Efficient Long-Range Machine Learning Force Fields for Liquid and Materials Properties

Aidan A. Fike; Biswajit Santra; Garvit Agarwal; James Stevenson; John L. Weber; Karl Leswing; Leif D. Jacobson; Mathew D. Halls; Richard A. Friesner; Rishabh D. Guha

REVIEW 3 major objections 5 minor 1 cited by

Efficient Long-Range Machine Learning Force Fields for Liquid and Materials Properties

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read By predicting atomic partial charges inside the network, the MPNICE force field reaches near-best accuracy at 5–20x lower inference cost.

desk verdict A broad, honest benchmark paper for a charge-aware MLFF; the architecture and new datasets are real contributions, but the headline 5-20x speedup is not actually measured. read the letter →

arxiv 2505.06462 v2 pith:SC23DYPS submitted 2025-05-09 physics.chem-ph cond-mat.mtrl-sci

John L. Weber , Rishabh D. Guha , Garvit Agarwal , Yujing Wei , Aidan A. Fike , Xiaowei Xie , James Stevenson , Biswajit Santra

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Richard A. Friesner Karl Leswing Mathew D. Halls Robert Abel Leif D. Jacobson

This is my paper · ORCID

classification physics.chem-phcond-mat.mtrl-sci

keywords machinelearningforcefieldsmessagepassingneuralnetworksatomicpartialchargeschargeequilibrationlong-rangeelectrostaticsmoleculardynamicsinorganiccrystalsionizationenergies

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 claims that a machine-learned force field can have electrostatics built in without sacrificing speed. The proposed architecture, MPNICE, iteratively predicts atomic partial charges at every message-passing step, so long-range interactions are represented explicitly rather than absorbed into a purely local energy. Across organic and inorganic benchmarks, the authors find accuracy close to the best available models while running 5–20 times faster at inference. The same charge representation also makes charge-dependent properties—vertical ionization energies, dielectric tensors, Born effective charges, and the long-range correction to phonons—computable from the trained model without retraining. If the claim holds, large-scale molecular dynamics of liquids and materials no longer needs to choose between fidelity and tractability.

What carries the argument

The load-bearing object is the iterative charge-equilibration loop inside the message-passing stack. With the total charge fixed, each atom's charge is $q_i = -(\chi_{\mathrm{eff},i} - \lambda)/J_{ii}$, with $\lambda$ chosen so that $\sum_i q_i = Q_{\mathrm{tot}}$, where $\chi_{\mathrm{eff},i}$ is an MLP-predicted electronegativity and $J_{ii}$ a self-interaction term; this is an approximation to the Qeq method. The loop makes charges internal variables rather than fixed inputs, so long-range electrostatics enter the energy while the messages themselves stay within a finite cutoff, and it gives the model a channel through which an external electric field can be applied as a linear perturbation of the electronegativities. That field perturbation is what turns the same trained model into a predictor of dielectric tensors, Born charges, and non-analytic phonon corrections.

What would settle it

Run the inorganic model on a set of roughly 50 polar crystals for which reference values from density-functional perturbation theory are available for the dielectric tensor, Born effective charges, and LO-TO splitting, then compare magnitudes. The paper's NaCl example already shows reduced magnitudes and small off-diagonal artifacts; if systematic underestimation or large errors in crystals with asymmetric unit cells appears broadly, the claim that the charge representation supports reliable electric response properties is false.

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Extended reading notes

Core claim

MPNICE is an invariant message-passing potential in which each atom carries a node-feature vector, a local environment expansion (atomic environment vectors), and a running atomic partial charge. After each interaction block, an MLP predicts an effective electronegativity for each atom, and charges are updated through an analytic charge-equilibration step that enforces global charge conservation and makes the predicted charges feed the next block and the final energy. The final energy is a sum of per-atom terms plus an explicit electrostatic energy from the equilibrated point charges and, optionally, a dispersion correction; multiple output heads let one body of shared features serve different reference levels of theory. The authors demonstrate that this design yields rotamer, tautomer, crystal-ranking, liquid-density, and elastic/phonon accuracies at or near the level of the best existing transferable models, while the charge variables give direct access to ionization energies and to response tensors such as dielectric constants and Born charges.

Load-bearing premise

The inorganic models inherit whatever bias the semi-empirical tight-binding charges carry, because the paper trains them to reproduce those charges rather than true or density-functional-theory charges and then uses the charges to build electrostatic energies and response tensors.

