Pith. sign in

REVIEW 5 major objections 5 minor 65 references

Efficient Grand Canonical Global Optimization with On-the-fly-trained Machine-learning Interatomic Potentials

T0 review · 5 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper's central claim is that a single grand-canonical search—varying geometry and composition together under a Gibbs-energy acquisition function—finds stable structures and chemical states with fewer first-principles evaluations than i

desk verdict A real algorithmic step for grand-canonical search with on-the-fly MLIPs, but the efficiency claim is undercut by a lax success criterion and an uncontrolled baseline. read the letter →

arxiv 2509.19968 v2 pith:QJ5YW5OL submitted 2025-09-24 cond-mat.mtrl-sci physics.chem-ph

Jon Eunan Quinlivan Dominguez , Mads-Peter Verner Christiansen , Konstantin M. Neyman , B{o}jrk Hammer , Albert Bruix This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.chem-ph
keywords grandcanonicalglobaloptimizationmachine-learninginteratomicpotentialsGaussianprocessregressionSOAPdescriptorabinitiothermodynamicsevolutionaryalgorithmscatalyststructurepredictionsurfaceoxidereconstructions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper implements and tests a global optimization algorithm that changes both atomic geometry and chemical composition in one run, ranking candidates by their Gibbs energy of formation at a chosen temperature and pressure rather than by raw potential energy. To keep the search affordable, it trains a machine-learning interatomic potential on the fly using sparse Gaussian process regression over local atomic environments, so expensive first-principles calculations are reserved for a small number of promising candidates. The authors show on three test systems—free Ir3Ox clusters, Pt3Ox clusters on ceria, and the Pd(100) surface—that the algorithm reproduces known stable phases and, in some cases, finds structures more stable than those from previous single-stoichiometry searches, while using fewer total first-principles evaluations than the canonical approach. The result matters because computational models of catalysts need structures that are representative of the actual reaction conditions, and enumerating every possible stoichiometry is often the main bottleneck.

What carries the argument

The load-bearing machinery is the combination of a size-extensive surrogate potential and an ab initio thermodynamics acquisition function. The surrogate is a sparse Gaussian process regression model using the smooth overlap of atomic positions (SOAP) descriptor to represent each atom's local environment; total energy is the sum of per-atom contributions, so the model can be applied to structures with any number of atoms. The acquisition function F = ΔG_model − κ σ ranks candidates by their predicted Gibbs energy of formation (computed from the surrogate plus the chemical potentials of reservoirs) with a penalty proportional to the prediction uncertainty, so the search is steered toward comp

What would settle it

Take a set of held-out geometries across several stoichiometries of an ionic system (e.g., a small metal-oxide cluster with known charge transfer), ask the surrogate to predict their relative energies, and compare with first-principles single-point energies; if the per-stoichiometry error in relative energy is comparable to the gaps that determine the phase diagram, the acquisition function will mis-rank candidates and the claimed efficiency gain loses meaning.

Watch

Extended reading notes

Core claim

The central claim is that the most stable structure and chemical state of a system under specified reaction conditions can be found by a single grand-canonical global optimization, and that this is more efficient than running a canonical global-minimum search for every stoichiometry separately. Efficiency comes from an on-the-fly trained, size-extensive surrogate potential built from sparse Gaussian process regression and SOAP descriptors: total energy is the sum of per-atom contributions, so the same model ranks structures with different numbers of atoms. Candidates are selected by an acquisition function that combines the surrogate's predicted Gibbs energy of formation with an uncertainty

Load-bearing premise

The search relies on the surrogate potential's ability to rank structures across different compositions, which assumes a structure's total energy is a sum of contributions from local atomic environments; if long-range charge or electrostatics breaks that locality, the Gibbs-energy ordering of candidates can be wrong.

Editorial extensions

If this is right

  • A single GCGO run can identify the most stable structure and composition at a target chemical potential, removing the need for separate global searches for every stoichiometry.
  • The search allocates first-principles evaluations primarily to stoichiometries that are competitive at the target conditions, avoiding wasteful sampling of very unstable compositions.
  • One run can produce global minima for several stoichiometries; in the Pt3Ox/CeO2 test, the algorithm found structures 0.70 eV and 0.56 eV more stable than previously reported minima for Pt3O6 and Pt3O4.
  • The success rate is highest when a single stoichiometry is clearly most stable; near phase boundaries, where several stoichiometries are close in Gibbs energy, the search can get stuck on smaller, easier-to-optimize compositions.
  • The algorithm applies to both cluster systems and extended surface reconstructions, so it can be used to model catalysts under reactive environments more generally.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A fairer efficiency comparison would give the canonical approach the same total first-principles budget and measure the quality of the best structure found; the paper's conclusions are based on a comparison with previously published canonical runs that used different stopping criteria.
  • The cross-stoichiometry transferability of the local SOAP+GPR surrogate is the key fragility; systems with strong charge transfer or long-range electrostatics could violate the locality assumption, so stress-testing on ionic oxides would be a prudent validation.
  • The Gibbs-energy acquisition function neglects vibrational and entropic contributions; including them would extend the method to finite-temperature phase stability without changing the overall search framework.
  • The active-learning loop could accommodate more expressive surrogate architectures—for example, equivariant message-passing networks—which might improve cross-composition accuracy while keeping the on-the-fly training and uncertainty ranking.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The manuscript implements a grand canonical global optimization (GCGO) algorithm in the AGOX framework. The algorithm combines GOFEE-style on-the-fly training of a sparse Gaussian Process Regression (GPR) model with SOAP descriptors, and uses a Gibbs-energy-of-formation acquisition function to compare candidates across stoichiometries. The search is demonstrated on Ir3Ox clusters (using a MACE MLIP as the target level of theory in the statistical benchmark), Pt3Ox clusters supported on CeO2(111) (using DFT as the target), and Pd(100) surface oxides (using DFT). The central claim is that GCGO finds stable structures and chemical states under given reaction conditions more efficiently than canonical approaches that optimize each stoichiometry independently.

