Symbolic Regression Discovery of New Perovskite Catalysts with High Oxygen Evolution Reaction Activity

Baicheng Weng; Corey G. Grice; Qingde Sun; Qingyu Yan; Rilong Zhu; Wan-Jian Yin; Yanfa Yan; Zhilong Song

REVIEW 3 major objections 5 minor 6 references

Symbolic Regression Discovery of New Perovskite Catalysts with High Oxygen Evolution Reaction Activity

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A single ratio of two geometric factors, μ/t, quantitatively predicts the oxygen-evolution activity of oxide perovskites and guided the discovery of four new catalysts that beat the current benchmark.

desk verdict New μ/t descriptor for OER perovskites is genuinely useful and supported by out-of-sample data, but the BET normalization assumption and thin experimental validation make the outperformance claim shakier than the authors let on. read the letter →

arxiv 1908.06778 v1 pith:5YH7Z6KD submitted 2019-08-19 cond-mat.mtrl-sci

Baicheng Weng , Zhilong Song , Rilong Zhu , Qingyu Yan , Qingde Sun , Corey G. Grice , Yanfa Yan , Wan-Jian Yin This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords symbolicregressionoxygenevolutionreactionoxideperovskiteselectrocatalysisdescriptortolerancefactoroctahedralhigh-throughputscreening

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 argues that symbolic regression, applied to a self-consistent set of eighteen measured oxide perovskite catalysts, can distill oxygen-evolution activity into an analytical formula: VRHE = 1.612 μ/t + 1.073 eV, where μ is the octahedral factor and t is the tolerance factor. If true, this replaces expensive electronic-structure descriptors with a two-parameter geometric rule computed from tabulated ionic radii. The paper used the rule to screen 3,545 charge-balanced perovskite compositions, synthesized five new ones, and reports that four, including Sr0.25Ba0.75NiO3, show lower overpotential at 5 mA cm−2 than the benchmark catalyst BSCF. The same μ/t line also tracks an independent literature dataset with accuracy comparable to the established eg volcano. A sympathetic reader would take the paper's core claim to be that OER activity in oxide perovskites is essentially a structural-geometry problem, capturable by one ratio.

What carries the argument

The load-bearing object is the ratio μ/t, where μ = rB/rO is the octahedral factor (B-site cation radius over oxygen radius) and t = (rA + rO)/(√2(rB + rO)) is the tolerance factor, a geometric measure of how well A, B, and O ions pack into the perovskite lattice. The descriptor enters through the fitted equation VRHE = 1.612 μ/t + 1.073 eV, chosen from the Pareto front after symbolic regression searched roughly 43.2 million analytical formulas built from simple operators (+, −, ×, ÷, √) and physically motivated terminals. Its work in the argument is to turn OER activity into a quantity computable from ionic radii and charge balance alone, and to supply a monotonic design rule, decrease μ and increase t, that replaces the non-monotonic volcano relationship. The paper also uses μ/t together with perovskite stability criteria to justify screening A-site cations from K, Rb, Cs and B-site cations from 3d transition metals.

What would settle it

Measure OER activity on epitaxial thin films of several perovskites spanning the μ/t range, with identical thickness, orientation, and roughness so loading and BET normalization are unnecessary; if the μ/t versus overpotential slope departs markedly from 1.612 eV per unit μ/t, the reported correlation is an artifact of powder-film normalization rather than an intrinsic property.