Editorial extensions

If this is right

Stable, zero-shot liquid simulations: one Organic MPNICE model simulates 62 common solvents with roughly 4% average density error and reproduces water's diffusion coefficient and hydration free energy closely, suggesting transferable models can be dropped into condensed-phase molecular dynamics without task-specific fitting.
Charge-dependent observables become available from a single trained model: vertical ionization potentials and electron affinities for small molecules, and the LO-TO splitting in polar crystals such as NaCl, can be computed directly from the predicted charge representation.
Cheaper inorganic screening: Inorganic MPNICE ranks monoelemental crystals and thousands of metal-organic framework structures with energy mean absolute errors comparable to much larger general models, and can be used to estimate bulk and shear moduli near equilibrium.
Delta learning with a cheap baseline: the delta-learned organic model reaches roughly 0.2 kcal/mol on torsion scans and 0.3 kcal/mol on tautomer energies, indicating that semi-empirical corrections inside this architecture recover much of the cost of high-level reference data.
Multi-task and shared-force training give a usable single model: a hybrid trained on both organic and inorganic data keeps inorganic total energies accurate and predicts qualitatively correct geometries for unseen Pt/Ir organometallic complexes, though with reduced domain-specific peak accuracy.

Reading between the lines

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

The point-charge representation is the main pressure point: the paper's own NaCl example shows dielectric and Born-charge magnitudes running low relative to reference values, with small off-diagonal artifacts in symmetric cells. A natural extension is to give each atom a learned polarizability or higher multipoles, and the architecture's derivative machinery could then be tested against density-fu
If the 5–20x inference advantage persists for larger models and longer cutoffs, the practical simulation envelope shifts: the reported 17,000-atom water box at roughly 0.07 ns/day would scale to multi-nanosecond simulations of electrolytes, interfaces, and amorphous battery coatings on a single mid-range GPU.
The shared-force hybrid trick—fixing the energy scale to one dataset and letting forces carry the other—looks like a general recipe for multi-fidelity training that could be tested on other incompatible pairs of reference theories beyond the organic/inorganic split.
The dependence on semi-empirical charges suggests an explicit experiment: retrain the inorganic model on density-functional-theory-quality partial charges and compare dielectric and Born-charge predictions. If the errors shrink, the architecture's response claims are limited by the charge labels rather than by the model form.

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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

The core of this paper is a large, well-designed benchmark suite for a charge-aware invariant message-passing force field, and on that front it mostly delivers. What's genuinely new: the iterative Qeq charge equilibration combined with message passing, the shared-force hybrid training that lets one output head serve two levels of theory, the external-field response formalism with dielectric tensors and Born charges, and two new reference datasets (Torsion2000 and DLPNO-CCSD(T) TorsionNet500). The benchmarks are extensive and the results are competitive: MPNICE matches or beats existing transferable organic potentials on rotamers, tautomers, and crystal ranking, and the inorganic models sit near SevenNet and MatterSim on Matbench Discovery while using fewer parameters. The zero-shot LiAlO2 diffusion barrier is a nice applications-level validation.

The soft spots are real but localized. The biggest is the speed claim. The abstract says "5-20x faster inference versus models with comparable accuracy," but Section 3.4 gives only MPNICE timings; MatterSim and SevenNet both OOM on the smallest diamond cell and no comparative number ever appears. The conclusion repeats "an order of magnitude faster," which is not supported by data in the paper. Given that efficiency is half the contribution, this needs fixing--either by reporting timings on systems where the competitors fit, or by softening the claim to "competitive speed" and discussing memory trade-offs. The Desmond-vs-ASE engine mismatch also makes the comparison hard to interpret.

Other concerns are more minor. The elastic moduli statistics exclude outliers (>600 or <-50 GPa); that's worth reporting, but the outlier counts are given, so it's transparent. The MACE-OFF23 torsion comparison uses a different metric (mean barrier height vs RMSD), as the authors note. The inorganic models train to GFN1-xTB charges, and the authors honestly acknowledge the resulting bias in the dielectric tensor. That's an external approximate target, not a circularity.

All told, this is a solid, honest engineering-plus-benchmarks paper with one load-bearing gap in its central efficiency claim. It deserves peer review--the architecture, datasets, and response-property formalism are valuable even if the speedup needs to be substantiated. I'd cite the Torsion2000 and DLPNO-CCSD(T) benchmarks in my own work, and I'd bring it to a reading group focused on MLFF charge models.