Significance. If the efficiency claim were fully supported, the paper would be a useful contribution: it addresses a real bottleneck in computational catalysis, the code is released as part of an open-source package, the Pd(100) test reproduces known surface-oxide phases, and the algorithm demonstrably explores multiple stoichiometries in a single run. However, the evidence for the headline claim is weakened by the success metric used in the Ir3Ox benchmark, which ignores stoichiometry, and by the uncontrolled comparison with the GOFEE baseline for Pt3Ox. The paper is therefore best viewed as a promising algorithmic demonstration whose quantitative performance claims need substantial revision.

major comments (5)
  1. [Section III A, Fig. 3b] The success criterion is defined as finding a candidate with ΔGf within 0.5 eV of the true global minimum, and the text explicitly states that this ignores whether the candidate has the same stoichiometry as the true minimum. The paper itself notes that requiring the correct stoichiometry at λ2 (ΔμO = -1.15 eV) drops the success rate to roughly 10%. Because the method's purpose is to identify both stable structure and chemical state, a metric that rewards the wrong composition cannot support the Conclusion's claim of finding 'stable configurations and compositions'. The bias toward smaller, simpler stoichiometries is also attributed to the search operators themselves, so the benchmark does not demonstrate efficiency for the near-degenerate cases that motivate a grand canonical method.
  2. [Section III B, Section II B 2] The comparison with the canonical GOFEE approach is uncontrolled. The GOFEE baseline used 800 single-point evaluations per stoichiometry, while each GCGO run used about 3000 total. Moreover, GCGO found structures that are 0.56–0.70 eV more stable than the previously reported GOFEE minima, which indicates that the baseline had not converged. A fair head-to-head requires matched evaluation budgets, an identical success criterion that includes stoichiometry, and ideally the same target level of theory for both algorithms. As written, the data do not establish that GCGO is more efficient than canonical approaches.
  3. [Section II B 1 and Section III A] The main statistical benchmark for Ir3Ox uses a MACE machine-learning potential as the 'target level of theory' rather than first-principles DFT. This setup tests the search algorithm on a cheap MLIP target, but it does not measure the number of DFT evaluations saved, which is the central efficiency claim of the paper. The large number of runs made possible by using MACE is acknowledged, but the conclusions are stated in terms of reducing first-principles calculations. Results obtained with a MACE target should be presented as a search-behavior study, not as a benchmark of DFT-evaluation efficiency.
  4. [Section II A and Fig. 2] The size-extensive local surrogate is essential for ranking candidates across different stoichiometries, yet its cross-stoichiometry accuracy is never quantified. The parity plots in Fig. 2 pool all compositions and all steps into a single plot, so the reader cannot see whether errors are concentrated in rarely sampled stoichiometries. Since a wrong relative Gibbs-energy ranking between stoichiometries directly misdirects the acquisition function, the manuscript should report per-stoichiometry error metrics (e.g., MAE/RMSE as a function of x) and, ideally, the error in predicted ΔGf at the target chemical potentials.
  5. [Section III A] The 'true' global minima used to score success in the Ir3Ox benchmark are the best structures found by the GCGO runs themselves plus additional single-stoichiometry GCGO executions. This is partially self-referential: the success rates are relative to structures discovered by the same algorithm, so they could be inflated if a lower-energy structure was never sampled. An independent reference for at least some of these small clusters (e.g., exhaustive sampling or literature global minima) would strengthen the validation.
minor comments (5)
  1. [Abstract and author list] Typos: 'nanostructued', 'Theab initio', and the author name 'Bjrk' should be 'Bjørk'.
  2. [Section II B 3] The text says '15 searches at each of five different chemical potentials ... adding up to a total of 45 GCGO runs.' Fifteen times five is 75, not 45. Please correct the count or the per-potential number of runs.
  3. [Section II B 2 vs III B] The allowed stoichiometry range for Pt3Ox is given as x ∈ {1,...,6} in the methods section but as x ∈ {0,...,6} in the results. Please make this consistent.
  4. [Section III B, Fig. 6 text] The text refers to 'Pt6O5 and Pt6O4' after describing a Pt3Ox run; these should presumably be Pt3O5 and Pt3O4. Also, 'GOGC' appears in one place instead of 'GCGO'.
  5. [Fig. 3 caption] The caption says 'shown as dotted vertical lines if Fig. 3a' — 'if' should be 'in'.

