Efficient local atomic cluster expansion for BaTiO$_3$ close to equilibrium

Anna Gr\"unebohm; Anton Bochkarev; Lan-Tien Hsu; Matous Mrovec; Maxim N. Popov; Ralf Drautz; Yury Lysogorskiy

REVIEW 5 major objections 6 minor 78 references

Efficient local atomic cluster expansion for BaTiO$_3$ close to equilibrium

T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read For BaTiO3 near equilibrium, a short-range machine-learned atomic cluster expansion potential reproduces the ferroelectric phase transitions, field-driven switching, and key defects just as well as a model with explicit long-range Coulomb…

desk verdict A careful, honest ACE-for-BTO benchmark whose central 'no need for explicit Coulomb' claim is real but underdetermined by the absence of any long-range-sensitive test. read the letter →

arxiv 2505.17991 v1 pith:PLJUWJMI submitted 2025-05-23 cond-mat.mtrl-sci

Anna Grünebohm , Matous Mrovec , Maxim N. Popov , Lan-Tien Hsu , Yury Lysogorskiy , Anton Bochkarev , Ralf Drautz This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords bariumtitanateatomicclusterexpansionmachinelearninginteratomicpotentialsferroelectricityphasetransitionslong-rangeinteractionsdomainwallsoxygenvacancies

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

This paper asks whether a machine-learned interatomic potential for barium titanate (BaTiO3) must explicitly include long-range Coulomb interactions, or whether a purely short-range local potential can do the job. The authors build two atomic cluster expansion (ACE) models with identical short-range architecture: one fitted directly to DFT energies, and one in which nominal ionic charges are subtracted from the training energies and added back via an Ewald sum. They find that both models reproduce the sequence of ferroelectric phase transitions, field-driven polarization switching, and the properties of oxygen vacancies, stacking faults, and domain walls with similar accuracy. The paper concludes that for BTO close to equilibrium, explicit long-range electrostatics is not required, and omitting it roughly halves simulation cost.

What carries the argument

The atomic cluster expansion (ACE) provides a complete, hierarchical basis of local atomic-environment functions that obey translation, rotation, inversion, and permutation symmetries, with a Finnis-Sinclair square-root embedding $\sqrt{\phi_i^{(2)}}$ that accelerates convergence of the expansion. The comparison is carried by two parametrizations: the purely local ACE and the ACE+ hybrid, in which nominal charges (Ba$^{+2}$, Ti$^{+4}$, O$^{-2}$) are removed from the DFT training energies and re-added as a long-range Ewald Coulomb term. Field coupling is applied either directly to the atomic charges (ACE+) or through fictitious forces according to $F_i = \rho_i E_{\mathrm{ext}}$ (ACE). The square-root embedding is what lets a modest training set of 2261 near-equilibrium structures parametrize the potential energy surface tightly enough to distinguish the 1 meV/atom energy differences between the ferroelectric phases.

What would settle it

Run the published ACE potential on a charged oxygen vacancy in a large supercell or on a (001) surface with TiO2 termination and compare the energies and relaxations to DFT; a short-range model that fails to reproduce the resulting long-range fields would falsify the claim that explicit charges are unnecessary. A simpler check is the zone-center phonon spectrum of cubic BaTiO3, where the ACE model cannot reproduce the LO-TO splitting that an explicit-charge model and DFT both show.

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Extended reading notes

Core claim

The central claim is that for BaTiO3 in the near-equilibrium regime — the ground-state phases, their temperature-driven transitions, homogeneous polarization switching, and the investigated defect structures — a short-range ACE potential fitted to DFT energies captures the physics as well as an ACE+ model that treats nominal +2/+4/−2 ionic charges with an explicit Ewald-summated Coulomb term. The two potentials give essentially the same energy-volume curves, elastic constants, soft-mode phonon instabilities, transition temperatures (both underestimating experiment, as PBEsol DFT does), the mixed displacive and order-disorder character of the transitions, and field hysteresis shapes. Adding explicit charges does not improve accuracy for these properties; it lowers the coercive field, destabilizes thin domain walls at finite temperature, and more than doubles simulation time. The paper's lesson is a practical one: long-range electrostatics can be left implicit in local machine-learned potentials for this class of near-equilibrium ferroelectric problems.

