Advances in modeling complex materials: The rise of neuroevolution potentials

Cheng Qian; Feng Ding; Penghua Ying; Rui Zhao; Shunda Chen; Yanzhou Wang; Zheyong Fan

REVIEW 3 major objections 7 minor 1 cited by

Advances in modeling complex materials: The rise of neuroevolution potentials

T0 review · 3 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This review argues that a neuroevolution-trained machine-learned potential can deliver near-first-principles accuracy at speeds that make million-atom molecular dynamics routine.

desk verdict A useful, reproducible review of the NEP method with several new case studies, but the headline speed advantage is a software-stack comparison, not a settled property of the NEP architecture. read the letter →

arxiv 2501.11191 v1 pith:LC67OAUJ submitted 2025-01-19 cond-mat.mtrl-sci physics.comp-ph

Penghua Ying , Cheng Qian , Rui Zhao , Yanzhou Wang , Feng Ding , Shunda Chen , Zheyong Fan This is my paper · ORCID

classification cond-mat.mtrl-sciphysics.comp-ph PACS 71.15.Pd34.20.-b

keywords neuroevolutionpotentialmachine-learnedinteratomicpotentialsmoleculardynamicsGPUMDcomputationalefficiencyamorphouscarbonshort-rangeorderhigh-entropyalloys

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 review argues that the neuroevolution potential (NEP), a machine-learned interatomic potential trained on density-functional-theory data and implemented in the open-source GPUMD package, has reached the point where it can serve as a near-first-principles engine for routine molecular dynamics. The central evidence is a head-to-head benchmark against four other machine-learned potentials on a shared carbon dataset, in which NEP is roughly an order of magnitude faster than its nearest GPU-based rival on large systems while still reproducing the energetics and bonding statistics that matter for materials physics. If that claim holds, simulations that once required massive computing campaigns, such as short-range order in alloys, radiation cascades, fracture, and tribology, become accessible on desktop GPUs. The review covers about three dozen NEP applications and contributes new case studies of its own: platinum surface reconstruction, carbon-nanotube growth on an iron cluster, superlubric sliding of twisted bilayer hexagonal boron nitride, and mechanical loading of a quinary complex alloy.

What carries the argument

The load-bearing object is the NEP descriptor-network pair. Every atom contributes a site energy $U_i = \mathcal{N}(\mathbf{q}_i)$, where the descriptor vector $\mathbf{q}_i$ is assembled from radial functions expanded in Chebyshev polynomials with trainable, species-pair-dependent coefficients and from angular components built by summing products of radial functions with spherical harmonics; total energy is the sum of site energies. Deliberately cheap descriptors are what make the speed claim concrete, and a species-pair-dependent coefficient set is what lets multi-element models cost almost the same as single-element ones. Training uses a separable natural evolution strategy, a derivative-free, black-box optimizer, on a loss that jointly fits energy, force, and virial with $L_1$ and $L_2$ penalties. The generalization argument behind the 16-element UNEP-v1 model is that one- and two-component structures already outline the descriptor space, so higher-component alloys are interpolation points rather than new territories; that is the mechanism that lets a model trained on binaries describe a quinary alloy with no retraining.

What would settle it

Re-run the diamond-system speed benchmark of Figure 8 with all five methods on identical hardware, one GPU or NEP through its LAMMPS CPU interface, each with its most optimized native implementation; if NEP is not clearly the fastest at $10^6$ atoms, the headline efficiency claim collapses. On the accuracy side, train a fresh NEP on the same carbon dataset and quench amorphous carbon at 3.0 g cm$^{-3}$; if the resulting sp$^3$ fraction falls outside the 60-80% range reported for the other methods, the adequate-accuracy half of the claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that NEP occupies a genuinely new point in the accuracy-cost plane of interatomic potentials: training accuracy on par with the best machine-learned potentials, a descriptor whose evaluation cost is nearly independent of the number of chemical species, and inference speed that lets a single GPU drive million-atom systems. The speed advantage is quantified in the benchmark: on a common 6088-structure carbon dataset, NEP is the fastest of the five methods on one V100 GPU and can sustain simulations of about six million atoms on that card, MACE and NequIP are the slowest, DP sits in between, and GAP on 64 CPU cores matches DP on one GPU. Accuracy is presented as adequate rather than best-in-class: MACE posts the lowest root-mean-square errors, while NEP and DP are comparable to each other and ahead of GAP; in physically decisive tests, namely the sp$^3$ fraction of quenched amorphous carbon and the binding and sliding energy landscapes of bilayer graphene, NEP is among the models that agree with DFT and experiment. The review's application chapters are then offered as evidence of what this combination unlocks: million-atom radiation cascades, nano-tribology of incommensurate interfaces, short-range order sampled at experimental length scales, and phase transitions followed at near-experimental heating rates.

