Explicit Electric Potential-Embedded Machine Learning Framework: A Unified Description from Atomic to Electronic Scales

Chungen Liu; Jingwen Zhou; Xuwei Liu; Yawen Yu

arxiv: 2604.07322 · v2 · submitted 2026-04-08 · ⚛️ physics.chem-ph · cond-mat.mtrl-sci

Explicit Electric Potential-Embedded Machine Learning Framework: A Unified Description from Atomic to Electronic Scales

Jingwen Zhou , Yawen Yu , Xuwei Liu , Chungen Liu This is my paper

Pith reviewed 2026-05-10 17:00 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.mtrl-sci

keywords electrochemical interfacesmachine learning force fieldselectron density predictionexplicit electric potentialPt(111)/waterequivariant graph neural networksconstant-potential simulationsab initio molecular dynamics

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The pith

An explicit electric potential-embedded machine learning framework simultaneously predicts atomic forces and electron density distributions for electrochemical interfaces.

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

The paper develops a unified framework that incorporates explicit electric potential directly into machine learning models to describe both atomic-scale dynamics and electronic charge distributions under varying conditions. Data comes from constant-potential ab initio molecular dynamics regulated efficiently in Hy-DFT, which trains two equivariant graph neural network modules: PE-MACE for forces and PE-EDP for densities. On the Pt(111)/water interface the models reproduce radial distribution functions, reveal potential-driven water reorganization over long times, and match DFT charge profiles. This matters because it opens the door to larger and longer simulations of interfaces that remain computationally prohibitive with pure first-principles methods alone.

Core claim

The authors present a three-part framework—data generation via Hy-DFT-regulated constant-potential AIMD, Potential-Embedded MACE for atomic forces, and Potential-Embedded Electron Density Prediction for charge distributions—that embeds the external potential explicitly as input. Both PE-MACE and PE-EDP, built on equivariant graph neural networks, achieve high accuracy on training and test data from the Pt(111)/water system; constant-potential machine-learning molecular dynamics yields radial distribution functions consistent with AIMD, long trajectories show voltage-induced interfacial water changes, and planar charge profiles plus Bader charges align with direct DFT results.

What carries the argument

The Potential-Embedded MACE (PE-MACE) and Potential-Embedded Electron Density Prediction (PE-EDP) modules, which take explicit electric potential as an input feature within equivariant graph neural networks to output forces and electron densities.

If this is right

Constant-potential machine-learning molecular dynamics reproduces radial distribution functions obtained from ab initio simulations while accessing longer timescales.
Long-time simulations reveal reorganization of interfacial water driven by changes in the applied electric potential.
Planar-integrated charge profiles and Bader charge analysis from the density-prediction module remain consistent with DFT reference data.
The same trained models can be applied across a range of potentials without retraining, enabling efficient exploration of voltage-dependent interface behavior.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could scale simulations to system sizes and simulation lengths that remain out of reach for direct DFT while retaining electronic-structure information.
Extension to other electrode materials, solvents, or electrolytes would require only new training data generated under the same protocol.
Coupling the framework with additional property predictors (such as free-energy surfaces or reaction barriers) could follow naturally from the shared potential embedding.

Load-bearing premise

Models trained on data from a limited set of potentials and the Pt(111)/water interface will generalize accurately to arbitrary potentials and other electrode-electrolyte combinations without significant loss of fidelity.

What would settle it

Direct comparison of the trained models against new DFT calculations for a different applied potential or a different interface (for example, a different metal surface) that shows large systematic errors in forces or electron density.

Figures

Figures reproduced from arXiv: 2604.07322 by Chungen Liu, Jingwen Zhou, Xuwei Liu, Yawen Yu.

