Toward machine learning interatomic potentials for modeling uranium mononitride

Kashi N. Subedi; Lorena Alzate-Vargas; Michael W.D Cooper; Nicholas Lubbers; Richard A. Messerly; Roxanne M. Tutchton; Tammie Gibson

REVIEW 5 major objections 5 minor 46 references

Toward machine learning interatomic potentials for modeling uranium mononitride

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper develops the first machine learning interatomic potentials for uranium mononitride, showing they reproduce DFT-level thermophysical properties, defect energetics, and radiation-damage behavior at molecular dynamics cost.

desk verdict First MLIPs for UN with a solid active-learning pipeline; defect validation is partly in-sample, but the finite-temperature and transfer tests are real progress and the paper deserves refereeing. read the letter →

arxiv 2411.14608 v2 pith:7C47E5DP submitted 2024-11-21 cond-mat.mtrl-sci

Lorena Alzate-Vargas , Kashi N. Subedi , Nicholas Lubbers , Michael W.D Cooper , Roxanne M. Tutchton , Tammie Gibson , Richard A. Messerly This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords uraniummononitridemachinelearninginteratomicpotentialactiveneuralnetworkdensityfunctionaltheorynuclearfueldefectenergeticsmoleculardynamics

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

Uranium mononitride is a leading candidate for accident-tolerant nuclear fuel, but its atomistic modeling has been stuck between expensive density functional theory and less accurate classical potentials. This paper develops the first machine learning interatomic potentials for UN, one ANI-type and one HIP-NN-type, trained on a 12,336-configuration DFT dataset assembled through active learning. Both potentials reproduce the DFT reference for lattice parameter, heat capacity, bulk modulus, phonons, and point-defect energies, and they show promise for diffusion, noble-gas impurities, and radiation cascades. The result matters because it gives fuel performance models a fast, validated way to simulate UN under realistic reactor conditions.

What carries the argument

The central machinery is an active-learning pipeline that builds a 12,336-configuration DFT (PBE) training set, combined with two local neural network potentials. The ANI potential is a Behler–Parrinello-style network that sums atomic energies with species-specific radial and angular symmetry function descriptors. The HIP-NN potential is a graph-based, message-passing network whose atomic-environment features are learned end-to-end; its core identity is $A_{i,b} = \sum_{\nu,j,b} V_{\nu}\,\mathrm{abs}_\nu(r_{ij}) Z_{j,b}$, which sums learned sensitivity functions of pairwise distances over all neighbors. Both potentials conserve energy by construction (forces are gradients of the total energy via automatic differentiation) and use only local atomic environments within cutoff radii of 5–7 Å. The active-learning loop, driven by a query-by-committee ensemble of eight ANI models under oscillating temperature and density perturbations, selects only high-uncertainty configurations for DFT labeling, covering crystalline, defective, and disordered states.

What would settle it

Compute the same stoichiometric defect formation energies and migration barriers with a DFT method that reproduces UN's experimental antiferromagnetic ordering and lattice parameter (e.g., PBE+U with a Hubbard U whose phonons remain real). If those values differ from the PBE reference by more than the MLIPs' training error (roughly 0.5 eV for defects), the potentials' agreement with PBE would not transfer to the more accurate reference, and a retrained potential would be needed.

Watch

Extended reading notes

Core claim

We have developed two machine learning interatomic potentials for uranium mononitride — an ANI neural network potential and a HIP-NN message-passing potential — trained on a DFT (PBE) dataset that was enriched by an active learning loop to cover crystalline, defective, and disordered configurations. Both potentials reproduce the reference DFT energies and forces to within about 2.5 meV/atom and 0.1 eV/Å respectively, and they capture temperature-dependent lattice parameter, specific heat, and bulk modulus from 300 K to 2700 K in close agreement with DFT-MD and experiment. They also match DFT for stoichiometric point-defect formation energies and migration barriers, and the HIP-NN potential demonstrates credible nitrogen diffusion trends, xenon incorporation energies (with a hybrid classical description for Xe), and a million-atom collision cascade. This establishes the first reliable machine learning interatomic potentials for atomic-scale modeling of UN at finite temperatures, bridging the gap between accurate but costly DFT and the larger-scale simulations needed for fuel performance models.

Load-bearing premise

The entire training set is labeled with PBE density functional theory using ferromagnetic ordering on uranium, and the paper assumes this reference energy surface is accurate for the high-temperature, defective, and disordered configurations the potentials are meant to explore, so any PBE error is inherited by the potentials.