Load-bearing premise

The speed comparison assumes that the chosen software setups are typical: GAP runs on 64 CPU cores rather than a GPU, and every non-NEP model runs inside LAMMPS while NEP runs in its native GPUMD engine, so a rival model with a differently optimized or differently hosted implementation could close the measured gap.

Editorial extensions

If this is right

Near-first-principles molecular dynamics of million-atom systems becomes routine on a single desktop GPU, and multi-GPU runs reach tens of millions to one hundred million atoms.
The NEP-ZBL combination puts primary radiation damage within reach at sizes where defect-cluster statistics become physically meaningful, for both elemental metals and high-entropy alloys.
Short-range order in alloy systems can be sampled by Monte Carlo and molecular dynamics at volumes matching characterization tools such as atom-probe tomography, not just at DFT-cell sizes.
A periodic-table foundation model becomes a data-efficient target: training on elemental and binary structures may be enough for accurate multicomponent predictions.
Disordered and hydrogen-bonded materials, including amorphous carbon and water, can be modeled at near-quantum-chemical accuracy with empirical-potential-level cost when nuclear quantum effects are added.

Reading between the lines

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

A direct test of the speed claim's portability would be a five-model comparison inside a single engine, such as running NEP and its rivals through their LAMMPS interfaces on the same GPU, which would separate the method's intrinsic cost from the GPUMD engine's optimizations.
If the UNEP-v1 descriptor-space interpolation argument is right, a NEP foundation model trained only on elemental and binary data could be stress-tested first on ternary and quaternary high-entropy alloys outside the original 16 elements.
The force re-weighting trick used for GeSn, which emphasizes small forces in the loss to improve energy-landscape minimization, could be exported to surface-reconstruction and phase-transition models where near-equilibrium forces dominate the physics.
The water result suggests a general recipe, train a NEP on a many-body-corrected reference and add nuclear quantum effects through path integrals, that could be carried to other hydrogen-bonded or proton-transferring systems.

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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

Two things to know. First, this is a well-organized and honest review of the NEP method by the people who developed it, and it includes several genuinely new case studies: Pt(001) surface reconstruction, CNT growth on an Fe55 cluster, twisted hBN superlubricity, and a small suite of mechanical simulations of a compositionally complex alloy. Second, the headline efficiency claim—that NEP is dramatically faster than DP, GAP, MACE, and NequIP—is not actually established by the benchmark they run. The speed comparison pits NEP in its native GPUMD package against DP/MACE/NequIP running inside LAMMPS and GAP on 64 CPU cores. That conflates the NEP architecture with GPUMD's optimized kernels and neighbor lists. The paper itself notes that NEP has a separate LAMMPS CPU implementation, but they never benchmark that version. As it stands, Fig. 8 shows GPUMD is fast, not that NEP as a regression model is inherently faster than the others.

What the paper does well: the carbon benchmark is genuinely useful. It compares training accuracy, physical observables (bilayer graphene binding/sliding, amorphous carbon sp3 fraction), and speed across five MLP families. The new models are trained on published datasets, full hyperparameters are given in the text, and the authors deposited data and models on Zenodo. That is reproducible and deserves credit. The review also surveys a broad range of applications and is candid about NEP's limitations, including the lack of explicit electrostatics and the absence of a full periodic-table foundation model.

The soft spots are proportionate. The selection bias the reader flagged (pre-trained NEP and GAP vs. self-trained others) is real but minor, since the training choices look reasonable and accuracy is not the load-bearing claim. More important is the speed figure, which the abstract and conclusions lean on heavily. The new case studies are valid demonstrations, not deep validations: Pt(001) is compared only to a prior DP study, the CNT growth model has a force RMSE of about 385 meV/Å, and the fatigue simulations run 10 cycles with no error bars. That is acceptable for illustrative purposes, but the framing should say so.

Who should read this: anyone considering NEP for large-scale MD or wanting a compact map of its application space. It deserves a serious referee, not a desk reject. The main revision needed is to either run a controlled speed benchmark (same engine, accuracy-matched models) or substantially soften the efficiency claim. I'd also ask for error bars on the mechanical case studies.