Circularity Check

2 steps flagged · score 6.0 of 10

Partial circularity: Ir3Ox 'true' minima are the algorithm's own outputs and Pt3Ox reference minima come from the authors' own unconverged GOFEE work; Pd(100) comparison is external and independent.

  1. self definitional [Section III A (Performance analysis for free-standing Ir3Ox particles), phase diagram description and Fig. 3]
    "The global minima correspond to the best structures found for each stoichiometry along the 75 GCGO executions as well as in additional single-stoichiometry executions of the GCGO algorithm carried out as consistency tests."

    The success criterion defines the 'true' global minima as the best candidates produced by the same GCGO algorithm being tested. Cumulative success is therefore the rate at which a run rediscovers the algorithm's own best output, not the rate at which an independently known ground truth is found. This is a self-referential benchmark: the target of the search is constructed from the search's own results. The paper's own caveat that imposing the correct stoichiometry lowers the lambda2 success rate to ~10% shows that the 0.5 eV DeltaGf-only metric can count a run successful even when the identified composition is wrong, which is the central claimed capability.

  2. self citation load bearing [Section III B (Performance analysis for Pt3Ox particles on CeO2(111)), Fig. 5b and preceding text]
    "we reproduce the results obtained in a previous work employing the GOFEE method for the catalytically relevant Pt3Ox/CeO2(111) system ... As a measure of the GCGO success rate, Fig. 5b shows the number of executions, as a function of target Delta-mu_O and stoichiometry, where a structure 0.1 eV less stable or better than the GOFEE candidate to the global minimum was found."

    The reference 'global minimum' for the Pt3Ox benchmark is the GOFEE candidate from Ref 15, a paper authored by two of the current authors. The success metric is explicitly 'better than the GOFEE candidate', not comparison to an externally established minimum. The paper itself reports that GCGO found structures 0.70 eV and 0.56 eV more stable than those Ref 15 minima for Pt3O6 and Pt3O4, showing the prior self-citation baseline was not converged. Hence the claimed 'higher efficiency than Canonical approaches' for this system is measured against the authors' own earlier, demonstrably incomplete search, making the comparison self-referential rather than a test against the true global minimum.

full rationale

The core algorithm is not circular: the GCGO acquisition function (Eq. 3), the SOAP+GPR local surrogate, and the addition/removal composition operators are defined independently of the benchmark results, and the Pd(100) comparison to Rogal et al. is external and gives independent support. However, the two cluster benchmarks that carry the main efficiency claim are partially self-referential. For Ir3Ox, the 'true' global minima used to score success are the best candidates found by the same GCGO algorithm, so the success rate measures self-consistency rather than independent identification; the paper explicitly acknowledges that success rates use only a DeltaGf criterion and that requiring the correct stoichiometry drops the lambda2 success rate to ~10%, undermining the claim that GCGO finds both structure and composition. For Pt3Ox, the reference minima come from the authors' own previous GOFEE work, and the paper shows these were not converged (GCGO finds 0.56-0.70 eV lower structures), so the comparison to canonical GOFEE is not a fair or independent benchmark. Additional correctness risks, such as unquantified cross-stoichiometry MLIP accuracy and the uncontrolled evaluation budgets in the Pt3Ox comparison, are noted but are not themselves circularity. Overall, the validation is partly circular, but the external Pd(100) result and the independent implementation details prevent the circularity from being total.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The algorithm does not introduce new physical entities. The central claim depends on the local-energy decomposition ansatz, the standard vibrational-free Gibbs approximation, and the quality of the reference models (MACE for Ir3Ox, DFT for the others), plus a set of user-chosen hyperparameters (kappa, SOAP settings, inducing point cap, success thresholds) that are not tuned or ablated.

free parameters (4)
  • kappa (uncertainty weight) = 2
    User-defined weight in the acquisition function F = dG_M - kappa*sigma; no sensitivity analysis is provided.
  • SOAP descriptor parameters = R_cut=5 (presumably Angstrom), n_max=3, l_max=2, sigma=1
    Chosen by hand for all runs; no systematic tuning or justification is given in the paper.
  • CUR inducing points cap = 1000
    Arbitrary cap on the sparse GPR inducing points; stated as a run parameter without justification.
  • Success thresholds = 0.5 eV (Ir3Ox), 0.1 eV (Pt3Ox)
    Evaluation thresholds chosen by hand to define success; the 0.5 eV threshold is loose and directly affects reported success rates.
assumptions (3)
  • domain assumption Gibbs energy can be approximated by potential energies, neglecting vibrational and entropic contributions (Eq. 2).
    Standard ab initio thermodynamics approximation invoked in Section II A; it assumes vibrational contributions cancel or are negligible, which is questionable for small clusters.
  • domain assumption Total energies decompose into a sum of atomic environment contributions (SOAP/GAP local model), making the surrogate size-extensive across stoichiometries.
    Invoked in Section II A to justify using one model across compositions; fails if long-range or charge-transfer effects dominate, as in ionic oxide clusters.
  • domain assumption The MACE MLIP accurately represents the DFT reference for Ir3Ox.
    Used as the target level of theory in the statistical benchmark in Section II B 1; errors in MACE become ground-truth errors for success-rate measurement.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Efficient Grand Canonical Global Optimization with On-the-fly-trained Machine-learning Interatomic Potentials." pith.science (2026). https://pith.science/paper/QJ5YW5OL