Editorial extensions

If this is right

Both MLIPs reproduce the PBE phonon dispersion including the optical modes that classical potentials miss, so the potentials support lattice dynamics and thermal property predictions.
Defect formation energies for uranium and nitrogen Frenkel pairs and Schottky defects match DFT within a few tenths of an eV, enabling large-scale defect kinetics simulations.
The HIP-NN potential runs a 1 keV collision cascade in a four-million-atom cell, demonstrating that radiation damage simulations beyond DFT's reach are feasible.
Nitrogen diffusion in hypo-stoichiometric UN is predicted to be vacancy-assisted at low temperature and interstitial-dominated at higher temperature, consistent with experimental mechanisms.
The ~0.7% lattice underestimate and the 39–43% error in the C44 elastic constant are attributed to the PBE functional rather than the MLIP fitting, so the potentials would improve automatically with a better reference functional.

Reading between the lines

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

Because all training labels are ferromagnetic PBE, the potentials are effectively surrogates for that specific functional; users should check against antiferromagnetic or PBE+U data before trusting defect energetics near magnetic transitions.
The active-learning recipe of oscillating temperature and density, seeding defects, and query-by-committee selection could transfer to other actinide fuels, where reference data are scarce and expensive.
The hybrid treatment of xenon with a classical Buckingham potential introduces more than 2 eV of error at interstitial sites; retraining a multi-species MLIP that explicitly includes Xe would likely fix this and make fission-gas modeling fully consistent.
The potentials' ability to reproduce the sharp rise in heat capacity above 1500 K suggests they capture defect-generation physics, so free-energy or thermodynamic-integration studies could use them to predict melting and phase stability.

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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

First, what's new: this is the first MLIP for uranium mononitride, and it comes with two architectures (ANI and HIP-NN), a documented active-learning dataset of ~12k configurations, and a broad validation sweep: lattice parameter, elastic constants, phonons, heat capacity, bulk modulus vs temperature, migration barriers, nitrogen diffusion, Xe incorporation, and a 1 keV cascade. That is a lot of useful material for the nuclear fuels community, and the comparison against classical potentials is genuinely informative. The PBE vs PBE+U phonon check in Appendix C is a good methodological decision, and the authors are transparent about where the PBE reference is limiting (C44, lattice offset).

Where it gets soft. The concern about circularity is right: Table III's defect formation energies (UFP, NFP, Schottky) are computed for defect classes that were seeded into the active-learning dataset in early iterations (Section II.B). So 'excellent agreement' there is interpolation, not prediction. The paper would be stronger with a defect-excluded retraining test, or at least a held-out set of unseen defect geometries. Related: Table I reports only training RMSE, no test RMSE, so generalization error is not quantified for the final models. The Xe interstitial incorporation is off by >2 eV and the authors attribute that to the Buckingham hybrid; fair, but it limits the claim about noble gas accuracy. The migration barriers are more convincing because they weren't directly trained, though the text admits sampling with interstitials may have explored those regions.

Minor stuff: the uncertainty threshold values in Appendix B look swapped (mean force threshold 0.088 vs max 0.024 eV/Å) — likely a typo. And the data availability says potentials and dataset are pending LANL review; that's a practical block for anyone wanting to build on this now.

Bottom line: the central defect claim is partly circular, and the paper overstates it in the abstract. But the finite-temperature MD, diffusion, and cascade tests are genuinely out-of-sample, and the resource itself (first UN MLIPs, training pipeline, hyperparameters) is valuable. This deserves a serious referee. I'd send it to review with a request for artifact release and an out-of-sample defect test, or at least explicit acknowledgment of the in-sample nature of Table III.

Referee Report

5 major / 5 minor

Summary. The manuscript develops two neural-network interatomic potentials (ANI and HIP-NN) for uranium mononitride using a DFT-PBE training set enriched by an active-learning procedure. The potentials are tested against DFT and experiment for lattice parameters, elastic constants, phonon spectra, finite-temperature thermodynamic properties, stoichiometric point-defect formation energies, defect migration barriers, nitrogen self-diffusion, xenon incorporation energies, and a 1 keV collision cascade. The central claim is that these are the first machine-learning interatomic potentials for reliable atomic-scale modeling of UN at finite temperatures and that they reproduce DFT and experimental data closely enough to be used for defect and radiation-damage studies.