Referee Report

3 major / 5 minor

Summary. The paper introduces MPNICE, an invariant message-passing machine-learned force field that iteratively predicts atomic partial charges through an approximate Qeq scheme and includes explicit electrostatics and optional D3 dispersion. The authors train a suite of models for organic molecules (direct, delta-learned, and crystal-aware), for inorganic crystals (MPtrj, OMAT24a, and a sequential inorganic model), and for hybrid organic/inorganic multi-task and shared-force training. The accuracy benchmarks are extensive: torsion scans (Genentech, TorsionNet500, and a new Torsion2000 set), tautomer energies, organic crystal lattice energies and polymorph ranking, liquid densities, water properties, ionization energies and electron affinities, monoelemental crystal ranking, Matbench Discovery, QMOF, elastic moduli, phonon MDR benchmarks, the NaCl non-analytic phonon correction, Li diffusion in amorphous LiAlO2, and Pt/Ir organometallic structure optimization. The paper also claims in the abstract and conclusions that MPNICE achieves 5-20x faster inference than comparable models, a claim that Section 3.4 does not presently substantiate with comparative timing data.

Significance. If the benchmark results and the efficiency claim both hold, MPNICE would be a significant contribution: it combines near-best-class accuracy on several organic and inorganic tasks with a charge-aware architecture that enables charge-dependent properties without an equivariant backbone. The manuscript also provides reusable test data, notably DLPNO-CCSD(T) reference energies for TorsionNet500, a new Torsion2000 set, tautomer and crystal test geometries, and a large set of liquid-density benchmarks; these are valuable community assets. The shared-force hybrid training idea is original and is tested on a demanding organometallic zero-shot task. The authors are also appropriately explicit in Section 4 about limitations such as spin-state insensitivity, extrapolative use on reactive surfaces and defects, and untested organic/inorganic interfaces. The central efficiency claim, however, is currently unsupported by comparative measurements, and the charge-dependent property demonstrations inherit a documented bias from training to GFN1-xTB charges.

major comments (3)

[Abstract; Section 3.4, Fig. 12] The headline claim of "5-20x faster inference" and the conclusion's "order of magnitude faster than comparable models" are not supported by the evidence in Section 3.4. That section reports absolute MPNICE timings (76, 36, and 20 microseconds per atom for diamond, water, and aluminum) but provides no timing for MatterSim-v1.0.0-1M or SevenNet-0; both competitors are described as running out of memory on the smallest diamond cell, so no speedup ratio is measured anywhere. The comparison is also not apples-to-apples because MPNICE runs in the Desmond MD engine while the competitors run as ASE calculators, which can differ in neighbor-list handling, batching, and memory footprint. The authors should measure all models under a common driver at matched system sizes, report timings for at least one system where every model fits in memory, and state the resulting speedup factors; if this is not possible, the abstract and conclusions should be revised to claim only competitive or engine-specific performance.
[Section 3.2; Section 3.2.3] The inorganic models are trained to reproduce GFN1-xTB partial charges because MPtrj has no charge labels, and Section 3.2.3 explicitly states that the magnitudes of the dielectric tensor and Born effective charges are reduced relative to PBEsol and that unphysical off-diagonal terms appear for NaCl. Since the abstract and Section 4 present "direct prediction of charge-dependent properties" as a headline capability, the current evidence supports only qualitative response tensors for the studied NaCl case, with the successful LO-TO splitting partly due to error cancellation between Z* and the dielectric tensor. The authors should either validate the charge model against a higher-quality reference for at least one representative system, or explicitly qualify the charge-dependent-property claim in the abstract and conclusions as qualitative.
[Section 3.2.2, Table 9] Table 9 excludes elastic-moduli outliers (values below -50 or above 600 GPa) from the reported MAE and R2 statistics, and the number of excluded outliers is not negligible in absolute terms: Inorganic MPNICE has 82 excluded shear-modulus outliers, and its reported GVRH R2 is only 0.52 even after exclusion. Because Section 3.2.2 concludes that "all models achieve reasonable performance, comparable to previous reports of MACE MP 0," the authors should report outlier counts as fractions of the test set, give statistics both with and without outlier exclusion, and justify the exclusion threshold with a sensitivity analysis.

minor comments (5)