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Extended reading notes

Core claim

The central discovery claim is the descriptor: the overpotential versus the reversible hydrogen electrode at 5 mA cm−2 disk current, normalized by loading and BET surface area, is linear in μ/t for oxide perovskites, VRHE = 1.612 μ/t + 1.073 eV, with MAE 21.6 meV on the eighteen training compounds. Lower μ/t means higher activity. Because μ = rB/rO and t = (rA + rO)/(√2(rB + rO)), the formula says that larger A-site cations and smaller B-site cations, or higher B-site valence, which shrinks rB, should improve OER activity. The paper reports that all nine Pareto-front formulas from the symbolic regression agree on this qualitative direction, and that the μ/t line reproduces the trend of independently reported data with Pearson correlation 0.928, comparable to the eg descriptor's 0.923. Newly synthesized perovskites with low μ/t, including Cs0.4La0.6Mn0.25Co0.75O3, Cs0.3La0.7NiO3, SrNi0.75Co0.25O3, and Sr0.25Ba0.75NiO3, had measured VRHE below BSCF and close to the predicted values.

Load-bearing premise

Everything rests on the assumption that the measured overpotentials, normalized by catalyst loading and BET surface area, put all eighteen training perovskites on a common intrinsic activity scale; if film conductivity, surface reconstruction, or different rate-determining steps break that comparability, the fitted descriptor and all screening predictions inherit the distortion.

Editorial extensions

If this is right

Researchers can screen thousands of hypothetical perovskite compositions for OER activity using only tabulated ionic radii and charge balance, with no DFT calculations.
The descriptor supplies a concrete design rule: put large cations on the A site and small 3d transition-metal cations on the B site, or raise the B-site valence to shrink its radius.
Four newly synthesized perovskites, especially Sr0.25Ba0.75NiO3, are claimed to exceed BSCF in both activity and stability under galvanostatic testing.
The linear, monotonic form of the relationship means predicted activity improves continuously as μ/t decreases, unlike the volcano-shaped curves of earlier descriptors.
The same formula reproduces an independent literature dataset with correlation comparable to the established eg descriptor, supporting generality beyond the authors' own measurements.

Reading between the lines

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

If the descriptor is right, the practical discovery frontier is synthesizability, not electronic structure: activity should keep rising as μ/t falls until the perovskite structure stops forming, and the paper's failed Cs-rich syntheses mark that empirical boundary.
A natural testable extension is to apply the same μ/t screening to double perovskites and Ruddlesden–Popper phases, where the same geometric variables are defined but the paper does not claim coverage.
The μ/t rule implies that A-site substitution with even larger monovalent cations should further improve activity; a systematic mapping of the synthesis-stability boundary would turn the descriptor into a complete design map.
Because μ/t is purely geometric, the descriptor may also be useful for other perovskite electrocatalytic reactions, though that extension is not established by the paper.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

You should know two things about this paper. First, it finds a genuinely new descriptor, μ/t (octahedral factor over tolerance factor), that linearly predicts OER activity of oxide perovskites with a MAE around 21 meV on the authors' own data and, more importantly, on Suntivich's independent dataset. Second, the authors use this descriptor to screen over three thousand compositions, synthesize five new perovskites, and report four that outperform BSCF. If the descriptor generalizes, that is a cheap, DFT-free screen worth having.

The symbolic regression methodology is used competently. The training set is small but self-consistent, and the external validation is real out-of-sample evidence, not just a holdout from the same lab. The physical interpretation—large A-site cations and small B-site cations improve activity—is plausible and consistent with the descriptor.

The soft spots are in the experimental validation. The central assumption is that normalizing current by loading and BET surface area yields an intrinsic activity scale. That is a big assumption. The paper does not report BET areas for the new catalysts, so we cannot check whether the comparison against BSCF is fair on a common scale. If the new materials have lower BET areas, they would look better at the same normalized current than they are intrinsically. The external Suntivich validation inherits the same normalization, so it does not rescue the intrinsic-activity claim. That said, this normalization is standard in the electrocatalysis literature, so the claim is at least measured on a metric the field accepts.

The outperformance claim is also not as clean as the abstract suggests. The average VRHE values for the four new catalysts are 18–46 meV lower than BSCF, but the reported ranges overlap with BSCF's range for all four. The best new catalyst shows a 67 meV deviation from its predicted value, which is three times the training MAE. And eight of the thirteen attempted compositions failed to form pure perovskite; only the five pure ones were characterized. That is not a fatal flaw, but it tempers the discovery narrative.