Load-bearing premise

The central assumption is that the near-equilibrium training set covers enough different electrostatic environments to make the comparison fair; if charged or strongly distorted configurations fall outside that range, the equivalence of the two potentials is not established.

Editorial extensions

If this is right

A purely short-range ACE potential can reproduce the cubic–tetragonal–orthorhombic–rhombohedral transition sequence and the mixed displacive and order-disorder character, with transition temperatures in line with or better than other DFT-based models.
Field-induced polarization switching and the butterfly-shaped piezoelectric strain response are captured without explicit charges, using fictitious field forces; adding explicit charges mainly reduces the coercive field.
Oxygen-vacancy relaxation patterns, {110} stacking-fault energetics, and 180° domain-wall widths and energies in the tetragonal phase are described in good agreement with DFT references, even though point defects were not part of the training data.
Omitting explicit Coulomb interactions more than halves the simulation cost relative to the Ewald-based ACE+ model, making large-scale near-equilibrium BTO simulations more affordable.
The extrapolation-grade analysis indicates that the current parametrizations already operate in the extrapolative regime for relaxed stacking faults, so active-learning upfitting is needed before extended defects can be studied reliably.

Reading between the lines

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

If the observed equivalence holds beyond the tested configurations, the same design choice could be applied to other displacive perovskite ferroelectrics such as PbTiO3 or KNbO3, provided the training set samples the relevant polar distortions.
A testable extension would be to train ACE and ACE+ on data that deliberately include LO-TO-relevant displaced configurations or surface terminations and check whether the two models still agree; if they diverge, the near-equilibrium scope becomes the real boundary of the claim.
The paper's own admission that ACE fails to capture the LO-TO splitting suggests that for properties coupled to the macroscopic electric field—such as phonon transport or dielectric response under strong field gradients—an explicit-charge or charge-constrained extension would remain necessary even close to equilibrium.

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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

Here's the piece: two ACE potentials for BaTiO3, one purely local, one with explicit Coulomb via nominal charges, trained on the same DFT data and validated on the same property set. The controlled same-protocol comparison is genuinely new — prior BTO MLIPs (Allegro, SOAP-GAP) didn't do this in a single framework — and the validation is broad: E(V), elastic constants, phonons including the unstable modes, the full phase transition sequence, field-induced switching, oxygen vacancies, stacking faults, and domain walls. The paper is transparent about its own limits: it warns that 2261 configurations do not guarantee transferability, reports extrapolation grades up to 80 for stacking faults, and notes the PBEsol-based transition temperatures run low. That honesty earns real credit.

The soft spot is the one the stress-test flags: the equivalence claim is underdetermined because the validation suite never hits an observable that actually distinguishes a short-range model from a long-range one. The LO-TO splitting at Γ is explicitly not captured by ACE (Section III.1). For oxygen vacancies, they report relaxation patterns and the equatorial–apical energy difference, but not absolute formation energies — the quantity with a 1/L image-charge tail that a 6 Å cutoff cannot represent. Stacking-fault results sit in the extrapolative regime by the authors' own grade criterion, so they don't count as evidence of equivalence. And 142 domain-wall and 198 stacking-fault structures plus active-learning MD frames from the cooling/heating runs are inside the training data, so several 'predictions' are training-adjacent. None of this is hidden; the authors are careful to say 'close to equilibrium' and 'properties of the investigated defects.' But the abstract's wording oversteps the evidence. The real conclusion is narrower: for near-equilibrium bulk, switching barriers, and short-range relaxation around a few defects, a local ACE is sufficient. Whether long-range electrostatics matter for charged defects, surfaces, or LO-TO-coupled dynamics remains open.

One more thing: the training data and potentials are 'available upon reasonable request,' not openly released, so exact reproducibility is not currently possible.

Bottom line: this is a solid, useful engineering study and a fair comparison within its scope. It deserves a serious referee. The authors should soften the general claim, add at least one explicitly long-range-sensitive test (e.g., charged vacancy formation energy versus supercell size, or LO-TO splitting in the phonon calculation), and ideally release the data and parameters. I'd take it if I were an editor.