Significance. If the claims hold, the two potentials would be a valuable community resource for atomistic simulations of UN, enabling larger-scale and longer-time studies than DFT alone. The active-learning pipeline, the breadth of validation (phonon dispersion, thermal expansion, heat capacity, bulk modulus, and a four-million-atom cascade test), and the explicit comparison with classical potentials are notable strengths. The main gaps are that defect validation is performed on configurations that were seeded into the training set, no held-out test error is reported, and some numerical results (Xe interstitial incorporation, C44) contradict the strength of the conclusions drawn from them.

major comments (5)

[Section II.B, Fig. 1(c), Table III] The defect validation is in-sample. Neutral Schottky defects and U/N Frenkel pairs were manually added to the training set in the early active-learning iterations, and Fig. 1(c) shows an uranium interstitial that entered in the final iteration. Table III then reports formation energies for exactly these defect classes. Agreement with DFT is therefore an interpolation test and does not support the conclusion that the potentials 'can be used for modeling defects' in unseen geometries. Please provide a defect-excluded retraining test (or at least a held-out set of defect configurations never used in training) and report those errors, or explicitly reframe the claim as in-sample reproduction.
[Table I] Only training RMSE values are reported for energy and forces. Since the active-learning ensemble uses randomized train/validation/test splits, held-out metrics should be available and should be reported alongside training RMSE. Without out-of-sample error, the abstract's claim that the potentials are 'reliable' for atomic-scale modeling is not quantitatively supported.
[Table V and Conclusions] The conclusion states that xenon incorporation energies are 'in close agreement with DFT', but Table V reports Xe_int = 16.85 eV versus the DFT reference of 14.68 eV, a discrepancy of more than 2 eV that the text itself acknowledges. This overstatement should be corrected. The Xe_int result should either be removed from the claim or be discussed explicitly as a known limitation of combining the MLIP with the Buckingham potential for Xe.
[Table II] The C44 values from both MLIPs differ from experiment by 39-43%. The manuscript attributes this discrepancy to the PBE functional, but the DFT-PBE value in Table II is 52 GPa while the MLIPs give 43-46 GPa, so the potentials also deviate from their own DFT reference by 12-17%. Please quantify this additional error and temper the elastic-constant validation claim, or provide evidence that the C44 discrepancy is entirely inherited from the training labels.
[Section II.C and Appendix C] All reference labels use ferromagnetic PBE, and the choice is justified by the absence of imaginary phonons compared with PBE+U. However, no sensitivity check is provided for the properties most relevant to the conclusions: defect formation energies and migration barriers could depend on magnetic ordering or on the Hubbard U. A limited check (for example, recomputing the Table III defect energies with an AFM or PBE+U setup) would address the main correctness risk in transferring the potentials to real UN, whose experimental ground state is antiferromagnetic.

minor comments (5)

[Figure 1] The caption assigns '(b) highly disordered structure' and '(c) structure containing an uranium interstitial', while the main text says Fig. 1(b) shows an uranium interstitial and Fig. 1(c) shows a highly disordered configuration. The labeling should be made consistent.
[Figure 6] The legend in Figure 6 shows 'Nvac 1.5%', while the text and caption describe concentrations of 0.5% and 1%. Please reconcile these numbers.
[Appendix B] The reported uncertainty thresholds appear inconsistent: the text gives a maximum-force threshold of 0.024 eV/Å, which is smaller than the mean-force threshold of 0.088 eV/Å. This is likely a typo and should be corrected.
[Throughout] The surname Tseplyaev is spelled 'Tseplayaev' in some places, and Figure 3's caption spells Kocevski as 'Koceveski'. Please unify the spelling.
[Data Availability] The data-availability statement says the dataset and potentials 'will be available after completing LANL reviewing process'. For reproducibility, please provide a repository link or DOI at publication time (or at minimum state 'available upon reasonable request').

Circularity Check

1 steps flagged · score 6.0 of 10

Defect formation energy validation is in-sample: UFP, NFP, and Schottky defect configurations were explicitly added to the active-learning training set, and Table III then 'validates' formation energies for those same defect types.

fitted input called prediction [Section II.B (Active learning) and Section III.A (Validation of models), Tables I and III]
"Additionally, to enhance diversity, configurations representing defect types–neutral Schottky defects, uranium and nitrogen Frenkel pairs–were manually added to the dataset in the early iterations of AL and subsequently used for sampling. ... The final training dataset used to train both ANI and HIP-NN potentials contains 12,336 atomic configurations, covering crystalline, defect-containing, and disordered structures."