Overall, this is a useful paper for people working on perovskite OER catalysts or materials informatics. It is not a breakthrough, but it is a solid contribution with a new descriptor and honest (if incomplete) experimental support. It deserves a serious referee, not a desk reject. I would recommend sending it to review, but the reviewers should push for BET data on the new catalysts and a discussion of the normalization assumption, and probably a fixed-disk-current comparison as a robustness check.

Best.

Referee Report

3 major / 5 minor

Summary. The paper uses symbolic regression on a newly measured, self-consistent dataset of 18 known oxide perovskite OER catalysts to derive an analytical descriptor for the oxygen evolution reaction overpotential. The selected two-parameter formula, VRHE = 1.612 μ/t + 1.073, where μ is the octahedral factor and t the tolerance factor, is used to screen 3,545 charge-balanced perovskite compositions. Thirteen low-μ/t candidates were chosen for synthesis; five formed phase-pure perovskites, and four of these are reported to have lower VRHE at a common normalized current density than Ba0.5Sr0.5Co0.8Fe0.2O3 (BSCF), the literature benchmark. The descriptor is also tested against independent measurements by Suntivich et al., showing a linear correlation with comparable mean absolute error.

Significance. If the descriptor is robust, the paper makes a useful contribution: an interpretable, parameter-light formula linking perovskite structural factors to OER activity, with a complete workflow from regression to experimental verification. The self-consistent dataset and the external comparison with Suntivich et al. are concrete strengths, as is the explicit screening of 3,545 compositions. The claim that four new perovskites outperform BSCF is potentially impactful and would be a strong demonstration of data-driven discovery. However, the validation currently rests on a normalization assumption and on mean values whose uncertainty intervals overlap with BSCF, so the significance of the central discovery claim is not yet established to the standard the paper aims for.

major comments (3)

[Methods, Table 1, Fig. 2c] The comparison of new catalysts with BSCF is made at a fixed normalized current density (10 mA cm−2 oxide), which is obtained by dividing the disk current density by the product of catalyst loading and BET surface area. The paper reports the BET area for BSCF (0.30 m2 g−1) and states that 10 mA cm−2 oxide corresponds to 5.0 mA cm−2 disk current for BSCF, but it does not report BET areas for any of the five new perovskites. If the new materials have different BET areas, the disk current densities at which VRHE is read differ, so the measured potentials may not be directly comparable. The Suntivich validation inherits the same BET normalization and therefore does not independently resolve this issue. Please report the BET areas for all new catalysts and demonstrate that the ranking is robust to alternative normalizations (for example, geometric current density or mass activity).
[Table 1, Fig. 3] The reported ranges of VRHE for BSCF (1.614–1.663 V) and for the four new catalysts (e.g., Cs0.4La0.6Mn0.25Co0.75O3: 1.562–1.623 V) overlap substantially. Since the central claim is that these new catalysts outperform BSCF, the average differences (16–46 mV) are not clearly separated given the stated experimental uncertainty. The paper should provide a statistical comparison, such as confidence intervals or a t-test, to show that the differences are significant beyond measurement noise. As presented, the claim of outperformance is not fully supported by the data.
[Results (synthesis of new perovskites)] Eight of the thirteen predicted compositions formed significant impurity phases and were excluded from electrochemical testing, leaving only the five phase-pure compounds as the validation set. This selection, together with the small number of new catalysts, weakens the evidence that the descriptor-guided screening identifies active materials with a reasonable success rate. The paper should report the fate of all thirteen candidates (including the eight impure ones) and discuss how the 5/13 success rate affects the claimed discovery capability of the descriptor.

minor comments (5)