Referee Report

5 major / 6 minor

Summary. The paper develops two atomic cluster expansion (ACE) potentials for BaTiO3, one purely short-range (ACE) and one augmented by explicit nominal-charge Coulomb interactions with Ewald summation (ACE+), trained on 2261 PBEsol DFT configurations concentrated near equilibrium. The authors validate both potentials against bulk energy-volume curves, elastic constants, phonon spectra and instabilities, finite-temperature phase transitions and hysteresis, field-induced polarization switching, oxygen-vacancy relaxations, stacking-fault gamma-surface profiles, and domain-wall properties. They report that the two models perform comparably across all these tests and conclude that explicit long-range Coulomb interactions are not needed for these near-equilibrium properties, so that an efficient short-range ACE potential suffices. The paper is transparent about its limited transferability and about specific failures such as the missing LO-TO splitting.

Significance. If the central claim holds, the paper provides a practically useful result: an efficient short-range machine-learning potential for BaTiO3 that captures the bulk phase sequence, switching, and several defect properties without the computational cost of explicit electrostatics, and it offers a controlled comparison of implicit versus explicit charge treatment. The validation suite is broad and includes many nontrivial targets (soft phonon instabilities, energy barriers between structural prototypes, first-order transition character, field hysteresis, defect relaxations), and the authors explicitly report extrapolation grades and computational-cost trade-offs. These strengths make the paper a useful contribution to the emerging literature on machine-learning potentials for polar oxides, provided the scope of the conclusion is matched to what the tests actually constrain.

major comments (5)

[Sec. III.1] The claim that explicit Coulomb interactions are unnecessary is underdetermined by the phonon validation, because the one property directly controlled by long-range electrostatics, the LO-TO splitting at Gamma, is admitted to be missed: the text states that the high-energy modes around Gamma are not predicted correctly by ACE because LO-TO splitting is not included in the training data. Since ACE+ with nominal charges is also a fixed-charge model without explicit dipoles, the reader cannot tell whether ACE+ reproduces the LO-TO splitting; the paper does not report ACE+ phonon spectra in the main text or the Supplementary Material. The authors should either report the LO-TO behavior of ACE+ or explicitly exclude dielectric/lattice-dynamical properties from the equivalence claim, otherwise the conclusion 'long-range Coulomb interactions are optional' is stated too broadly.
[Sec. IV (oxygen vacancies)] For oxygen vacancies, the validation is limited to the energy difference between equatorial and apical sites and to short-range relaxation patterns around the vacancy; absolute formation energies are not reported. A charged vacancy in a periodic supercell has an image-charge interaction that decays as 1/L with cell size, and a 6 Angstrom cutoff ACE cannot represent this interaction while an Ewald treatment can. Without formation-energy convergence tests with respect to supercell size, the equivalence of ACE and ACE+ is not established for charged point defects, which is a central class of defects in ferroelectric oxides. I recommend adding such a test or explicitly restricting the conclusion to the relative energetics and relaxations that were actually computed.
[Table I and Sec. IV] Several of the defect validations are not independent of the training data. Table I lists 198 stacking-fault structures and 142 domain-wall structures in the training set, so the agreement for these defects partly reflects fitting rather than prediction; the same applies to the 166 active-learning MD cooling/heating configurations that are used for the phase-transition simulations. Furthermore, the stacking-fault results are admitted to have extrapolation grades up to 80, placing them in the extrapolative regime and requiring further upfitting, as the authors themselves note. The paper should therefore not present stacking-fault and domain-wall agreement as primary evidence that the potentials 'capture' these defects without explicit Coulomb physics; independent predictions, such as the O180 BaO wall (which was not in the training set), should be separated and emphasized, and the strength of the defect claim should be downgraded accordingly.
[Sec. III.3] The comparison of polarization switching is largely qualitative because the coercive field was not resolved: the text states that the exact coercive field is difficult to pinpoint and that the value with P=0 was met only once, in an ACE+ simulation for the negative field direction, while in all other cases the minimal lattice parameter at the coercive field is not visible in the a(E) curves. The conclusion that ACE and ACE+ 'describe equally well' field-induced switching is therefore based on the shape of the hysteresis loops and not on a converged coercive-field comparison. The authors should either refine the field sampling to resolve the coercive field for both models or phrase the claim as a qualitative demonstration.
[Sec. II.2 and Supplementary Fig. S1] The conclusion in the abstract that short-range ACE potentials are sufficient 'allowing for efficient short-range machine learning potentials' should be explicitly bounded by the near-equilibrium scope that the authors themselves emphasize. Section II.2 states that the moderate number of configurations does not guarantee transferability, and Supplementary Fig. S1(b) shows that ACE+ produces an unphysical energy minimum at large interatomic separations. These limitations are consistent with the paper's title, but the abstract's general phrasing could be read as a broader statement about BTO. I suggest adding an explicit scope sentence, e.g., 'for the near-equilibrium bulk and the specific defects tested here,' and noting that dielectric properties such as LO-TO splitting are outside the demonstrated equivalence.