@misc{pith2026250919968,
  author       = {Pith},
  title        = {Pith review of: Efficient Grand Canonical Global Optimization with On-the-fly-trained Machine-learning Interatomic Potentials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QJ5YW5OL}},
  note         = {Machine review of arXiv:2509.19968}
}
read the original abstract

The characterization of nanostructured materials under reactive environments is challenging due to the complexity of the structural motifs involved and their chemical transformations. Global optimization approaches allow predicting stable structures for targeted materials but addressing the configurational and compositional search spaces is both computationally demanding and inefficient, especially when first principles calculations are required. In this work, we implement and evaluate a computationally efficient grand canonical global optimization algorithm able to identify stable structures and chemical states of targeted systems under given reaction conditions (e.g. reactant pressure and temperature). The algorithm leverages an on-the-fly trained machine-learning interatomic potential based on sparse Gaussian Process Regression and the smooth overlap of atomic positions descriptor to reduce the number of first principles energy evaluations carried out during global optimization searches. The \textit{ab initio} thermodynamics framework is incorporated to approximate the Gibbs energy of evaluated candidates, performing environment-aware optimizations over multiple stoichiometries. We demonstrate the computational performance of this approach and its ability to reproduce some literature examples.

Figures

Figures reproduced from arXiv: 2509.19968 by the authors.

Figure 1
Figure 1. FIG. 1. Execution diagram of the grand canonical global op [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. In order to evaluate the performance with statis [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 32 canonical work pages

  1. [1]

    author author M. A. \ Newton ,\ title title Dynamic adsorbate/reaction induced structural change of supported metal nanoparticles: heterogeneous catalysis and beyond , \ 10.1039/b707746g journal journal Chemical Society Reviews \ volume 37 ,\ pages 2644 ( year 2008 ) NoStop

    work page doi:10.1039/b707746g 2008

  2. [2]

    author author K. F. \ Kalz , author R. Kraehnert , author M. Dvoyashkin , author R. Dittmeyer , author R. Gl\" a ser , author U. Krewer , author K. Reuter , \ and\ author J. Grunwaldt ,\ title title Future challenges in heterogeneous catalysis: Understanding catalysts under dynamic reaction conditions , \ 10.1002/cctc.201600996 journal journal ChemCatChem...

    work page doi:10.1002/cctc.201600996 2016

  3. [3]

    author author P. L. \ Hansen , author J. B. \ Wagner , author S. Helveg , author J. R. \ Rostrup-Nielsen , author B. S. \ Clausen , \ and\ author H. Topsøe ,\ title title Atom-resolved imaging of dynamic shape changes in supported copper nanocrystals , \ 10.1126/science.1069325 journal journal Science \ volume 295 ,\ pages 2053–2055 ( year 2002 ) NoStop

    work page doi:10.1126/science.1069325

  4. [4]

    Grajciar , author C

    author author L. Grajciar , author C. J. \ Heard , author A. A. \ Bondarenko , author M. V. \ Polynski , author J. Meeprasert , author E. A. \ Pidko , \ and\ author P. Nachtigall ,\ title title Towards operando computational modeling in heterogeneous catalysis , \ 10.1039/c8cs00398j journal journal Chemical Society Reviews \ volume 47 ,\ pages 8307–8348 (...

    doi:10.1039/c8cs00398j 2018

  5. [5]

    Lykhach , author S

    author author Y. Lykhach , author S. M. \ Kozlov , author T. Skála , author A. Tovt , author V. Stetsovych , author N. Tsud , author F. Dvořák , author V. Johánek , author A. Neitzel , author J. Mysliveček , author S. Fabris , author V. Matolín , author K. M. \ Neyman , \ and\ author J. Libuda ,\ title title Counting electrons on supported nanoparticles ,...

    work page doi:10.1038/nmat4500 2015

  6. [6]

    author author R. L. \ Johnston ,\ 10.1201/9780367805814 title Atomic and Molecular Clusters \ ( publisher CRC Press ,\ year 2002 )\ p.\ pages 256 NoStop

    work page doi:10.1201/9780367805814 2002

  7. [7]

    Wang , author J.-X

    author author H. Wang , author J.-X. \ Liu , author L. F. \ Allard , author S. Lee , author J. Liu , author H. Li , author J. Wang , author J. Wang , author S. H. \ Oh , author W. Li , author M. Flytzani-Stephanopoulos , author M. Shen , author B. R. \ Goldsmith , \ and\ author M. Yang ,\ title title Surpassing the single-atom catalytic activity limit thr...