[Abstract and affiliations] There are several typos: 'unprecedente dly' in the abstract, 'Colledge' in the affiliation block, and 'Suntvich' in the main text. These should be corrected.
[Fig. 2c caption] The caption says 'The inset Figure are from Ref. [6] with permissions.' The grammar should be fixed, and the figure should indicate whether the inset is reproduced unchanged or reformatted.
[Table S3 and Results] The description of the hyperparameter grid search states that 43,200,000 analytical formulas were produced (432 parameter sets × 20 generations × 5,000 individuals). This is correct, but the text should clarify that the 8,640 individuals on the Pareto front are the per-generation best fits, not the full population.
[Discussion of Suntivich validation] The paper describes the Suntivich comparison as confirmation of 'generality.' Since the same seven compositions appear in the training dataset, the Suntivich data are independent measurements but not out-of-sample for new compositions; the comparison would be more accurately described as a cross-laboratory reproducibility check for known materials.
[Table 1] The units of VRHE are reported as V in the table header and text, but the descriptor formula and some figure labels use eV. The potential axis is labeled in V versus RHE, so the constants in the formula (1.612 and 1.073) should be stated as having units of V, not eV, to avoid confusion.

Circularity Check

1 steps flagged · score 2.0 of 10

The μ/t descriptor is an empirical SR fit, but the new-catalyst and independent-data claims are genuine out-of-sample predictions; only the in-sample 'predicted' values are circular by construction.

fitted input called prediction [Main text after Fig. 2b; Fig. 2c; Table 1 rows 1–18]
"The predicted VRHE values (marked as diamonds) of the 18 synthesized oxide perovskites using the selected descriptors were in good agreement with the obtained experimental values, as shown in Fig. 2c ... The formula VRHE = 1.612μ/t + 1.073 (eV) (E point at Fig. 2c), to develop strategies to accelerate the discovery of these materials."

The constants 1.612 and 1.073 are the output of the symbolic-regression fit whose fitness metric is the MAE against those exact 18 experimental VRHE values (Table 1). Calling the fitted function's output for the same 18 compounds 'predicted' is therefore a fitted parameter renamed as a prediction: agreement is enforced by the fitting procedure rather than by independent predictive power. This is a minor terminological circularity only; it does not affect the out-of-sample uses of the descriptor on the Suntivich dataset or on the newly synthesized perovskites.

full rationale

The derivation chain is not substantially circular. The descriptor μ/t is constructed from ionic radii (octahedral factor and tolerance factor), not from VRHE, so there is no self-definitional identity. The equation VRHE = 1.612μ/t + 1.073 is an empirical fit to 18 in-house measurements; the paper then uses that fitted formula to screen 3,545 compositions, synthesizes five new phases, and measures their OER activity. Those measurements are outside the fitting set and four of the new catalysts are reported to outperform BSCF in the authors' own measurements. The independent Suntivich dataset (Fig. S3b) is also out-of-sample and provides genuine external evidence. The only circular presentation is labeling the in-sample fit values for the 18 training perovskites as 'predicted,' which is statistically forced by construction but does not carry the paper's central discovery claim. The self-citations (refs. 9, 19, 20) are background or motivational and are not load-bearing for the descriptor's validity. Overall, no significant circularity; score reflects the minor in-sample 'prediction' mislabel.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the comparability of the OER measurements, the validity of averaging ionic properties for alloyed perovskites, and the representativeness of the 18-compound training set. The two fitted constants in the chosen formula are the only explicit free parameters; no new physical entities are introduced.

free parameters (2)

slope of μ/t descriptor = 1.612 (eV per unit μ/t)
Fitted to VRHE of 18 known perovskites via symbolic regression; appears in formula VRHE = 1.612 μ/t + 1.073 (eV).
intercept of μ/t descriptor = 1.073 eV
Fitted intercept of the chosen Pareto-front formula; not derived from first principles.

