{"id":"b1fc0188-7e1a-485f-bcb9-f8b7dc362d8d","arxiv_id":"2509.19968","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A grand canonical global optimization algorithm with on-the-fly trained Gaussian process potentials finds stable structures and stoichiometries of clusters and surfaces using fewer first-principles evaluations.","lead":"This paper implements a new algorithm that searches for stable structures and chemical compositions of materials simultaneously, using a machine-learned surrogate model to cut the number of expensive quantum-mechanics calculations. It is designed to predict which structures and stoichiometries of catalytic nanoparticles are stable under given temperature and pressure conditions.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"GCGO's efficiency claim is not established: the benchmark's success criterion ignores stoichiometry, and with the correct criterion success at one of three tested conditions drops to ~10% (Section III A, Fig. 3b), so the headline overstates reliability in the regime grand-canonical search targets.","rationale":"The paper is a methods implementation with released code and reproduces several known phases, which is real evidence. However, the central efficiency claim is supported mainly by the Ir3Ox cumulative success rates (Fig. 3b), and those rates are computed under a criterion that does not require the correct composition. The paper itself discloses that adding the stoichiometry requirement drops the λ2 success rate to ~10%. That is a direct, in-paper admission that the headline claim is inflated for the very conditions where grand-canonical search is supposed to excel: phase boundaries with competing stoichiometries. The same section attributes the failures to the algorithm's bias toward smaller, simpler stoichiometries, so this is not primarily a surrogate-accuracy issue; it is a search-operator issue that would affect the method even with a perfect MLIP. The Pt3Ox comparison is also not a controlled benchmark against the canonical approach, because the canonical baseline comes from an earlier paper with a smaller budget and appears not to have converged (GCGO found notably lower minima). A correct comparison should match total first-principles budget and apply the same strict success criterion. These concerns justify maintaining the CONDITIONAL verdict rather than accepting the efficiency claim at face value; they do not justify rejection, because the method is plausible, the code is available, and the Pd(100) case qualitatively reproduces known phases. The reader's weakest assumption about SOAP/GAP locality across stoichiometries is secondary: the reported failures are attributed to search bias, not to model transfer error, and the paper's parity plots, while not per-stoichiometry, at least show the on-the-fly model improving during runs. Therefore I partially agree with the reader: the benchmark is indeed the weak point, but the more immediate problem is the success criterion and the uncontrolled baseline, not the local-energy decomposition itself.","tokens_in":15946,"tokens_out":4278,"duration_ms":56291,"concrete_test":"Using the released AGOX code and the provided MACE reference set, reanalyze the 25 Ir3Ox executions for λ2 with success redefined as: (i) the candidate's stoichiometry equals the true global-minimum stoichiometry (Ir6O7), and (ii) its ΔGf is within 0.1 eV of the true minimum. Report cumulative success at 500 and 1000 single-point evaluations. In parallel, run single-stoichiometry GOFEE for each x∈{0,...,9} with the same total budget (1000 evaluations across all x) and compute the same strict success rate. If GCGO's strict success rate is not at least comparable to GOFEE's, the 'higher efficiency' conclusion in Section IV fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing weakness is internal to the benchmark, not the MLIP locality assumption. Section III A defines a GCGO run as successful if the best candidate's ΔGf is within 0.5 eV of the true global minimum, and then explicitly states this ignores whether the candidate has the same stoichiometry as the true minimum. For the phase-boundary condition λ2 (ΔμO = -1.15 eV), imposing correct stoichiometry drops the success rate to ~10%. Since the central claim is that GCGO finds stable configurations and compositions (Section IV), this success metric is too loose. The paper itself attributes the low rates to the algorithm's bias toward smaller, simpler stoichiometries (Ir3, Ir3O3), i.e., a search-operator/sampler problem that would persist even with a perfect surrogate. Thus the benchmark does not demonstrate 'higher efficiency than Canonical approaches' for the cases where multiple stoichiometries are close in energy—the cases that motivate a grand-canonical method. The Pt3Ox comparison is also uncontrolled: the canonical GOFEE baseline (Ref. 15) used 800 single-point evaluations per stoichiometry, while GCGO used ~3000 total, and GCGO found structures 0.56–0.70 eV more stable, indicating the baseline had not converged. A fair head-to-head with matched evaluation budgets and the same strict success criterion is missing.