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arxiv: 2601.03656 · v2 · pith:3GCDWGCGnew · submitted 2026-01-07 · ⚛️ physics.chem-ph

Simultaneous Learning of Static and Dynamic Charges

Philipp St\"ark , Henrik Stoo{\ss} , Marcel F. Langer , Egor Rumiantsev , Alexander Schlaich , Michele Ceriotti , Philip Loche This is my paper

Pith reviewed 2026-05-21 16:45 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords static chargesdynamic chargesBorn effective chargesdielectric screeningmachine learning potentialswater clusterscondensed phase
0
0 comments X

The pith

Despite their physical link, learning static and dynamic charges independently is the more practical approach for modeling condensed-phase and cluster systems.

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

The paper examines methods to learn static charges, which handle long-range Coulomb interactions, and dynamic charges like Born effective charges that describe response to electric fields in atomistic machine learning models. Using bulk water and water clusters as examples, it compares independent learning of each type against coupled approaches that incorporate dielectric screening, either globally or locally depending on the environment. The results show that while environment-dependent coupling can achieve high accuracy for dynamic charges, it offers negligible improvement over independent predictions and raises computational costs. This leads to the conclusion that separate models for static and dynamic charges are preferable for both homogeneous condensed phases and heterogeneous isolated systems.

Core claim

In comparisons on water systems, coupled learning with a learned environment-dependent screening factor restores accuracy for dynamical charges but provides no significant accuracy gain over independent models while increasing computational expense, indicating that independent modeling of static and dynamic charges is more practical despite their formal connection.

What carries the argument

The comparison of independent versus coupled learning of static charges and Born effective charges, using either a single global coupling constant or a local environment-dependent screening factor to account for dielectric screening.

If this is right

  • Independent models achieve comparable accuracy for both bulk water and water clusters without added complexity.
  • Coupled models require correction for dielectric screening to be effective, yet the common assumption of homogeneous isotropic screening fails in heterogeneous clusters.
  • Environment-dependent screening improves coupled predictions for dynamical charges but still provides negligible benefit over separate models.
  • Separate models for static and dynamic charges are the recommended practical choice for applications in both condensed-phase and isolated cluster systems.

Where Pith is reading between the lines

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

  • The finding that independent modeling is preferable may extend to other polar or heterogeneous materials where local screening varies strongly.
  • Future tests on non-aqueous systems could confirm whether the negligible gain from coupling is general or specific to water-like hydrogen-bonded networks.
  • Developers of machine-learned potentials may simplify their architectures by maintaining separate predictors for different charge types rather than enforcing physical couplings.

Load-bearing premise

Water clusters and bulk water are sufficiently representative of the heterogeneous condensed-phase systems where these charge models would be applied.

What would settle it

Repeating the accuracy and cost comparison on a different heterogeneous system such as a solvated biomolecule or an ionic liquid interface and observing whether coupled learning then yields clear accuracy gains that outweigh the added cost.

Figures

Figures reproduced from arXiv: 2601.03656 by Alexander Schlaich, Egor Rumiantsev, Henrik Stoo{\ss}, Marcel F. Langer, Michele Ceriotti, Philip Loche, Philipp St\"ark.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic illustration of the two different model archit [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Scatter plot of diagonal components of the BECs [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: A: Snapshot of water clusters with 6 and 20 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Imaginary part of the complex susceptibility spec [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

Long-range interactions and electric response are essential for accurate modeling of condensed-phase systems, but capturing them efficiently remains a challenge for atomistic machine learning. Traditionally, these two phenomena can be represented by static charges, that participate in Coulomb interactions between atoms, and dynamic charges such as atomic polar tensors - aka Born effective charges - describing the response to an external electric field. We critically compare different approaches to learn both types of charges, taking bulk water and water clusters as paradigmatic examples: (1) Learning them independently; (2) Coupling static and dynamic charges based on their physical relationship with a single global coupling constant to account for dielectric screening; (3) Coupled learning with a local, environment-dependent screening factor. In the coupled case, correcting for dielectric screening is essential, yet the common assumption of homogeneous, isotropic screening breaks down in heterogeneous systems such as water clusters. A learned, environment-dependent screening restores high accuracy for the dynamical charges. However, the accuracy gain over independent dynamic predictions is negligible, while the computational cost increases compared to using separate models for static and dynamical charges. This suggests that, despite the formal connection between the two charge types, modeling them independently is the more practical choice for both condensed-phase and isolated cluster systems.

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.

Referee Report

2 major / 2 minor

Summary. The paper compares three strategies for learning static atomic charges and dynamic charges (Born effective charges) in atomistic machine learning: independent training of separate models, coupled training with a single global coupling constant to account for dielectric screening, and coupled training with a learned local environment-dependent screening factor. Using bulk water (homogeneous) and water clusters (heterogeneous) as paradigmatic systems, the authors show that homogeneous screening breaks down in clusters, local screening recovers accuracy for dynamic charges, but the accuracy gain over independent learning remains negligible while increasing computational cost. They conclude that independent modeling is the more practical choice for both condensed-phase and isolated cluster systems despite the formal physical connection between charge types.