[Section 2, Eqs. (1)-(3)] The parameters eta, r_a, theta_a, and zeta in the AEV definitions are not all defined near the equations; please add explicit definitions and state the numerical values used for these parameters.
[Section 3.4, Fig. 12] The timings are averaged over 500 steps, but no variance or error bars are reported; please report standard errors and state whether the quoted times include only neural-network inference or also engine overhead such as neighbor-list construction and integration.
[Section 3.1.1 vs. Table 12 and Data Availability] The new torsion benchmark is referred to as "Torsion2000" in the text and Figure 2 but as "TorsionTest2000" in Table 12 and the Data Availability section; please standardize the name.
[Section 3.1.5] There is a typo in the sentence beginning "Interstingly, Kovacs et al. report..."; "Interstingly" should be "Interestingly".
[Section 3.2.3, Eqs. (20)-(21)] Please specify the exact definitions used for the fixed-ion dielectric tensor and Born effective charges, including the Ewald summation convention and whether clamped-ion conditions are imposed, so that the automatic-differentiation procedure can be reproduced.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: MPNICE accuracy benchmarks use external references and the charge target is an independent semi-empirical method; the unsupported speedup claim is an evidentiary gap, not circularity.

full rationale

This paper does not exhibit derivation circularity. The MPNICE architecture is benchmarked against external references: torsional energies are compared to literature levels of theory and new DLPNO-CCSD(T)/CBS estimates; tautomer, crystal, liquid, elastic, phonon, and Li-diffusion tests are checked against experiment or independent DFT datasets such as Materials Project, WBM, QMOF, and the PBE MDR benchmark. The inorganic charge model is trained to GFN1-xTB partial charges because MP trj lacks charge labels; this is an external, approximate semi-empirical target, and the authors explicitly acknowledge that training on xTB charges reduces the magnitude of the dielectric and Born-charge tensors relative to PBEsol. The response tensors and non-analytic phonon correction are computed from that independently trained charge model, not fitted to the target response properties, so they are not predictions by construction. Comparisons against the authors' prior QRNN models serve as baselines rather than as validation of MPNICE. Self-citations to the QRNN architecture and prior CSP workflow are present but are not load-bearing for the central accuracy claims. The abstract's '5-20x faster' claim is not substantiated by Section 3.4 because the comparison models ran out of memory and no speedup factor is reported; however, that is an evidentiary gap, not a circular derivation, so it does not raise the circularity score.

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

The central claims rest mainly on model training and benchmark choices rather than on derived equations. The key external inputs are the DFT reference levels, the GFN1-xTB charge labels, and the Qeq approximation; these are domain assumptions. The hand-chosen hyperparameters and loss settings are free parameters, but they are standard for this class of models.

free parameters (6)

AEV Gaussian parameters = Not reported (hand-chosen)
The two- and three-body symmetry functions in Eqs. 1-3 use hand-chosen Gaussian widths and shifts; these hyperparameters affect the representation but are not fitted to the target benchmarks.
Radial and angular cutoffs = 5.2 Å and 3.5 Å
Cutoffs are user choices that determine the local environment and computational cost; the central accuracy claims depend on them.
Qeq self-interaction Jii = Determined by atomic radii (values not tabulated)
Equations 9-10 require atomic self-interaction terms; these come from a prior parametrization and influence the predicted charges and electrostatics.
Atomic energy offsets = Fitted per element/level of theory
Methods state energy labels are centered by subtracting an offset energy per atom fitted with a linear model for each level of theory; this is a calibration step.
Model hyperparameters (Nint, Nk, N~k, MLP dims) = e.g., 3 interaction blocks, 64-128 node features, 32 message features
Architecture capacities are chosen by hand and vary across models; they are part of the design but not fitted to specific benchmarks.
Huber loss deltas and task weights sigma = Delta 10 meV; sigma trainable
Loss function (Eq. 22) includes hand-set Huber deltas and trainable noise parameters; these affect training but are standard practice.

assumptions (6)

standard math Neural networks with message passing can represent smooth potential energy surfaces.
The entire approach assumes the MPNICE functional form is sufficiently expressive; this is a standard approximation in the MLFF literature.
domain assumption DFT references (PBE, omegaB97X-D3BJ) are accurate enough ground truths for training and benchmarking.
All energies and forces are learned from these levels of theory; systematic DFT errors are inherited by the models.
domain assumption GFN1-xTB partial charges are suitable labels for learning atomic charges.
Inorganic models are trained to reproduce GFN1-xTB charges (Section 3.2); the authors note this leads to underestimated dielectric tensors, indicating the assumption is imperfect.
domain assumption Qeq charge equilibration with predicted electronegativities captures long-range electrostatics.
Equations 9-10 define charges from predicted chi_eff; the model relies on this approximation for all charge-dependent properties.
domain assumption Born-Oppenheimer approximation and classical nuclei.
MD simulations treat nuclei classically; nuclear quantum effects are ignored, as noted for water properties.
standard math Ewald summation for long-range Coulomb interactions.
Used for periodic systems; standard but an assumption about the boundary conditions.