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16327,"tokens_out":4271,"duration_ms":94585,"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":[{"comment":"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.","section":"Section III A, Fig. 3b"},{"comment":"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.","section":"Section III B, Section II B 2"},{"comment":"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.","section":"Section II B 1 and Section III A"},{"comment":"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.","section":"Section II A and Fig. 2"},{"comment":"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.","section":"Section III A"}],"minor_comments":[{"comment":"Typos: 'nanostructued', 'Theab initio', and the author name 'Bjrk' should be 'Bjørk'.","section":"Abstract and author list"},{"comment":"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.","section":"Section II B 3"},{"comment":"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.","section":"Section II B 2 vs III B"},{"comment":"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'.","section":"Section III B, Fig. 6 text"},{"comment":"The caption says 'shown as dotted vertical lines if Fig. 3a' — 'if' should be 'in'.","section":"Fig. 3 caption"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The manuscript is a reasonable contribution to an active area, and the open-source implementation is a strength. My main concern is that the headline efficiency claim is significantly stronger than the evidence: the success metric ignores stoichiometry, the Pt3Ox baseline is not converged, and the Ir3Ox benchmark uses an MLIP as the target. These are fixable with additional benchmarks and a more cautious interpretation, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"GCGO as implemented in AGOX is a genuine step forward: it takes the on-the-fly GPR/SOAP surrogate from GOFEE, makes it size-extensive, and adds a Gibbs-energy acquisition function, a K-means sampler, and an addition/removal generator. It then demonstrates the machinery on three chemically relevant systems, reproduces known phases, and the code is released. The authors are also candid about the algorithm's tendency to get stuck on smaller, simpler stoichiometries.\n\nThe soft spots land on the headline efficiency claim. The Ir3Ox statistical benchmark uses MACE as the target level of theory, which is acceptable for a methods test but weakens any claim about practical DFT savings. More importantly, the success criterion is 0.5 eV in Gibbs energy with no stoichiometry check. The paper reports that requiring the correct stoichiometry at λ2 drops success to about 10%. That is the regime a grand-canonical search is supposed to handle—multiple stoichiometries close in energy—so the claim of 'higher efficiency than canonical approaches' is not established. The Pt3Ox comparison is also uncontrolled: the GOFEE baseline used 800 evaluations per stoichiometry, while GCGO used 3000 total and found better minima, which likely reflects an underconverged baseline, not algorithmic superiority. A matched-budget head-to-head with the same success criterion is missing.\n\nThe locality assumption—that SOAP/GAP atomic energies transfer across stoichiometries—is a concern, but the paper's own analysis suggests the primary failure mode is sampling bias rather than surrogate error. Still, a per-stoichiometry error breakdown would have been useful.\n\nWho is this for? Method developers in structure prediction and anyone wanting a grand-canonical search tool in AGOX. It deserves a serious referee: the algorithm is plausible, the code is out, and the examples are relevant. But the validation needs substantial tightening before the efficiency claim is taken at face value. Recommend major revision.","headline":"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.","tokens_in":16799,"tokens_out":2737,"would_cite":true,"duration_ms":19176,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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","keywords":["grand canonical global optimization","machine-learning interatomic potentials","Gaussian process regression","SOAP descriptor","ab initio thermodynamics","evolutionary algorithms","catalyst structure prediction","surface oxide reconstructions"],"falsifier":"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.","tokens_in":15885,"feed_emoji":"⚛️","tokens_out":11278,"duration_ms":82341,"temperature":0.7,"pith_summary":"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.","feed_headline":"Grand-canonical search finds stable states with fewer DFT calls","feed_subtitle":"The algorithm varies geometry and composition together, cutting costly DFT calls.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Grand-canonical search finds stable states with fewer DFT calls","ML surrogate cuts DFT calls in grand-canonical search","One search for structure and stoichiometry","On-the-fly ML potentials speed up global optimization","Simultaneous composition-geometry search with ML efficiency"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Grand-canonical search finds stable states with fewer DFT calls","ML surrogate cuts DFT calls in grand-canonical search","One search for structure and stoichiometry","On-the-fly ML potentials speed up global optimization","Simultaneous composition-geometry search with ML efficiency"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000207,"raw_usage":{"total_tokens":1199,"prompt_tokens":669,"completion_tokens":530,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":413,"completion_tokens_details":{"reasoning_tokens":454}},"tokens_in":413,"tokens_out":530,"duration_ms":4898,"temperature":1.0,"reasoning_tokens":454,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T15:13:12.184586+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}