year=

    work page

  71. [91]

    The Journal of Chemical Physics , volume=

    Committee neural network potentials control generalization errors and enable active learning , author=. The Journal of Chemical Physics , volume=. 2020 , doi=

    work page 2020

  72. [92]

    Physical Chemistry Chemical Physics , volume=

    Addressing uncertainty in atomistic machine learning , author=. Physical Chemistry Chemical Physics , volume=. 2017 , doi=

    work page 2017

  73. [93]

    The Journal of Chemical Physics , volume=

    Fast uncertainty estimates in deep learning interatomic potentials , author=. The Journal of Chemical Physics , volume=. 2023 , doi=

    work page 2023

  74. [94]

    Machine Learning: Science and Technology , volume=

    Uncertainty quantification by direct propagation of shallow ensembles , author=. Machine Learning: Science and Technology , volume=. 2024 , doi=

    work page 2024

  75. [95]

    The Journal of Chemical Physics , volume=

    Multi-head committees enable direct uncertainty prediction for atomistic foundation models , author=. The Journal of Chemical Physics , volume=. 2025 , doi=

    work page 2025

  76. [96]

    Physical Review Materials , volume =

    Ouyang, Xinjian and Wang, Zhilong and Jie, Xiao and Zhang, Feng and Zhang, Yanxing and Liu, Laijun and Wang, Dawei , title =. Physical Review Materials , volume =. 2024 , month = oct, publisher =. doi:10.1103/PhysRevMaterials.8.103804 , url =

    work page doi:10.1103/physrevmaterials.8.103804 2024

  77. [97]

    2026 , eprint=

    Cutting Through the Noise: On-the-fly Outlier Detection for Robust Training of Machine Learning Interatomic Potentials , author=. 2026 , eprint=

    work page 2026

  78. [98]

    2026 , eprint=

    BLIPs: Bayesian Learned Interatomic Potentials , author=. 2026 , eprint=

    work page 2026

  79. [99]

    2025 , eprint=

    Orb-v3: atomistic simulation at scale , author=. 2025 , eprint=

    work page 2025

  80. [100]

    Tan, Aik Rui and Urata, Shingo and Goldman, Samuel and Dietschreit, Johannes C. B. and Gómez-Bombarelli, Rafael , year=. Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles , volume=. npj Computational Materials , publisher=. doi:10.1038/s41524-023-01180-8 , number=

    work page doi:10.1038/s41524-023-01180-8

Showing first 80 references.