Referee Report

3 major / 7 minor

Summary. This review provides a comprehensive overview of the neuroevolution potential (NEP) method, including its neural-network architecture, descriptor construction, loss function, and practical workflows implemented in the GPUMD package. The authors benchmark NEP against DP, GAP, MACE, and NequIP on a general-purpose carbon dataset, evaluating training accuracy, physical-property predictions (bilayer graphene binding and sliding energies, amorphous carbon sp3 fractions), and computational speed. They then survey NEP applications to structural properties, phase transitions, and mechanical behavior, and introduce several new case studies: a Pt(001) surface reconstruction model, a FeC model for carbon nanotube growth, an hBN sliding model for tribology, and UNEP-v1-based simulations of a complex alloy under compression, impact, and fatigue. The central conclusion is that NEP combines near first-principles accuracy with exceptional computational efficiency, enabling million-atom MD simulations on a single GPU.

Significance. If the efficiency claim is correct and the benchmark is fair, the paper makes a strong case for NEP as a practical tool for large-scale accurate atomistic simulations, with implications for materials discovery and mechanistic studies. The paper is strengthened by the open availability of code, training data, and scripts, and by the inclusion of new, reproducible case studies. However, the speed comparison conflates the NEP model with the GPUMD implementation, and the accuracy claims are tempered by the paper's own binding-energy results; these issues must be resolved before the headline claims about NEP's 'exceptional efficiency' and 'near-first-principles accuracy' are fully supported.

major comments (3)

[Sec. III.B.4, Fig. 8] The speed benchmark is not a controlled comparison of the NEP method against other MLP methods. NEP runs in its native GPUMD v3.9.5 on a single V100 GPU, while DP, MACE, and NequIP run in LAMMPS on the same GPU, and GAP runs on 64 CPU cores. The paper itself notes in Sec. II.B.6 that NEP has a separate CPU/LAMMPS implementation, but no speed test of that implementation is reported. As a result, the observed speed gap conflates the NEP architecture with GPUMD's optimized kernels, neighbor-list handling, and memory layout. In addition, no accuracy matching is performed: the models differ in accuracy (e.g., MACE is more accurate than NEP on the carbon training set, Figs. 3 and 4), so a smaller MACE or NequIP model could substantially narrow the speed gap. The conclusion in Sec. VII that NEP offers 'empirical potential-like efficiency' and enables routine million-atom near-first-principles MD rests on this uncontrolled comparison. We request either (a) a benchmark that includes NEP running in LAMMPS or the competing methods running in their native packages, with accuracy-matched model sizes, or (b) a revision of the claims to state explicitly that the speed advantage is demonstrated for the NEP implementation in GPUMD, not for the NEP method per se.
[Sec. III.B.2, Fig. 5] The paper repeatedly claims that NEP provides near-first-principles accuracy (abstract and Sec. VII), but its own Fig. 5 shows that NEP significantly overestimates the equilibrium interlayer spacing of AB-stacked bilayer graphene and deviates from the DFT binding energy curve. The text acknowledges that none of the MLPs accurately locate the global minimum, but this caveat is not carried through to the summary claims of 'near-first-principles accuracy' made elsewhere. Since this is a fundamental property (van der Waals binding) that is relevant to many of the applications discussed in the review, the authors should either temper the accuracy claim throughout the paper or provide evidence that this failure is an isolated outlier, not representative of typical NEP performance on the benchmarked systems.
[Sec. V.B, Fig. 20] The Pt(001) surface reconstruction is presented as a new case study demonstrating the capability of the NEP approach, but the only validation is qualitative consistency with one prior DP simulation (Qian et al.). No direct comparison is made to DFT energies of the reconstructed and unreconstructed surfaces, nor to any experimental characterization of the reconstruction. Given that the paper explicitly states that the NEP model's test RMSEs (7.76 meV/atom energy, 145.46 meV/Å force) are 'relatively higher' than the previous DP model, the claim that the NEP model reliably captures the subtle energetics of surface reconstruction would be more convincing with a quantitative benchmark, such as comparing surface energies of different reconstructions against DFT. As written, the case study illustrates that NEP can produce a similar trajectory to DP on one system, but it does not independently establish the accuracy of the NEP prediction.

minor comments (7)