    work page doi:10.1038/s41467-019-11856-9 2019

  8. [8]

    author author L. B. \ Vilhelmsen \ and\ author B. Hammer ,\ title title Systematic study of au _ 6 to au _ 12 gold clusters on mgo(100) f centers using density-functional theory , \ 10.1103/PhysRevLett.108.126101 journal journal Phys. Rev. Lett. \ volume 108 ,\ pages 126101 ( year 2012 ) NoStop

    work page doi:10.1103/physrevlett.108.126101 2012

Show all 65 references
  1. [9]

    author author L. B. \ Vilhelmsen \ and\ author B. Hammer ,\ title title A genetic algorithm for first principles global structure optimization of supported nano structures , \ 10.1063/1.4886337 journal journal The Journal of Chemical Physics \ volume 141 ,\ pages 044711 ( year...

    2014 doi

  2. [10]

    author author L. B. \ Vilhelmsen , author K. S. \ Walton , \ and\ author D. S. \ Sholl ,\ title title Structure and mobility of metal clusters in mofs: Au, pd, and aupd clusters in mof-74 , \ 10.1021/ja305004a journal journal Journal of the American Chemical Society \ volume 1...

    2012 doi

  3. [11]

    \ Liu , author Y

    author author J.-X. \ Liu , author Y. Su , author I. A. W. \ Filot , \ and\ author E. J. M. \ Hensen ,\ title title A linear scaling relation for co oxidation on ceo2-supported pd , \ 10.1021/jacs.7b13624 journal journal Journal of the American Chemical Society \ volume 140 ,\...

    2018 doi

  4. [12]

    Zhai \ and\ author A

    author author H. Zhai \ and\ author A. N. \ Alexandrova ,\ title title Fluxionality of catalytic clusters: When it matters and how to address it , \ 10.1021/acscatal.6b03243 journal journal ACS Catalysis \ volume 7 ,\ pages 1905–1911 ( year 2017 ) NoStop

    1905 doi

  5. [13]

    Zandkarimi \ and\ author A

    author author B. Zandkarimi \ and\ author A. N. \ Alexandrova ,\ title title Dynamics of subnanometer pt clusters can break the scaling relationships in catalysis , \ 10.1021/acs.jpclett.8b03680 journal journal The Journal of Physical Chemistry Letters \ volume 10 ,\ pages 460...

    2019 doi

  6. [14]

    Reichenbach , author M

    author author T. Reichenbach , author M. Walter , author M. Moseler , author B. Hammer , \ and\ author A. Bruix ,\ title title Effects of gas-phase conditions and particle size on the properties of cu(111)-supported znyox particles revealed by global optimization and ab initio...

    2019 doi

  7. [15]

    author author J. E. \ Quinlivan Domínguez , author K. M. \ Neyman , \ and\ author A. Bruix ,\ title title Stability of oxidized states of freestanding and ceria-supported ptox particles , \ 10.1063/5.0099927 journal journal The Journal of Chemical Physics \ volume 157 ,\ pages...

    2022 doi

  8. [16]

    Behler \ and\ author M

    author author J. Behler \ and\ author M. Parrinello ,\ title title Generalized neural-network representation of high-dimensional potential-energy surfaces , \ 10.1103/PhysRevLett.98.146401 journal journal Phys. Rev. Lett. \ volume 98 ,\ pages 146401 ( year 2007 ) NoStop

    2007 doi

  9. [17]

    Lubbers , author J

    author author N. Lubbers , author J. S. \ Smith , \ and\ author K. Barros ,\ title title Hierarchical modeling of molecular energies using a deep neural network , \ 10.1063/1.5011181 journal journal The Journal of Chemical Physics \ volume 148 ,\ pages 241715 ( year 2018 ) ,\ ...

    2018 doi

  10. [18]

    u tt , author F. Arbabzadah , author S. Chmiela , author K. R. \ M\

    author author K. T. \ Sch\" u tt , author F. Arbabzadah , author S. Chmiela , author K. R. \ M\" u ller , \ and\ author A. Tkatchenko ,\ title title Quantum-chemical insights from deep tensor neural networks , \ 10.1038/ncomms13890 journal journal Nature Communications \ volum...

    2017 doi

  11. [19]

    author author K. T. \ Schütt , author H. E. \ Sauceda , author P.-J. \ Kindermans , author A. Tkatchenko , \ and\ author K.-R. \ Müller ,\ title title Schnet – a deep learning architecture for molecules and materials , \ 10.1063/1.5019779 journal journal The Journal of Chemica...

    2018 doi

  12. [20]

    author author S. R. \ Xie , author M. Rupp , \ and\ author R. G. \ Hennig ,\ title title Ultra-fast interpretable machine-learning potentials , \ 10.1038/s41524-023-01092-7 journal journal npj Computational Materials \ volume 9 ,\ pages 162 ( year 2023 ) NoStop

    2023 doi

  13. [21]

    author author D. P. \ Kovács , author I. Batatia , author E. S. \ Arany , \ and\ author G. Csányi ,\ title title Evaluation of the mace force field architecture: From medicinal chemistry to materials science , \ 10.1063/5.0155322 journal journal The Journal of Chemical Physics...