assumptions (5)

domain assumption VRHE measured at 5 mA/cm2 disk current, normalized by loading and BET surface area, is an intrinsic and comparable measure of OER activity across different perovskites.
Methods: 'we selected low disk current densities of 5 mA·cm-2... normalized the data by the catalyst loading concentration and Brunauer-Emmet-Teller surface area. This ensures that the measured VRHE values are intrinsic values for all oxide perovskite catalysts and hence, comparable.'
domain assumption Arithmetic averaging of ionic radii, electronegativity, valence, and d-electron counts over A- and B-site cations yields valid effective parameters for solid-solution perovskites in computing t and μ.
Methods, Terminal set: 'the arithmetic averages of Nd, εd, χA, χB, QA, rA, and rB were taken for A- and B-site cations respectively, and t and μ are calculated based on averaged rA and rB values.' This is an assumption about how to represent alloyed perovskites.
domain assumption The 18 measured perovskites are a sufficient and representative training set for symbolic regression to discover a general descriptor.
The authors state reliable and comparable datasets are crucial, but do not justify representativeness quantitatively; training on 18 points from one lab limits extrapolation.
domain assumption Charge balance QA + QB = 6 fully constrains the A- and B-site compositions used in screening.
Methods, Terminal set: 'QB is trivially dependent on QA subject to charge balance QA + QB = 6.' This assumes fixed total valence and stoichiometric oxygen.
ad hoc to paper SR hyperparameters and Pareto-front selection with MAE as fitness identify physically meaningful descriptors rather than overfit artifacts.
The paper selected one of nine Pareto-front formulas (E point) based on accuracy and simplicity after inspecting the candidates; this model-selection step is not cross-validated.

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Cite this review

Pith. "Pith review of Symbolic Regression Discovery of New Perovskite Catalysts with High Oxygen Evolution Reaction Activity." pith.science (2026). https://pith.science/paper/5YH7Z6KD

@misc{pith2026190806778,
  author       = {Pith},
  title        = {Pith review of: Symbolic Regression Discovery of New Perovskite Catalysts with High Oxygen Evolution Reaction Activity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5YH7Z6KD}},
  note         = {Machine review of arXiv:1908.06778}
}

read the original abstract

Symbolic regression (SR) is an emerging method for building analytical formulas to find models that best fit data sets. Here, SR was used to guide the design of new oxide perovskite catalysts with improved oxygen evolution reaction (OER) activities. An unprecedentedly simple descriptor, {\mu}/t, where {\mu} and t are the octahedral and tolerance factors, respectively, was identified, which accelerated the discovery of a series of new oxide perovskite catalysts with improved OER activity. We successfully synthesized five new oxide perovskites and characterized their OER activities. Remarkably, four of them, Cs0.4La0.6Mn0.25Co0.75O3, Cs0.3La0.7NiO3, SrNi0.75Co0.25O3, and Sr0.25Ba0.75NiO3, outperform the current state-of-the-art oxide perovskite catalyst, Ba0.5Sr0.5Co0.8Fe0.2O3 (BSCF). Our results demonstrate the potential of SR for accelerating data-driven design and discovery of new materials with improved properties.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

6 extracted references · 5 canonical work pages

[1]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

W., James M

Yiqun Wang, N. W., James M. Rondinelli, Symbolic regression in materials science. arXiv:1901.04136v2 (2019)

arXiv 2019

[2] [2]

& Lipson, H, Distilling Free-Form Natural Laws from Experimental Data

Schmidt, M. & Lipson, H, Distilling Free-Form Natural Laws from Experimental Data. Science 324, 81-85 (2009)

work page 2009

[3] [3]

Koza, J. R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. (MIT Press, Cambridge, MA). (1992)

work page 1992

[4] [4]

Science 261, 872-878 (1993)

Forrest, S, Genetic Algorithms - Principles Of Natural -Selection Applied To Computation. Science 261, 872-878 (1993)

work page 1993

[5] [5]

T., Davies, D

Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A, Machine learning for molecular and materials science. Nature 559, 547-555 (2018)

work page 2018

[6] [6]

https://gplearn.readthedocs.io/en/latest/intro.html

work page