[Sec. II.B.1] The phrase 'int the output layer' should read 'in the output layer'.
[Sec. II.B.7] The word 'trainig' appears in the sentence describing RMSE values ('... for the trainig dataset'); correct to 'training'.
[Sec. V.B] The section title uses 'Pt(001)' while the text and Fig. 20 consistently use 'Pt(100)'; the Miller-index notation should be unified.
[Fig. 23] The caption refers to a 'neuroevolution potential (ENP) model' but the method is NEP; correct the abbreviation.
[Sec. V.B] The phrase 'As a hindsight' is ungrammatical; suggest rewording to something like 'To improve diversity, we augmented the dataset with 300 liquid structures...'.
[Sec. VII (Data availability)] The Data availability statement mentions a 'zenodo repository' but provides no URL or DOI; please include the direct identifier.
[Sec. III.B.4] The sentence 'simulations consisting of 100 steps were run' is ambiguous about whether timings include the 100 steps only or are averaged over a longer run after equilibration; please clarify the timing protocol.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: benchmark and case-study claims rest on external DFT/experimental data and independent MLP implementations.

full rationale

This paper is a review of the NEP method by its developers, and it cites prior NEP papers extensively (Refs. 9, 33, 61, 62, 92, etc.). However, none of the load-bearing claims reduces to those citations by construction. The central performance comparisons in Sec. III use a public carbon dataset (Rowe et al., Ref. 67), a pre-trained GAP model from that external work, a NEP model from Ref. 92, and newly trained DP, MACE, and NequIP models; accuracy is evaluated against DFT reference data and against experimental measurements for amorphous carbon. The speed benchmark (Fig. 8) is a measured quantity, not a fitted parameter renamed as a prediction; its main limitation is that NEP runs in GPUMD while other models run in LAMMPS and GAP uses CPUs, which is a benchmarking-fairness issue rather than circularity. New case studies (Pt reconstruction, CNT growth, bilayer hBN tribology) train NEP on published DFT datasets or on DFT data generated in the paper, and the predicted quantities (surface morphology, sp3 fractions, sliding energy surfaces, yield strength) are compared to independent DFT, experimental, or prior DP results. The UNEP-v1 generalization to n-component alloys is validated against external Materials Project and GNoME datasets and against experiments. No equation defines a predicted quantity in terms of fitted parameters, and no uniqueness claim is imported from a self-citation. Thus the derivation chain is self-contained with respect to the stated external references.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claim is a performance claim about NEP, not a new physical derivation. The main 'free' inputs are the hyperparameters of the trained models and the choice of DFT reference data; both are standard in the MLP literature.

free parameters (3)

NEP hyperparameters for bilayer hBN model = cutoff 6 4.5, n_max 8 8, basis_size 12 12, neuron 50, lambda_1 0.05, lambda_2 0.05
Chosen by the authors to balance accuracy and speed for the hBN sliding PES; not fitted to the target sliding energy.
NEP hyperparameters for Pt surface reconstruction model = cutoff 6 5, n_max 4 4, basis_size 8 8, neuron 80, lambda_1 0.0, lambda_e 1.0, lambda_f 1.0, lambda_v 0.1
Chosen to match the prior DP model's dataset and hyperparameters, not tuned to the reconstruction result.
NEP hyperparameters for FeC CNT growth model = cutoff 6 5, n_max 8 8, basis_size 8 8, neuron 30, lambda_1 0.05, lambda_2 0.05
Standard NEP hyperparameters; force RMSE is high (384 meV/Å), suggesting limits in accuracy for this system.

assumptions (3)

domain assumption DFT reference data (e.g., optB88-vdW for carbon, SCAN or MB-pol for water, PBE for various) are sufficiently accurate to represent the true interatomic interactions
All MLP training and evaluation in this review treat DFT or coupled-cluster data as ground truth; any systematic error in these reference methods propagates to the conclusions.
domain assumption The NEP descriptor set (radial and angular components up to l_max) is complete enough to capture the relevant physics of the materials studied
Section II.B.2 states the descriptor construction; the review assumes that the chosen hyperparameters (cutoff, n_max, l_max) provide a sufficient representation of the local environment for the applications shown.
domain assumption Molecular dynamics simulation protocols (e.g., melt-quench-anneal for amorphous carbon, 10 ns runs for Pt reconstruction) produce converged and representative results for the claimed properties
The paper uses these protocols without demonstrating convergence with respect to simulation length or number of independent runs for most case studies.