    2023 doi

  14. [22]

    author author M. K. \ Bisbo \ and\ author B. Hammer ,\ title title Efficient global structure optimization with a machine-learned surrogate model , \ 10.1103/PhysRevLett.124.086102 journal journal Phys. Rev. Lett. \ volume 124 ,\ pages 086102 ( year 2020 ) NoStop

    2020 doi

  15. [23]

    author author M. K. \ Bisbo \ and\ author B. Hammer ,\ title title Global optimization of atomic structure enhanced by machine learning , \ 10.1103/PhysRevB.105.245404 journal journal Phys. Rev. B \ volume 105 ,\ pages 245404 ( year 2022 ) NoStop

    2022 doi

  16. [24]

    author author V. L. \ Deringer , author D. M. \ Proserpio , author G. Csányi , \ and\ author C. J. \ Pickard ,\ title title Data-driven learning and prediction of inorganic crystal structures , \ 10.1039/c8fd00034d journal journal Faraday Discussions \ volume 211 ,\ pages 45–5...

    2018 doi

  17. [25]

    author author J. Behler ,\ title title Constructing high‐dimensional neural network potentials: A tutorial review , \ 10.1002/qua.24890 journal journal International Journal of Quantum Chemistry \ volume 115 ,\ pages 1032–1050 ( year 2015 ) NoStop

    2015 doi

  18. [26]

    Jinnouchi , author F

    author author R. Jinnouchi , author F. Karsai , \ and\ author G. Kresse ,\ title title On-the-fly machine learning force field generation: Application to melting points , \ 10.1103/PhysRevB.100.014105 journal journal Phys. Rev. B \ volume 100 ,\ pages 014105 ( year 2019 ) NoStop

    2019 doi

  19. [27]

    Li , author J

    author author Z. Li , author J. R. \ Kermode , \ and\ author A. De Vita ,\ title title Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces , \ 10.1103/PhysRevLett.114.096405 journal journal Phys. Rev. Lett. \ volume 114 ,\ pages 096405 ( year 2015 ) NoStop

    2015 doi

  20. [28]

    Lin , author Y

    author author Q. Lin , author Y. Zhang , author B. Zhao , \ and\ author B. Jiang ,\ title title Automatically growing global reactive neural network potential energy surfaces: A trajectory-free active learning strategy , \ 10.1063/5.0004944 journal journal The Journal of Chemi...

    2020 doi

  21. [29]

    author author T. D. \ Loeffler , author T. K. \ Patra , author H. Chan , author M. Cherukara , \ and\ author S. K. R. S. \ Sankaranarayanan ,\ title title Active learning the potential energy landscape for water clusters from sparse training data , \ 10.1021/acs.jpcc.0c00047 j...

    2020 doi

  22. [30]

    Schmitz , author E

    author author G. Schmitz , author E. L. \ Klinting , \ and\ author O. Christiansen ,\ title title A gaussian process regression adaptive density guided approach for potential energy surface construction , \ 10.1063/5.0015344 journal journal The Journal of Chemical Physics \ vo...

    2020 doi

  23. [31]

    Timmermann , author Y

    author author J. Timmermann , author Y. Lee , author C. G. \ Staacke , author J. T. \ Margraf , author C. Scheurer , \ and\ author K. Reuter ,\ title title Data-efficient iterative training of gaussian approximation potentials: Application to surface structure determination of...

    2021 doi

  24. [32]

    Xu , author X.-M

    author author J. Xu , author X.-M. \ Cao , \ and\ author P. Hu ,\ title title Accelerating metadynamics-based free-energy calculations with adaptive machine learning potentials , \ 10.1021/acs.jctc.1c00261 journal journal Journal of Chemical Theory and Computation \ volume 17 ...

    2021 doi

  25. [33]

    author author M.-P. V. \ Christiansen , author N. Rønne , \ and\ author B. Hammer ,\ title title Atomistic global optimization x: A python package for optimization of atomistic structures , \ 10.1063/5.0094165 journal journal The Journal of Chemical Physics \ volume 157 ,\ pag...

    2022 doi

  26. [34]

    Rønne , author M.-P

    author author N. Rønne , author M.-P. V. \ Christiansen , author A. M. \ Slavensky , author Z. Tang , author F. Brix , author M. E. \ Pedersen , author M. K. \ Bisbo , \ and\ author B. Hammer ,\ title title Atomistic structure search using local surrogate model , \ 10.1063/5.0...

    2022 doi

  27. [35]

    author author A. P. \ Bart\'ok , author M. C. \ Payne , author R. Kondor , \ and\ author G. Cs\'anyi ,\ title title Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons , \ 10.1103/PhysRevLett.104.136403 journal journal Phys. Rev. Lett. \...