minor comments (6)

[Fig. 3 caption] The caption says 'without backfolding and without LO-TO splitting'; the text already acknowledges that high-energy modes around Gamma are not correct, but the caption could state explicitly that all phonon plots in Figs. 3 and 4 are computed within the local, nonpolar framework, so readers do not infer a fully dielectric phonon spectrum.
[Supplementary Material, Fig. S3] The caption of Fig. S3 says the color coding and arrows are the same as Fig. 8; this is helpful, but the figure would benefit from a direct comparison of the relaxation magnitudes with DFT, as is done for ACE in the main text.
[Sec. II.2 and Table I] Table I would be easier to interpret if the number of structures in the MD active-learning set were reported separately for cooling and heating, and if the text indicated whether any of those configurations were subsequently used in the validation runs shown in Figs. 5 and 7.
[Sec. III.2 and Fig. 5] The statement that 'both ACEs give the expected sequence C -> T -> O -> R with decreasing temperature' is clear, but the transition-temperature extraction from a 1 K/ps ramp is rather fast; a sentence comparing the observed hysteresis to the intrinsic Landauer-paradox contribution would help readers judge how much of the hysteresis is dynamical.
[Data availability] The statement that DFT training data and ACE parameters can be obtained 'upon reasonable request' is not ideal for reproducibility; I recommend depositing the training set and potential files in a public repository.
[Abstract/Introduction] A few symbol artifacts appear in the rendered text, e.g., 'Pï100ð' instead of [100] directions; these should be corrected in the final version.

Circularity Check

0 steps flagged · score 1.0 of 10

No construction-level circularity; the potentials are fitted to DFT data and tested on emergent observables, with disclosed training-set overlap and extrapolation limits that weaken but do not circularize the conclusions.

full rationale

Both ACE and ACE+ are fits to the same DFT energies, so agreement with DFT is a fitting-quality statement rather than a derivation that re-imports its conclusion. The paper is explicit that ACE is trained on the full DFT energy while ACE+ subtracts nominal-charge Coulomb energy before training; the comparison tests whether a local expansion can absorb electrostatics on the chosen data distribution. The phase-transition, switching, and defect results are emergent MD or relaxation outcomes, not fitted parameters. Some validation targets do overlap the training set: Table I lists 142 domain-wall and 198 stacking-fault structures, and Sec. II.2 describes active-learning MD configurations added from cooling/heating runs between 375 and 125 K. However, this overlap does not force the reported transition temperatures, domain-wall energies, or stacking-fault profiles by construction, and the paper discloses the associated limits, including 'the chosen moderate number of configurations does not guarantee transferability', 'the high-energy modes around Gamma are not predicted correctly by ACE' because LO-TO splitting was not in the training data, and stacking-fault configurations with extrapolation grades 'up to 80'. Independent anchors are also present: oxygen vacancies are stated not to have been in the training data, the BaO-centered orthorhombic 180-degree wall is stated not to have been part of the training data, the 4+4 and 2+6 NEB barriers are compared with Kotiuga DFT, and elastic constants and transition temperatures are compared with DFT and experiment. These caveats weaken the breadth of the claim that long-range Coulomb is unnecessary, but they are limitations and underdetermination, not circular reasoning. No equation is defined in terms of the claim, no fitted parameter is renamed as a prediction, and no load-bearing self-citation is used to forbid alternatives. The residual score of 1 reflects the minor in-sample validation overlap and the paper's own extrapolation warnings, not a construction-level circularity.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The paper's central claim rests on a large set of fitted ACE coefficients and on several assumptions about PBEsol accuracy, local descriptors, and the fictitious-force treatment of electric fields. No new physical entities are introduced; the two potentials are parameterizations. The largest uncharged debt is the assumption that a 6 angstrom local environment implicitly captures electrostatics, which is precisely what the paper sets out to test.

