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REVIEW 3 major objections 6 minor 52 references

Interpretable machine learned predictions of adsorption energies at the metal--oxide interface

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that formate adsorption energies at the metal–oxide interface of inverse catalysts can be predicted with about 0.17 eV RMSE from features of the clean cluster alone, making low-cost computational screening of CO2…

desk verdict Solid, well-executed ML screening study for formate on inverse catalysts; the clean-to-relaxed feature assumption is the main soft spot and needs quantitative support. read the letter →

arxiv 2505.21428 v1 pith:LDA2U652 submitted 2025-05-27 cond-mat.mtrl-sci

Marius Juul Nielsen , Luuk H. E. Kempen , Julie de Neergaard Ravn , Raffaele Cheula , Mie Andersen This is my paper
classification cond-mat.mtrl-sci
keywords interpretablemachinelearningadsorptionenergypredictioninversecatalystsCO2hydrogenationformatebindingworkfunctiondescriptormetal–oxideinterfaceDFTscreening
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 tries to establish that machine learning can predict adsorption energies at the metal–oxide interface of inverse catalysts without relaxing every binding configuration. It builds a dataset of 2,863 formate binding energies from density functional theory across In$_{y}$O$_{x}$ and Zn$_{y}$O$_{x}$ clusters on Au(111), Cu(111), and Pd(111), using only features of the clean cluster as inputs. The best model, a graph-based Gaussian process, reaches an out-of-sample RMSE of about 0.17 eV, and the interpretable models indicate the work function — itself correlated with cluster oxygen content — is the dominant descriptor. If correct, this provides a cheap route to screening active sites and supplying adsorption energies for microkinetic models of CO2 hydrogenation.

What carries the argument

The load-bearing construct is the clean-to-relaxed mapping: every model is trained on features computed only from clean cluster structures — stoichiometric, geometric, and electronic descriptors including work function, Bader charges, and projected density-of-states moments — while targets are adsorption energies from fully relaxed cluster+formate configurations. Binding sites are enumerated as on-top and bridge sites, and a SOAP fingerprint with farthest-point sampling selects a diverse DFT subset. The interpretable SISSO descriptor is a linear expression of rung-limited algebraic features; its identified descriptors (Equations (6)–(9)) and XGBoost feature importance together carry the physical argument that work function, d-band center/width/filling, and electronegativity control adsorption.

What would settle it

Select the configurations from the dataset where the DFT relaxation moves the formate to a different binding site or changes the cluster geometry beyond a small threshold; if predictions on that subset show errors much larger than the overall 0.17 eV RMSE while rigid configurations stay accurate, the clean-to-relaxed feature mapping is the limiting assumption.

Watch

Extended reading notes

Core claim

The central claim is that adsorption energies of formate at the metal–oxide interface can be predicted from a single DFT calculation of the clean cluster, without relaxing each adsorbate configuration. The authors enumerate on-top and bridge sites on In$_{y}$O$_{x}$ and Zn$_{y}$O$_{x}$ clusters on Au(111), Cu(111), and Pd(111), sample diverse configurations by farthest-point sampling in SOAP space, and train four models on 2,863 relaxed DFT energies. The WWL-GPR graph model achieves the lowest test RMSE (0.174 eV), followed by XGBoost (0.192 eV) and RBF-GPR (0.206 eV), while the interpretable SISSO descriptor performs worse (0.261 eV) but reveals structure. Feature importance and SISSO terms both put the work function first; work function correlates with cluster oxygen content, and formate binds more strongly on oxygen-poor clusters where metal atoms lack oxygen coordination.

Load-bearing premise

The load-bearing premise is that features of the clean cluster alone carry enough information to predict the adsorption energy of the relaxed cluster-plus-formate configuration; this fails if adsorption dissociates the formate or significantly reconstructs the cluster, a limitation the authors state at the end of Section III B and connect to a prior nanosilicate study.

Editorial extensions

If this is right

  • A single DFT calculation of the clean cluster can yield screening-level adsorption energies (RMSE about 0.17 eV) for all enumerated sites, letting expensive DFT relaxations be reserved for promising candidates.
  • Introducing about 280 DFT data points from an unseen material brings test RMSE within 0.02 eV of the full-data model, so extending the workflow to new metal–oxide combinations requires only a moderate data investment.
  • Cluster oxygen content, through its correlation with the work function, is a practical tuning knob: oxygen-poor clusters bind formate more strongly, a trend directly relevant to CO2 hydrogenation activity.
  • The models cannot be expected to work when the adsorbate dissociates or the surface reconstructs strongly; within the six studied systems such restructuring is reported to be a lesser issue.
  • The workflow can likely be extended to other adsorbates and binding motifs, allowing simultaneous prediction of many site/adsorbate combinations from the same clean-cluster calculation.