    2010 doi

  28. [36]

    author author A. P. \ Bartók , author S. De , author C. Poelking , author N. Bernstein , author J. R. \ Kermode , author G. Csányi , \ and\ author M. Ceriotti ,\ title title Machine learning unifies the modeling of materials and molecules , \ 10.1126/sciadv.1701816 journal jou...

    2017 doi

  29. [37]

    Chmiela , author A

    author author S. Chmiela , author A. Tkatchenko , author H. E. \ Sauceda , author I. Poltavsky , author K. T. \ Schütt , \ and\ author K.-R. \ Müller ,\ title title Machine learning of accurate energy-conserving molecular force fields , \ 10.1126/sciadv.1603015 journal journal...

    2017 doi

  30. [38]

    author author V. L. \ Deringer , author N. Bernstein , author A. P. \ Bartók , author M. J. \ Cliffe , author R. N. \ Kerber , author L. E. \ Marbella , author C. P. \ Grey , author S. R. \ Elliott , \ and\ author G. Csányi ,\ title title Realistic atomistic structure of amorp...

    2018 doi

  31. [39]

    Klawohn , author J

    author author S. Klawohn , author J. P. \ Darby , author J. R. \ Kermode , author G. Csányi , author M. A. \ Caro , \ and\ author A. P. \ Bartók ,\ title title Gaussian approximation potentials: Theory, software implementation and application examples , \ 10.1063/5.0160898 jou...

    2023 doi

  32. [40]

    Reuter \ and\ author M

    author author K. Reuter \ and\ author M. Scheffler ,\ title title First-principles atomistic thermodynamics for oxidation catalysis: Surface phase diagrams and catalytically interesting regions , \ 10.1103/PhysRevLett.90.046103 journal journal Phys. Rev. Lett. \ volume 90 ,\ p...

    2003 doi

  33. [41]

    Reuter , author C

    author author K. Reuter , author C. Stampf , \ and\ author M. Scheffler ,\ title Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions , \ in\ 10.1007/978-1-4020-3286-8_10 booktitle Handbook of Materials Modeling \ ( publisher Springe...

    2005 doi

  34. [42]

    author author K. Reuter ,\ title Ab initio thermodynamics and first-principles microkinetics for surface catalysis , \ in\ 10.1007/978-3-319-44439-0_7 booktitle Operando Research in Heterogeneous Catalysis \ ( publisher Springer International Publishing ,\ year 2016 )\ p.\ pag...

    2016 doi

  35. [43]

    Bonilla-Petriciolet , author G

    author author A. Bonilla-Petriciolet , author G. P. \ Rangaiah , \ and\ author J. G. \ Segovia-Hernández ,\ title title Constrained and unconstrained gibbs free energy minimization in reactive systems using genetic algorithm and differential evolution with tabu list , \ 10.101...

    2010 doi

  36. [44]

    author author G. P. \ Rangaiah ,\ title title Evaluation of genetic algorithms and simulated annealing for phase equilibrium and stability problems , \ 10.1016/s0378-3812(01)00528-3 journal journal Fluid Phase Equilibria \ volume 187–188 ,\ pages 83–109 ( year 2001 ) NoStop

    2001 doi

  37. [45]

    Teh \ and\ author G

    author author Y. Teh \ and\ author G. Rangaiah ,\ title title A study of equation-solving and gibbs free energy minimization methods for phase equilibrium calculations , \ 10.1205/026387602320776821 journal journal Chemical Engineering Research and Design \ volume 80 ,\ pages ...

    2002 doi

  38. [46]

    Zhang , author W

    author author Z. Zhang , author W. Gee , author R. H. \ Lavroff , \ and\ author A. N. \ Alexandrova ,\ title title Gocia: a grand canonical global optimizer for clusters, interfaces, and adsorbates , \ 10.1039/d4cp03801k journal journal Physical Chemistry Chemical Physics \ vo...

    2025 doi

  39. [47]

    Chen , author C

    author author D. Chen , author C. Shang , \ and\ author Z.-P. \ Liu ,\ title title Automated search for optimal surface phases (asops) in grand canonical ensemble powered by machine learning , \ 10.1063/5.0084545 journal journal The Journal of Chemical Physics \ volume 156 ,\ ...

    2022 doi

  40. [48]

    Couzini\' e , author Y

    author author Y. Couzini\' e , author Y. Seki , author Y. Nishiya , author H. Nishi , author T. Kosugi , author S. Tanaka , \ and\ author Y.-i. \ Matsushita ,\ title title Machine learning supported annealing for prediction of grand canonical crystal structures , \ 10.7566/JPS...

    2025 doi

  41. [49]

    \ Li , author Y.-F

    author author J.-L. \ Li , author Y.-F. \ Li , \ and\ author Z.-P. \ Liu ,\ title title In situ structure of a mo-doped pt–ni catalyst during electrochemical oxygen reduction resolved from machine learning-based grand canonical global optimization , \ 10.1021/jacsau.3c00038 jo...