free parameters (5)

ACE expansion coefficients c_v^(p) = not reported
The energy is expanded as E_i = phi_i^(1) + sqrt(phi_i^(2)) with coefficients fitted to 2261 DFT structures; all subsequent predictions depend on these fitted values (Sec. II.1).
ACE cutoff radius = 6 angstrom
Chosen as the short-range cutoff for both potentials; not derived from data, and central to the implicit vs explicit long-range comparison.
Additional repulsive short-range term parameters = not specified
Added for small atomic distances to ensure stability; stated not to influence thermodynamic observables, but the parameters are not given.
Nominal charges in ACE+ = Ba +2, Ti +4, O -2
Fixed by hand for the long-range Coulomb subtraction and Ewald summation; not fitted to reproduce polarization or field response.
Ewald real-space cutoff = 7 angstrom
Convergence parameter for the Coulomb energy, chosen so the energy converges within 10^-5 eV/atom; it affects the numerical result but is not a physics parameter.

assumptions (6)

standard math The ACE basis is complete and preserves translation, rotation, inversion, and permutation symmetries.
Taken from prior ACE publications (Refs. 38-40) and used in Sec. II.1 to define the representation.
domain assumption The square-root embedding form E_i = phi_i^(1) + sqrt(phi_i^(2)) is sufficient to represent the BTO potential energy surface.
This functional form is assumed from prior ACE work; no evidence is given that it captures all relevant couplings for this material.
domain assumption PBEsol DFT energies and forces are accurate ground truth for BTO.
All training labels and most validation references come from PBEsol (Sec. II.2), so the central comparison is relative to this functional's PES, not to experiment.
domain assumption A 6 angstrom local cutoff captures all chemically relevant interactions for the tested properties.
This short-sightedness assumption is exactly what the paper tests by omitting explicit charges; it is load-bearing for the conclusion that long-range Coulomb is unnecessary.
domain assumption The fictitious forces F_i = rho_i * E_ext correctly mimic an applied electric field for the charge-free ACE model.
Eq. (4), Sec. III.3; if this mapping is inaccurate, the ACE hysteresis comparison against ACE+ is invalid.
domain assumption Nominal charges give a meaningful measure of local polarization via Eq. (3).
The authors state this approach underestimates polarization magnitude but is used to compare the two models.

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Cite this review

Pith. "Pith review of Efficient local atomic cluster expansion for BaTiO$_3$ close to equilibrium." pith.science (2026). https://pith.science/paper/PLJUWJMI

@misc{pith2026250517991,
  author       = {Pith},
  title        = {Pith review of: Efficient local atomic cluster expansion for BaTiO$_3$ close to equilibrium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PLJUWJMI}},
  note         = {Machine review of arXiv:2505.17991}
}

read the original abstract

Barium titanate (BTO) is a representative perovskite oxide that undergoes three first-order ferroelectric phase transitions related to exceptional functional properties. In this work, we develop two atomic cluster expansion (ACE) models for BTO to reproduce fundamental properties of bulk as well as defective BTO phases. The two ACE models do not target full transferability but rather aim to examine the influence of implicit and explicit treatment of long-range Coulomb interactions. We demonstrate that both models describe equally well the temperature induced phase transitions as well as polarization switching due to applied electric field. Even though the parametrizations are based on a limited number of configurations that are mostly not far away from the equilibrium, the ACE models are able to capture also properties of important crystal defects, such as oxygen vacancies, stacking faults and domain walls. A systematic comparison shows that the phase transitions as well as the fundamental properties of the investigated defects can be described with similar accuracy with or without explicit treatment of charges and Coulomb interactions allowing for efficient short-range machine learning potentials.

Figures

Figures reproduced from arXiv: 2505.17991 by the authors.

**Figure 2.** FIG. 2: ACE predictions of properties of bulk BTO [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4: Phonon densities of states at 0 K (primitive [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: FIG. 5: Changes of the three (a) polarization [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: FIG. 7: Field hysteresis (a, b) in the T phase at 250 K [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 9.** Figure 9: FIG. 9: Energy profiles along the [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 10.** Figure 10: FIG. 10: Polarization profiles for (a) T 180 [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

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Pith tools

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