Reading between the lines

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

  • Editorial extension: because work function is experimentally accessible, the descriptor ranking suggests a fast experimental prescreen by work function before DFT, a step the paper itself does not propose.
  • Editorial extension: the clean-to-relaxed assumption is likely to be tested harder by more reactive adsorbates such as CO or atomic H than by formate, since those bind more invasively and may induce reconstruction; a hybrid workflow that re-checks reconstructed sites with a surrogate potential would be a natural extension.
  • Editorial extension: the disagreement between XGBoost and SISSO over electronegativity's role suggests that descriptor importance is partly a function of model class; combining both views may be needed before drawing mechanistic conclusions, which the paper does not resolve.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This manuscript presents a supervised machine-learning workflow for predicting formate adsorption energies at the metal–oxide interface of inverse catalysts, specifically In_yO_x and Zn_yO_x clusters supported on Au(111), Cu(111), and Pd(111). The data set contains 2,863 DFT-relaxed adsorption energies derived from 25,117 enumerated binding configurations across 141 stoichiometries and 1,629 cluster structures. A key feature of the workflow is that all model features are computed from clean cluster structures only, while the prediction targets are relaxation energies of the cluster-plus-formate systems. Four models are compared: RBF-GPR, XGBoost, SISSO, and WWL-GPR. The best model, WWL-GPR, achieves a total test RMSE of 0.174 eV, which the authors argue is useful for screening. Learning-curve analyses show that roughly 100–280 training points from an unseen material are needed to approach full-model accuracy. Interpretability analysis identifies the work function, correlated with cluster oxygen content, as the dominant descriptor, along with Pauling electronegativity and d-band features. A supplementary comparison shows that the foundational pretrained models CHGNet and MACE-MP-0a perform substantially worse than the trained models.

Significance. If the clean-to-relaxed transfer assumption holds, the workflow has clear practical value: it promises adsorption-energy estimates for many binding sites at the cost of a single DFT calculation of the clean cluster, and it identifies physically plausible descriptors with experimental relevance. The study is carefully executed in several respects: the train/test split is stratified by material and site type, hyperparameters are selected by 5-fold cross-validation, per-material test metrics are reported, learning curves for unseen materials are included, and the comparison with foundational pretrained models is disclosed in the supplement. The main significance, however, is bounded by the unquantified assumption that adsorption does not substantially reconstruct the cluster or change the binding site, an assumption the paper itself flags in Section III B. The work-function/oxygen-content correlation is a credible and testable physical finding, but the strength of the screening claim depends on closing the clean-to-relaxed gap quantitatively.