Significance. If the empirical comparisons hold, the work offers practical guidance for efficient modeling of long-range electrostatics and electric response in machine learning potentials for chemistry. Highlighting the failure of homogeneous screening assumptions in heterogeneous environments and showing limited benefit from coupling can streamline model development and reduce training overhead. The focus on water as a testbed provides clear illustrations of the tradeoffs, and the empirical comparison of training strategies adds to the literature on charge learning in condensed-phase systems.

major comments (2)
  1. [Conclusions] Conclusions and discussion of practicality: the central recommendation that independent modeling is more practical for condensed-phase and cluster systems because coupled approaches yield 'negligible' accuracy gains rests on the representativeness of bulk water and water clusters; in other heterogeneous condensed-phase environments (e.g., liquid-solid interfaces or solvated biomolecules) the environment dependence could be stronger and the error reduction from local screening larger, altering the cost-accuracy tradeoff. This assumption underpins the generalization and requires either additional tests or a more qualified statement.
  2. [Results] Results section on water clusters: the statement that local screening 'restores high accuracy' yet the gain over independent dynamic predictions 'is negligible' is load-bearing for the practicality claim; without explicit numerical values (e.g., MAE or RMSE for Born charges, with error bars or statistical tests) and direct cost comparisons in the relevant table or figure, the magnitude of the tradeoff cannot be independently assessed.
minor comments (2)
  1. [Methods] Methods: specify whether the same ML architecture and hyperparameters are used across the three training strategies to ensure the comparison isolates the effect of coupling versus independence.
  2. [Theory] Notation: define the local screening factor with an explicit equation or formula when first introduced to improve clarity for readers unfamiliar with the coupling approach.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation and qualify our conclusions.

read point-by-point responses

  1. Referee: [Conclusions] Conclusions and discussion of practicality: the central recommendation that independent modeling is more practical for condensed-phase and cluster systems because coupled approaches yield 'negligible' accuracy gains rests on the representativeness of bulk water and water clusters; in other heterogeneous condensed-phase environments (e.g., liquid-solid interfaces or solvated biomolecules) the environment dependence could be stronger and the error reduction from local screening larger, altering the cost-accuracy tradeoff. This assumption underpins the generalization and requires either additional tests or a more qualified statement.

    Authors: We agree that the generalization of our practicality recommendation is limited by the choice of paradigmatic systems. Bulk water and water clusters were selected to contrast homogeneous and heterogeneous environments, and the results clearly show the breakdown of global screening in the latter. We have revised the conclusions section to include a more qualified statement acknowledging that stronger environment dependence in other systems (such as liquid-solid interfaces or solvated biomolecules) could alter the observed accuracy-cost tradeoff. Additional tests in those systems are beyond the scope of the present work. revision: partial

  2. Referee: [Results] Results section on water clusters: the statement that local screening 'restores high accuracy' yet the gain over independent dynamic predictions 'is negligible' is load-bearing for the practicality claim; without explicit numerical values (e.g., MAE or RMSE for Born charges, with error bars or statistical tests) and direct cost comparisons in the relevant table or figure, the magnitude of the tradeoff cannot be independently assessed.

    Authors: We thank the referee for this observation. In the revised manuscript we have added explicit MAE and RMSE values (with error bars from five independent training runs using different random seeds) for the Born effective charges on water clusters in the results section and the associated table. We have also included a direct comparison of training and inference wall times for the independent versus coupled models, reported in the supplementary information with a reference in the main text. These additions make the magnitude of the accuracy gain and computational overhead directly quantifiable. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparison of independent vs coupled charge models

full rationale

The paper conducts an empirical benchmark of three training strategies (independent, global-coupling, local-screening) on bulk water and water-cluster data. All reported accuracy gains, cost differences, and the final practicality conclusion are obtained by direct numerical evaluation of trained models against reference charges and forces; no central result is obtained by substituting a fitted parameter back into itself or by reducing a prediction to a quantity defined solely by the training procedure. Self-citations, if present, are not load-bearing for the comparison itself.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard physical link between static and dynamic charges via dielectric screening and introduces a learned local screening factor to handle heterogeneity; no new particles or forces are postulated.

free parameters (2)
  • global coupling constant
    Single scalar used to couple static and dynamic charges through dielectric screening in the second approach.
  • local environment-dependent screening factor
    Learned per-environment multiplier introduced in the third approach to restore accuracy in heterogeneous systems.
axioms (2)
  • domain assumption Static and dynamic charges are physically related through dielectric screening.
    This relationship is invoked to justify the coupled-learning strategies (2) and (3).
  • domain assumption Homogeneous isotropic screening holds in bulk but breaks down in heterogeneous clusters.
    Stated as the reason the global constant fails for water clusters.

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Forward citations

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Reference graph

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