Section III.A then validates 'the accuracy of the defect formation energies of uranium Frenkel pair (UFP), nitrogen Frenkel pair (NFP), and bound/unbound Schottky defects (SD)' and reports these as 'predictions' in Table III. These are exactly the defect classes whose configurations were manually seeded into the active-learning training data. The close agreement therefore demonstrates that the networks can fit their own training labels for these defect environments, not that they transfer to unseen defect geometries. Table I reports only training RMSE, so no held-out defect test is provided.

full rationale

The paper's main circularity is confined to the defect-formation-energy validation. The authors openly state that uranium and nitrogen Frenkel pairs and neutral Schottky defects were manually added to the training set during active learning, and the final dataset explicitly covers defect-containing structures. Table III then reports formation energies for these same defect types as 'predictions,' with no held-out test RMSE in Table I. This is an in-sample fit check rather than a transfer test for defect modeling. The thermophysical properties (lattice parameter, heat capacity, bulk modulus), NEB migration barriers, Xe incorporation, and collision cascades are not direct training targets and provide independent support for the potentials. There is no load-bearing self-citation chain, no imported uniqueness theorem, and no renaming of known results; the PBE reference functional is an accuracy limitation, not circularity. Overall the defect claim partially reduces to the training set by construction, warranting a score of 6 rather than a higher value because substantial out-of-sample validation remains.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's central claim rests on fitting neural network weights to a DFT-labeled dataset; the fitted weights and hand-chosen data-selection thresholds are the effective free parameters. No new physical entities are introduced. The key axioms are the accuracy of PBE DFT as the training reference and the coverage of the active learning sampling. Validation against the same DFT reference for defect configurations included in training adds circularity burden.

free parameters (3)

Neural network weights (ANI and HIP-NN) = Not enumerated; trained on 12,336 DFT-labeled configurations
All predictions depend on these fitted weights; the paper does not provide them or the training data.
Active learning uncertainty thresholds = Energy 28 eV/atom; mean force 0.088 eV/Å; max force 0.024 eV/Å
Hand-chosen thresholds in Appendix B determine which configurations are added to the training set, shaping model accuracy.
MLIP hyperparameters = ANI cutoff 7.0 Å, 32 radial and 64 angular basis functions; HIP-NN nfeature=60, nν=20, ℓ=1
Architectural choices adapted from prior UO2 optimization, not tuned for UN; they affect descriptor resolution and model capacity.

assumptions (4)

domain assumption PBE (GGA) DFT with ferromagnetic U ordering is an accurate reference potential energy surface for UN.
All training labels come from this method (Section II.C); PBE+U was rejected due to imaginary phonons. PBE's known underestimation of lattice parameter is visible in the results.
domain assumption The active learning protocol samples the configuration space relevant to the target properties.
Training set is built from ramped and oscillating temperature and density MD (Section II.B and Appendix B); coverage of rare defect geometries is inferred, not guaranteed.
ad hoc to paper Buckingham potential parameters for Xe-U and Xe-N from Kocevski et al. are transferable to the MLIP environment.
Used in Section II.D to compute Xe incorporation energies; the authors note accuracy is likely limited by this classical description.
domain assumption Electronic heat capacity correction c_e from DFT can be added to MD-derived vibrational heat capacity.
Applied in Fig. 4 to compare with experiment (Section III.B); standard practice but an external correction, not predicted by the MLIP.

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Cite this review

Pith. "Pith review of Toward machine learning interatomic potentials for modeling uranium mononitride." pith.science (2026). https://pith.science/paper/7C47E5DP

@misc{pith2026241114608,
  author       = {Pith},
  title        = {Pith review of: Toward machine learning interatomic potentials for modeling uranium mononitride},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7C47E5DP}},
  note         = {Machine review of arXiv:2411.14608}
}

read the original abstract

Uranium mononitride (UN) is a promising accident-tolerant fuel because of its high fissile density and high thermal conductivity. In this study, we developed the first machine learning interatomic potentials for reliable atomic-scale modeling of UN at finite temperatures. We constructed a training set using density functional theory (DFT) calculations that was enriched through an active learning procedure, and two neural network potentials were generated. Both potentials successfully reproduce key thermophysical properties of interest, such as temperature-dependent lattice parameter, specific heat capacity, and bulk modulus. We also evaluated the energy of stoichiometric defect reactions and defect migration barriers and found close agreement with DFT predictions, demonstrating that our potentials can be used for modeling defects in UN. Additional tests provide evidence that our potentials are reliable for simulating diffusion, noble gas impurities, and radiation damage.

Figures

Figures reproduced from arXiv: 2411.14608 by the authors.

**Figure 2.** UN phonon band dispersion calculated by MLIPs. Experimental data [ [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Lattice parameter as a function of temperature for both MLIPs, in comparison with [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Specific heat capacity as a function of temperature for both MLIPs, in comparison with [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

**Figure 5.** Figure 5: Bulk modulus as a function of temperature for both MLIPs, in comparison with DFT [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: Nitrogen self-diffusion vs inverse temperature using HIP-NN for an stoichiometric [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Snapshots of sites containing interstitial defects or vacancies during a collision cascade. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

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