**Figure 2.** Figure 2: Schematic of the PE-MACE model architecture. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Schematic of the PE-EDP model architecture. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

**Figure 4.** Figure 4: Comparison of the PE-MACE model accuracy on the training and test sets. (a, [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗

**Figure 5.** Figure 5: Potential-dependent structure of interfacial water at the Pt(111)/water interface [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

**Figure 6.** Figure 6: Comparison of the planar-averaged electron density ¯ρ [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

read the original abstract

To further develop accurate and large-scale simulations of electrochemical interfaces, we propose a unified explicit electric potential framework to simultaneously predict atomic forces and electron density distributions. The framework consists of three components: data generation, model training, and application. The data generation component, implemented in Hy-DFT, efficiently regulates the potential during constant-potential ab initio molecular dynamics (CP-AIMD), reducing the number of single-point calculations required for convergence. The model training component includes two modules: Potential-Embedded MACE (PE-MACE) and Potential-Embedded Electron Density Prediction (PE-EDP). PE-MACE implements an explicit electric potential machine learning force field (EEP-MLFF) based on the MACE architecture. We develop PE-EDP to overcome the limitation of EEP-MLFF in describing atom forces. PE-EDP, also based on equivariant graph neural networks, predicts electron density distributions under arbitrary potentials. Using the Pt(111)/water interface as a model system, both PE-MACE and PE-EDP show high accuracy on training and test sets. Radial distribution functions from CP-MLMD agree well with CP-AIMD, and long-timescale simulations reveal potential-induced reorganization of interfacial water. Planar-integrated charge profiles and Bader analysis from PE-EDP are consistent with DFT results. These results demonstrate that the framework can simultaneously describe atomic dynamics and electron density distributions under arbitrary potentials, providing a useful tool for studying electrochemical interfaces.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

PE-MACE and PE-EDP embed potential into equivariant networks for forces and densities on Pt/water, but the arbitrary-potential claim rests on in-distribution accuracy without range or OOD checks.

read the letter

The paper introduces two modules that take an explicit electric potential as input: PE-MACE, which extends the MACE architecture to predict forces under constant potential, and PE-EDP, an equivariant GNN that outputs electron density distributions. Both are trained on CP-AIMD trajectories generated with Hy-DFT for the Pt(111)/water interface. The results show low errors on train and test splits, radial distribution functions that match the reference simulations, and planar charge profiles plus Bader charges that stay consistent with DFT. The longer MLMD runs also illustrate potential-driven water restructuring, which is the practical payoff for electrochemical modeling. The data-generation step with Hy-DFT appears efficient for producing the constant-potential trajectories needed for training. The architecture choices are sensible given the symmetry requirements for forces and densities. The main limitation is the missing validation for the central claim. The abstract asserts a unified description under arbitrary potentials, yet the reported tests give no span of the training potentials, no indication whether test points fall inside or outside that span, and no out-of-distribution evaluations on other interfaces or potential values. Without those, the results demonstrate interpolation within the sampled window rather than reliable extrapolation. Error bars and uncertainty quantification are also absent, so it is hard to judge how much the reported accuracy can be trusted for production use. This work is aimed at groups already running or building ML force fields for electrochemical interfaces who need a concrete example of potential embedding. A reader looking for implementation details on how to wire potential into MACE-style networks could extract useful code-level ideas. The paper is coherent enough on its own terms to merit peer review, mainly so referees can press for the missing range and transferability tests before any broader claims are accepted.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an explicit electric potential-embedded machine learning framework for electrochemical interfaces, comprising Hy-DFT for generating constant-potential AIMD data, PE-MACE (equivariant GNN force field) for atomic forces, and PE-EDP (equivariant GNN) for electron density prediction. Trained and tested on Pt(111)/water data, the models report high accuracy on in-distribution sets, RDF agreement with AIMD, potential-induced water reorganization in long simulations, and consistent planar charge profiles/Bader charges with DFT. The central claim is that this enables a unified atomic-to-electronic description under arbitrary potentials.

Significance. If the generalization claim holds, the framework would be a useful advance for large-scale simulations of electrochemical interfaces by coupling ML force fields with explicit potential-dependent electron densities. The equivariant GNN architecture and Hy-DFT data generation are technically sound choices, and the reported consistency with DFT on the model system provides a reasonable starting point. However, the evidence for broad applicability remains moderate due to limited validation details.

major comments (2)