major comments (3)
  1. [II D, III B] Features are computed only from clean cluster structures (Section II D), while the targets are relaxed adsorption energies from Eq. (4). The authors acknowledge in Section III B that the models 'cannot be expected to work well' if the adsorbate dissociates or the surface reconstructs significantly, and they cite their nanosilicate study [49] as an example of such failures. They then state that for the present clusters 'cluster reconstruction seems to be a lesser issue,' but no quantitative evidence is provided. This is the load-bearing assumption for the central 0.17 eV RMSE claim. Please report, for the 2,863 relaxed data points, what fraction of the initially enumerated on-top/bridge assignments survive DFT relaxation; provide statistics on cluster-atom displacements or RMSD between clean and adsorbate-covered clusters; and show how model errors vary with the magnitude of reconstruction. Without such a check, the reported RMSE may partly reflect a mismatch between the structure the features describe and the structure the target energy describes, and the screening claim for new clusters is not yet supported.
  2. [III B, Table III] All reported RMSEs come from a single stratified 80/20 split, and the differences among the best models are small: WWL-GPR gives a total test RMSE of 0.174 eV versus 0.192 eV for XGBoost and 0.206 eV for RBF-GPR in Table III. Without repeated splits, bootstrap resampling, or another uncertainty estimate, it is not possible to determine whether the model ordering is statistically meaningful or whether the 0.17 eV figure itself has a substantial sampling uncertainty. Because the paper selects the 'best' model and uses this RMSE as the headline screening metric, please provide confidence intervals or repeated-split statistics for the total and per-material RMSEs.
  3. [Abstract, III B] The abstract states that the models can predict binding energies for 'unseen formate binding configurations' and can be used for prediction on 'structures outside of the original training data set.' The 0.17 eV RMSE, however, is for held-out configurations of the six material combinations already present in the training data. Section III B and Figure 4 show that for a completely unseen material the RMSE is on the order of 0.1 eV worse and that roughly 100–280 training points from that material are needed to approach full-model accuracy. Please qualify the screening claim in the abstract and conclusion so that it refers to unseen configurations and sites on materials represented in the training set, and state explicitly the additional data cost for genuinely new material combinations.
minor comments (6)
  1. [Table III] The column headers in Table III are garbled in the manuscript text; please reformat the table so that each model has a clear, unambiguous column header.
  2. [Figure 5] The rendered axis labels and legend for Figure 5 are incomplete; please ensure that the feature names and the importance-score axis are fully visible and labeled.
  3. [Table S1 and Section III C] The manuscript uses both 'Pauling electronegativity' (Section III C) and 'Pauli electronegativity' (Table S1); please standardize to 'Pauling electronegativity.'
  4. [Introduction] There is a duplicated article in Section I: 'where the the endothermic RWGS reaction'; please correct this typo.
  5. [III A] The paper notes that some slow-converging calculations, particularly on Pd-supported systems, were omitted; please state whether the omitted configurations are distributed uniformly across site types and stoichiometries, since a systematic omission could bias per-material error metrics.
  6. [III C and S3.1.3] The rung-3 SISSO descriptor uses a primary-feature subset preselected by XGBoost feature importance, which is acknowledged in the supplement; please also state this caveat in the main-text interpretation paragraph, since it complicates the cross-model comparison of feature importance.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ML predictions are evaluated on held-out DFT data with independently computed clean-structure features.

full rationale

This paper is an explicitly supervised machine-learning study, not a first-principles derivation. The target quantity (relaxed adsorption energies, Eq. 4) and the features (clean-structure descriptors, Section II D) are independently computed. The headline RMSE of about 0.17 eV is obtained on a stratified held-out test set (Section II E 5, Table III, Fig. 3), so the reported 'prediction' is a genuine out-of-sample evaluation rather than a fit renamed as prediction. The SISSO descriptors (Eqs. 6-9) are fitted on training data and then evaluated on test data; this is standard model assessment, not circular reasoning. Self-citations appear as upstream input (ref. 25 provides the clean cluster structures), as methodological provenance (refs. 45 and the WWL-GPR graph representation), and as an acknowledged failure mode (ref. 49 for nanosilicate reconstruction). None of these citations restate the target adsorption energies or force the model output; ref. 25 supplies input structures whose adsorption energies are newly computed here, and ref. 49 is invoked as a limitation, not as a support for the central claim. The clean-to-relaxed gap that the authors discuss is an accuracy limitation explicitly acknowledged in Section III B, not a circular step. The comparison against the foundational pretrained models CHGNet and MACE-MP-0a in Section S4 provides an external benchmark that further confirms the models are evaluated against DFT data rather than being constructed to reproduce their own inputs. No equation is shown to reduce to another by construction, and no fitted parameter is presented as an independent prediction.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

All central quantities are DFT-PBE+D4 labels plus ML fits. The paper introduces no new physical entities; the load-bearing choices are the feature-from-clean-structure mapping, the on-top/bridge site enumeration, the prior structure database of Kempen and Andersen, and the single-split evaluation protocol. Model hyperparameters and SISSO coefficients are fitted to the same data by design, and while that is normal supervised ML, numerical values of SISSO coefficients are not reported, which limits external reuse.