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Cite this review

Pith. "Pith review of Efficient Long-Range Machine Learning Force Fields for Liquid and Materials Properties." pith.science (2026). https://pith.science/paper/SC23DYPS

@misc{pith2026250506462,
  author       = {Pith},
  title        = {Pith review of: Efficient Long-Range Machine Learning Force Fields for Liquid and Materials Properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SC23DYPS}},
  note         = {Machine review of arXiv:2505.06462}
}

abstract

Machine learning force fields (MLFFs) have emerged as a sophisticated tool for cost-efficient atomistic simulations approaching DFT accuracy, with recent message passing MLFFs able to cover the entire periodic table. We present an invariant message passing MLFF architecture (MPNICE) which iteratively predicts atomic partial charges, including long-range interactions, enabling the prediction of charge-dependent properties while achieving 5-20x faster inference versus models with comparable accuracy. We train direct and delta-learned MPNICE models for organic systems, and benchmark against experimental properties of liquid and solid systems. We also benchmark the energetics of finite systems, contributing a new set of torsion scans with charged species and a new set of DLPNO-CCSD(T) references for the TorsionNet500 benchmark. We additionally train and benchmark MPNICE models for bulk inorganic crystals, focusing on structural ranking and mechanical properties. Finally, we explore multi-task models for both inorganic and organic systems, which exhibit slightly decreased performance on domain-specific tasks but surprising generalization, stably predicting the gas phase structure of $\simeq500$ Pt/Ir organometallic complexes despite never training to organometallic complexes of any kind.

Figures

Figures reproduced from arXiv: 2505.06462 by the authors.

**Figure 2.** Violin plots showing the distribution of relative energy RMSDs for separate torsion [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** Correlation plot showing the lower energy range of relative tautomer energies from [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Highlighted results for organic crystal structure ranking. Panel (a) shows the RMSD in relative energy between MLFF models and loosely optimized PBE-D3 structures in kcal/mol (left axis) as bars and also a horizontal line indicating the R2 value (right axis). Panel (b)…

**Figure 5.** Figure 5: Equilibrated densities for a set of 62 common organic solvents versus experiment, [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]

**Figure 6.** Figure 6: Structure Factors for liquid water for Organic [PITH_FULL_IMAGE:figures/full_fig_p024_6.png]

**Figure 7.** Figure 7: DFT vs MLFF convex hull distance for Inorganic [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]

**Figure 8.** Figure 8: Parity plot between Inorganic MPNICE+D3 and PBE-D3 for the normalized total energies of >20k metal organic frameworks in the QMOF dataset. For an additional test of OOD energetic ranking, we ran Inorganic MPNICE on the QMOF dataset of over 20k optimized Metal Organic F…

**Figure 9.** Figure 9: Parity plots for Inorganic MPNICE on the Materials Project elastic dataset showing the bulk modulus (left) and shear modulus (right) for 11.6k datapoints. Note that the plots exclude 2 and 82 outliers for which Inorganic MPNICE predicted a nonphysical bulk and shear m…

**Figure 10.** Figure 10: Inorganic MPNICE phonon band structure (THz) for NaCl (3x3x3 supercell pictured in inset), calculated using Inorganic MPNICE with and without the non-analytic correction (NAC) and compared to PBEsol calculated by ref. 81. Including the non-analytic corrections is nece…

**Figure 11.** Figure 11: (a) An optimized organometallic structure using Organic MPNICE. Metallic bonding was not present in the training set and so the ligand field is significantly distorted (b) an example structure with high RMSD optimized using Hybrid MPNICE I. The model incorrectly assoc…

**Figure 12.** Figure 12: Inference efficiency comparison of various MLFF models. A red ‘X’ denotes a [PITH_FULL_IMAGE:figures/full_fig_p042_12.png]

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