[Abstract] Abstract: The assertion that the framework delivers a 'unified description ... under arbitrary potentials' is not supported by the reported results. High accuracy, RDF agreement, and charge profile consistency are shown only on training/test sets drawn from the same Hy-DFT CP-AIMD distribution for the Pt(111)/water system; no span of sampled potentials, in-distribution vs. out-of-distribution split, or extrapolation tests are described. This directly undermines the 'arbitrary potentials' scope.
[Abstract] Abstract and validation sections: No error bars, confidence intervals, or full validation protocol details (e.g., exact potential ranges tested, data exclusion criteria, or cross-validation scheme) are provided. This leaves the 'high accuracy' and 'consistent' claims difficult to assess quantitatively and is load-bearing for the reproducibility of the central results.

minor comments (2)

[Methods] Clarify the precise definition and input representation of the explicit electric potential embedding in both PE-MACE and PE-EDP (e.g., how the potential value is featurized and injected into the GNN layers).
[Results] Figure captions and results text should explicitly state the potential values or ranges used for each reported RDF, charge profile, and simulation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped clarify the scope and presentation of our results. We address each major comment below and have revised the manuscript to improve precision and reproducibility.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion that the framework delivers a 'unified description ... under arbitrary potentials' is not supported by the reported results. High accuracy, RDF agreement, and charge profile consistency are shown only on training/test sets drawn from the same Hy-DFT CP-AIMD distribution for the Pt(111)/water system; no span of sampled potentials, in-distribution vs. out-of-distribution split, or extrapolation tests are described. This directly undermines the 'arbitrary potentials' scope.

Authors: We agree that the original abstract phrasing could imply broader generalization than the reported evidence directly demonstrates. The explicit embedding of the electric potential as an input feature in both PE-MACE and PE-EDP is designed to enable the models to accept any potential value, providing the architectural basis for use under arbitrary potentials within the trained chemical system. All presented results (accuracy, RDFs, charge profiles) are indeed from in-distribution data on Pt(111)/water. In the revised manuscript we have updated the abstract to 'enabling a unified description from atomic to electronic scales under applied electric potentials' and added explicit details on the sampled potential range, the train/test split (with no temporal overlap), and confirmation that tests remain in-distribution. This tempers the claim to match the current evidence while preserving the framework's intended generality. revision: yes
Referee: [Abstract] Abstract and validation sections: No error bars, confidence intervals, or full validation protocol details (e.g., exact potential ranges tested, data exclusion criteria, or cross-validation scheme) are provided. This leaves the 'high accuracy' and 'consistent' claims difficult to assess quantitatively and is load-bearing for the reproducibility of the central results.

Authors: We thank the referee for noting this omission. The revised manuscript now reports error bars and confidence intervals on all accuracy metrics (forces, densities, and derived quantities) in the abstract and main text. We have expanded the methods and results sections to include the full validation protocol: the exact range of potentials sampled in the Hy-DFT CP-AIMD trajectories, data exclusion criteria (convergence thresholds and initial equilibration frames), and the cross-validation scheme (k-fold splitting of the trajectory data). These additions make the quantitative claims fully assessable and reproducible. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard supervised ML on independent DFT data

full rationale

The paper generates training data via Hy-DFT CP-AIMD under controlled potentials for the Pt(111)/water system, trains two equivariant GNN modules (PE-MACE for forces, PE-EDP for densities) on this data, and reports accuracy on separate training/test splits plus agreement with held-out DFT observables (RDFs, planar charge profiles, Bader charges). No equation or step reduces a claimed prediction to a fitted input by construction, no self-citation chain bears the central claim, and no ansatz or uniqueness theorem is smuggled in. The assertion of applicability to arbitrary potentials is an empirical generalization claim, not a definitional tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on standard assumptions about equivariant neural networks representing physical symmetries and on the accuracy of the underlying constant-potential DFT data generation; no new physical entities are postulated.

free parameters (1)

Model hyperparameters for PE-MACE and PE-EDP
Standard neural network parameters fitted during training on the generated dataset.

axioms (1)

domain assumption Equivariant graph neural networks can accurately capture atomic interactions and electron densities when electric potential is explicitly embedded as input.
Invoked in the model training component for both PE-MACE and PE-EDP.

pith-pipeline@v0.9.0 · 5574 in / 1306 out tokens · 78119 ms · 2026-05-10T17:00:56.142926+00:00 · methodology

discussion (0)

Reference graph

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