free parameters (7)
  • RBF-GPR kernel hyperparameters (A, length scale, noise) = A=4.52, l=4.54, sigma_n=0.198
    Tuned by 5-fold CV on training-validation data; listed in Table S2. They set the smoothness and noise level of the black-box model.
  • XGBoost hyperparameters = n_estimators=250, max_depth=7, eta=0.05, colsample_bytree=0.5, gamma=0.05, random_state=42
    Selected by grid search with 5-fold CV (Table S3); random_state fixes subsampling and improves reproducibility but is a chosen seed.
  • WWL-GPR hyperparameters = inner weight=0.74, outer weight=0.14, edge_ss=0.87, edge_sa=0.65, edge_aa=0.25, gpr_reg=0.0092, gpr_len=30
    Optimized for the graph kernel model (Table S4); these control node weighting and Gaussian process noise.
  • SISSO linear coefficients C_i = not reported
    Equation (5) defines E_ads as a linear expansion; the coefficients are fit to training data by pySISSO but their numerical values are not given in the paper.
  • SISSO rung-3 primary feature subset = 11 features chosen by XGBoost importance
    Rung-3 SISSO is trained with a reduced feature set selected from the same dataset (Section II E 3, S3.1.3); this is a hand/model-chosen restriction that can affect the descriptor.
  • pDOS energy window definition = pDOS threshold 0.01 inverse angstrom cubed per eV; upper limit Fermi level if band edge below
    Hand-chosen integration range for d- and sp-band features (supplementary S1); different windows would change feature values and could change descriptor rankings.
  • Gas-phase formate reference energy in FPM comparison = not reported (fit per FPM)
    In Supplement S4 the formate energy is left as a free fitting parameter when evaluating CHGNet and MACE-MP-0a; this is disclosed but is a fit, not a first-principles value.
assumptions (6)
  • domain assumption PBE with D4 dispersion is an adequate reference for formate adsorption energies on these interfaces.
    All 2,863 labels use this DFT setting (Section II C); no experimental or higher-level validation of absolute E_ads is provided.
  • ad hoc to paper Clean-cluster local and global features suffice to predict relaxed adsorption energies.
    Section II D states features are obtained only from clean structures; this is the central modeling premise and is acknowledged to fail under dissociation/reconstruction (Section III B).
  • domain assumption On-top and bridge site enumeration captures the important binding configurations.
    Section II B defines sites only as on-top and bridge; other coordination modes are not enumerated.
  • domain assumption The prior global structure optimization database (Kempen and Andersen 2025) supplies reliable cluster structures.
    Section II A takes clean structures from reference 25; errors or missing metastable structures would propagate into the binding site set.
  • domain assumption Stratified 80/20 split test points are representative of unseen sites on the same materials.
    Section II E 5: a single stratified split is used; no repeated splitting or uncertainty quantification is reported.
  • domain assumption The WWL graph kernel with one-step WL refinement preserves the chemical information needed for adsorption energies.
    Section II E 4 and Supplement S3.1.4; this is inherited from the WWL-GPR method of Xu et al., not re-derived here.

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Pith. "Pith review of Interpretable machine learned predictions of adsorption energies at the metal--oxide interface." pith.science (2026). https://pith.science/paper/LDA2U652

@misc{pith2026250521428,
  author       = {Pith},
  title        = {Pith review of: Interpretable machine learned predictions of adsorption energies at the metal--oxide interface},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LDA2U652}},
  note         = {Machine review of arXiv:2505.21428}
}
abstract

The conversion of $\mathrm{CO_2}$ to value-added compounds is an important part of the effort to store and reuse atmospheric $\mathrm{CO_2}$ emissions. Here we focus on $\mathrm{CO_2}$ hydrogenation over so-called inverse catalysts: transition metal oxide clusters supported on metal surfaces. The conventional approach for computational screening of such candidate catalyst materials involves a reliance on density functional theory (DFT) to obtain accurate adsorption energies at a significant computational cost. Here we present a machine learning (ML)-accelerated workflow for obtaining adsorption energies at the metal--oxide interface. We enumerate possible binding sites at the clusters and use DFT to sample a subset of these with diverse local adsorbate environments. The data set is used to explore interpretable and black-box ML models with the aim to reveal the electronic and structural factors controlling adsorption at metal--oxide interfaces. Furthermore, the explored ML models can be used for low-cost prediction of adsorption energies on structures outside of the original training data set. The workflow presented here, along with the insights into trends in adsorption energies at metal--oxide interfaces, will be useful for identifying active sites, predicting parameters required for microkinetic modeling of reactions on complex catalyst materials, and accelerating data-driven catalyst design.

Figures

Figures reproduced from arXiv: 2505.21428 by the authors.

Figure 1
Figure 1. FIG. 1. Visualizations of the types of binding sites conside [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Kernel density estimate plot illustrating the distribu [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Parity plots for adsorption energy models. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Learning curve for XGBoost models trained on incremental [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Features with feature importance scores above 0.035 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Grid plot illustrating the relationship between the oxy [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Pith tools

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