    2023 doi

  42. [50]

    Calvo , author D

    author author F. Calvo , author D. Schebarchov , \ and\ author D. J. \ Wales ,\ title title Grand and semigrand canonical basin-hopping , \ 10.1021/acs.jctc.5b00962 journal journal Journal of Chemical Theory and Computation \ volume 12 ,\ pages 902–909 ( year 2016 ) NoStop

    2016 doi

  43. [51]

    Bonilla-Petriciolet , author G

    author author A. Bonilla-Petriciolet , author G. P. \ Rangaiah , \ and\ author J. G. \ Segovia‐Hern \'a ndez ,\ title title Evaluation of stochastic global optimization methods for modeling vapor-liquid equilibrium data , \ https://api.semanticscholar.org/CorpusID:17044710 jou...

    2010

  44. [52]

    author author A. P. \ Bart\'ok , author R. Kondor , \ and\ author G. Cs\'anyi ,\ title title On representing chemical environments , \ 10.1103/PhysRevB.87.184115 journal journal Phys. Rev. B \ volume 87 ,\ pages 184115 ( year 2013 ) NoStop

    2013 doi

  45. [53]

    author author M. W. \ Mahoney \ and\ author P. Drineas ,\ title title Cur matrix decompositions for improved data analysis , \ 10.1073/pnas.0803205106 journal journal Proceedings of the National Academy of Sciences \ volume 106 ,\ pages 697–702 ( year 2009 ) NoStop

    2009 doi

  46. [54]

    Batatia , author S

    author author I. Batatia , author S. Batzner , author D. P. \ Kovács , author A. Musaelian , author G. N. C. \ Simm , author R. Drautz , author C. Ortner , author B. Kozinsky , \ and\ author G. Csányi ,\ https://arxiv.org/abs/2205.06643 title The design space of e(3)-equivaria...

    2022 arXiv

  47. [55]

    Batatia , author D

    author author I. Batatia , author D. P. \ Kovacs , author G. N. C. \ Simm , author C. Ortner , \ and\ author G. Csanyi ,\ title title MACE : Higher order equivariant message passing neural networks for fast and accurate force fields , \ in\ https://openreview.net/forum?id=YPpS...

    2022

  48. [56]

    author author S. K. \ Volker Blum , Mariana Rossi \ and\ author M. Scheffler ,\ https://arxiv.org/abs/2208.12335 title The fhi-aims code: All-electron, ab initio materials simulations towards the exascale , \ ( year 2022 ),\ http://arxiv.org/abs/2208.12335 arXiv:2208.12335 [co...

    2022 arXiv

  49. [57]

    author author J. P. \ Perdew , author K. Burke , \ and\ author M. Ernzerhof ,\ title title Generalized gradient approximation made simple , \ 10.1103/physrevlett.77.3865 journal journal Physical Review Letters \ volume 77 ,\ pages 3865–3868 ( year 1996 ) NoStop

    1996 doi

  50. [58]

    Burke , author J

    author author K. Burke , author J. P. \ Perdew , \ and\ author Y. Wang ,\ title Derivation of a generalized gradient approximation: The pw91 density functional , \ in\ 10.1007/978-1-4899-0316-7_7 booktitle Electronic Density Functional Theory \ ( publisher Springer US ,\ year ...

    1998 doi

  51. [59]

    author author J. P. \ Perdew , author J. A. \ Chevary , author S. H. \ Vosko , author K. A. \ Jackson , author M. R. \ Pederson , author D. J. \ Singh , \ and\ author C. Fiolhais ,\ title title Atoms, molecules, solids, and surfaces: Applications of the generalized gradient ap...

    1992 doi

  52. [60]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Hafner ,\ title title Ab initiomolecular dynamics for liquid metals , \ 10.1103/physrevb.47.558 journal journal Physical Review B \ volume 47 ,\ pages 558–561 ( year 1993 ) NoStop

    1993 doi

  53. [61]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Furthm\" u ller ,\ title title Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , \ 10.1016/0927-0256(96)00008-0 journal journal Computational Materials Science \ volume 6 ,\ p...

    1996 doi

  54. [62]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Furthm\" u ller ,\ title title Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set , \ 10.1103/physrevb.54.11169 journal journal Physical Review B \ volume 54 ,\ pages 11169–11186 ( year 1996...

    1996 doi

  55. [63]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Hafner ,\ title title Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements , \ 10.1088/0953-8984/6/40/015 journal journal Journal of Physics: Condensed Matter \ volume 6 ,\ pages 8245–8257 ( year 1994 ) NoStop

    1994 doi

  56. [64]

    Rogal , author K

    author author J. Rogal , author K. Reuter , \ and\ author M. Scheffler ,\ title title First-principles statistical mechanics study of the stability of a subnanometer thin surface oxide in reactive environments: Co oxidation at pd(100) , \ 10.1103/PhysRevLett.98.046101 journal ...

    2007 doi

  57. [65]

    author author J. J. \ Mortensen , author A. H. \ Larsen , author M. Kuisma , author A. V. \ Ivanov , author A. Taghizadeh , author A. Peterson , author A. Haldar , author A. O. \ Dohn , author C. Schäfer , author E. . \ Jónsson , author E. D. \ Hermes , author F. A. \ Nilsson ...

    2024

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.