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Cite this review

Pith. "Pith review of Advances in modeling complex materials: The rise of neuroevolution potentials." pith.science (2026). https://pith.science/paper/LC67OAUJ

@misc{pith2026250111191,
  author       = {Pith},
  title        = {Pith review of: Advances in modeling complex materials: The rise of neuroevolution potentials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LC67OAUJ}},
  note         = {Machine review of arXiv:2501.11191}
}

read the original abstract

Interatomic potentials are essential for driving molecular dynamics (MD) simulations, directly impacting the reliability of predictions regarding the physical and chemical properties of materials. In recent years, machine-learned potentials (MLPs), trained against first-principles calculations, have become a new paradigm in materials modeling as they provide a desirable balance between accuracy and computational cost. The neuroevolution potential (NEP) approach, implemented in the open-source GPUMD software, has emerged as a promising machine-learned potential, exhibiting impressive accuracy and exceptional computational efficiency. This review provides a comprehensive discussion on the methodological and practical aspects of the NEP approach, along with a detailed comparison with other representative state-of-the-art MLP approaches in terms of training accuracy, property prediction, and computational efficiency. We also demonstrate the application of the NEP approach to perform accurate and efficient MD simulations, addressing complex challenges that traditional force fields typically can not tackle. Key examples include structural properties of liquid and amorphous materials, chemical order in complex alloy systems, phase transitions, surface reconstruction, material growth, primary radiation damage, fracture in two-dimensional materials, nanoscale tribology, and mechanical behavior of compositionally complex alloys under various mechanical loadings. This review concludes with a summary and perspectives on future extensions to further advance this rapidly evolving field.

Figures

Figures reproduced from arXiv: 2501.11191 by the authors.

**Figure 2.** FIG. 2. Parity plots of (a) energy, (b) forces, and (c) stress [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** FIG. 3. Energies (top), forces (middle), and virials (bottom) from different machine-learned potential models (including DP, [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (21 more)

**Figure 6.** Figure 6: FIG. 6. Sliding energy profiles for bilayer graphene predicted [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 5.** Figure 5: FIG. 5. Binding energy of AB-stacked bilayer graphene as [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 8.** Figure 8: FIG. 8. Computational speeds as a function of the number of [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

**Figure 9.** Figure 9: FIG. 9. The neuroevolution potential (NEP) model trained [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

**Figure 10.** Figure 10: FIG. 10. Visualizations of disordered carbon structures. (a-d) nanoporous carbon (NPC) and (e-g) amorphous carbon (a-C). [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

**Figure 11.** Figure 11: FIG. 11. Evaluation of force accuracies of a few water mod [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 13.** Figure 13: FIG. 13. Root mean square errors (RMSEs) for energy (a) and [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]

**Figure 14.** Figure 14: FIG. 14. Energy and structural variations arising from different types of short-range orders (SROs) in Ge [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

**Figure 15.** Figure 15: FIG. 15. Performance evaluation of UNEP-v1 using the training and test datasets. (a–c) Parity plots for energy, stress, [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

**Figure 16.** Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p020_16.png]

**Figure 17.** Figure 17: FIG. 17. Phase transition in CsPbI [PITH_FULL_IMAGE:figures/full_fig_p022_17.png]

**Figure 19.** Figure 19: FIG. 19. Schematic illustration of two different phase trans [PITH_FULL_IMAGE:figures/full_fig_p022_19.png]

**Figure 20.** Figure 20: FIG. 20. Training and molecular dynamics simulation results of the neuroevolution potential (NEP) model for simulating the [PITH_FULL_IMAGE:figures/full_fig_p024_20.png]

**Figure 21.** Figure 21: FIG. 21. Training and molecular dynamics simulation results of the NEP model for simulating CNT growth on the Fe [PITH_FULL_IMAGE:figures/full_fig_p025_21.png]

**Figure 22.** Figure 22: FIG. 22. Defect distributions in MoTaVW alloy during a [PITH_FULL_IMAGE:figures/full_fig_p026_22.png]

**Figure 23.** Figure 23: FIG. 23. Mechanical properties two-dimensional materials. (a-b) Atomic snapshots of monolayer quasi-hexagonal-phase [PITH_FULL_IMAGE:figures/full_fig_p028_23.png]

**Figure 24.** Figure 24: FIG. 24. Tensile strength of monolayer quasi-hexagonal-phase [PITH_FULL_IMAGE:figures/full_fig_p028_24.png]

**Figure 25.** Figure 25: FIG. 25. (a-d) Sliding potential energy surfaces for bilayer [PITH_FULL_IMAGE:figures/full_fig_p029_25.png]

**Figure 26.** Figure 26: FIG. 26. Mechanical properties of Cu [PITH_FULL_IMAGE:figures/full_fig_p031_26.png]

**Figure 27.** Figure 27: FIG. 27. (a-c) Atomic structure types at 0, 5, and 10 [PITH_FULL_IMAGE:figures/full_fig_p031_27.png]

**Figure 28.** Figure 28: FIG. 28. Uniaxial fatigue simulation of the Cu [PITH_FULL_IMAGE:figures/full_fig_p032_28.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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