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arxiv: 2605.26897 · v1 · pith:J2BWEUV2new · submitted 2026-05-26 · ❄️ cond-mat.mtrl-sci · physics.atom-ph

Active learning of collinear magnetic Moment Tensor Potentials using the spin-MLIP package from soft-constrained spin-polarized DFT calculations: a case study of Fe-Pd

Arseniy Burov , Alexey S. Kotykhov , Dmitry A. Aksyonov , Ivan S. Novikov , Vladimir V. Ladygin This is my paper

Pith reviewed 2026-06-29 16:57 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.atom-ph
keywords magnetic moment tensor potentialsactive learningspin-polarized DFTFe-Pdmolecular dynamicsmachine learning interatomic potentialscollinear magnetism
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The pith

A workflow trains magnetic Moment Tensor Potentials from soft-constrained DFT data and reproduces magnetization and density of states versus volume in Fe-Pd.

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

The paper presents a workflow that performs active learning of collinear magnetic Moment Tensor Potentials during molecular dynamics runs. Training data come from spin-polarized DFT calculations that softly constrain magnetic moments away from equilibrium values. The resulting potentials are tested on the Fe-Pd crystal, where magnetization and density of states as functions of supercell volume match the underlying DFT results and also align with measured density of states.

Core claim

An active-learning procedure implemented in the spin-MLIP package, driven by soft-constrained spin-polarized DFT calculations performed in VASP and MD trajectories run in LAMMPS, produces magnetic Moment Tensor Potentials whose predicted magnetization and density of states versus volume in Fe-Pd agree with direct DFT calculations and with experimental density of states.

What carries the argument

The magnetic Moment Tensor Potential (mMTP), an extension of the standard Moment Tensor Potential that incorporates collinear magnetic moments as additional degrees of freedom and is fitted on-the-fly from non-equilibrium magnetic-moment data.

If this is right

  • Magnetization in Fe-Pd varies with supercell volume in the same way under the mMTP as under direct DFT.
  • Density of states computed from the mMTP at different volumes matches both DFT and experimental curves.
  • The active-learning loop runs entirely within the spin-MLIP, VASP, and LAMMPS codes without manual intervention.
  • The fitted mMTP remains stable during the molecular-dynamics trajectories used for further data acquisition.

Where Pith is reading between the lines

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

  • The same workflow could be applied to other magnetic alloys provided suitable soft-constrained DFT data can be generated.
  • Once trained, the mMTP could enable longer or larger simulations than direct DFT while retaining magnetic degrees of freedom.

Load-bearing premise

Soft-constrained spin-polarized DFT calculations supply accurate and diverse non-equilibrium magnetic moment data that suffice to train an mMTP transferable enough to stay reliable throughout active-learning MD trajectories.

What would settle it

An MD trajectory in which the mMTP magnetization or density of states at a volume outside the training set deviates measurably from fresh DFT calculations performed at the same volume.

Figures

Figures reproduced from arXiv: 2605.26897 by Alexey S. Kotykhov, Arseniy Burov, Dmitry A. Aksyonov, Ivan S. Novikov, Vladimir V. Ladygin.

Figure 1
Figure 1. Figure 1: Workflow of mMTP training incorporating soft-constrained DFT calculations. The upper gray panel shows the pretraining stage, in [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The number of selected configurations during active learning in total and at each iteration [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dependence of magnetization and pressure on lattice parameter at [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Total phonon DOS for Fe0.68Pd0.32 calculated with mMTP and DFT for different lattice parameters at 300 K. atoms and lattice parameters were chosen close to the experimental values. We observe that mMTP correctly captures the qualitative evolution of the DOS with pressure, namely its shift toward higher frequencies as the lattice parameter decreases. 4. Conclusion In this work, we presented the workflow for… view at source ↗
Figure 5
Figure 5. Figure 5: Fe phonon DOS for Fe0.68Pd0.32 calculated with mMTP and compared with experiment from [40] for different corresponding lattice parameters at 300 K. (MC) spin flips (MDMC) which enables finding deeper energy minima and achieve results that better agree with the DFT ones. 5. Acknowledgments The publication was prepared within the framework of the Academic Fund Program at HSE University (grant No. 26-00-054 “… view at source ↗
read the original abstract

Explicit incorporation of magnetic degrees of freedom in machine-learning interatomic potentials (magnetic MLIPs) plays a crucial role in the correct description of magnetic materials and their properties. An important ingredient for fitting of magnetic MLIPs is spin-polarized density functional theory (DFT) calculations with non-equilibrium magnetic moments, i.e. DFT calculations with constraints on magnetic moments. In this study, we present a workflow for active learning of magnetic Moment Tensor Potential (mMTP) during molecular dynamics (MD) simulations. Magnetic MTP and its active learning algorithm were implemented in the open-source spin-MLIP code, DFT soft-constrained spin-polarized calculations were performed with the VASP code, and MD simulations were conducted in the open-source LAMMPS code. We test our workflow on the Fe-Pd crystal. The dependencies of magnetization and density of states (DOSs) on the volume of a supercell (or, pressure) are in good agreement with those calculated with DFT. Furthermore, the calculated DOSs correspond to the experimental ones.

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 / 1 minor

Summary. The manuscript presents a workflow for active learning of collinear magnetic Moment Tensor Potentials (mMTPs) implemented in the open-source spin-MLIP package. Training data are generated from soft-constrained spin-polarized DFT calculations in VASP; MD simulations are performed in LAMMPS. The workflow is tested on Fe-Pd, with the claim that magnetization and DOS versus supercell volume (pressure) from mMTP agree with independent DFT results and that the computed DOS matches experimental data.

Significance. An open-source active-learning implementation for magnetic MLIPs addresses a practical need in modeling magnetic materials. If the quantitative validation holds, the integration of soft-constrained DFT labels with mMTP active learning could enable more reliable simulations of pressure-dependent magnetic properties. The reproducibility afforded by the released spin-MLIP code is a clear strength.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'the dependencies of magnetization and density of states (DOSs) on the volume of a supercell (or, pressure) are in good agreement with those calculated with DFT' supplies no quantitative error metrics (MAE, RMSE, R²), training-set sizes, or active-learning uncertainty quantification, rendering the agreement impossible to evaluate.
  2. [Abstract] Abstract / workflow description: no per-configuration deviations from target moments are reported for the soft-constrained VASP calculations, nor is any comparison given to hard-constrained reference data; without this, it is unclear whether the training labels are sufficiently accurate and unbiased for a transferable mMTP whose predictions remain reliable throughout the active-learning MD loop.
minor comments (1)
  1. [Abstract] The abstract states that 'the calculated DOSs correspond to the experimental ones' without specifying which experimental dataset or energy range is used for the comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major comment below and indicate the corresponding revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'the dependencies of magnetization and density of states (DOSs) on the volume of a supercell (or, pressure) are in good agreement with those calculated with DFT' supplies no quantitative error metrics (MAE, RMSE, R²), training-set sizes, or active-learning uncertainty quantification, rendering the agreement impossible to evaluate.

    Authors: We agree that quantitative metrics strengthen the claim. In the revised manuscript we have updated the abstract and results section to report MAE, RMSE and R² for magnetization and DOS versus volume, together with the final training-set size and active-learning uncertainty estimates obtained from the mMTP committee. revision: yes

  2. Referee: [Abstract] Abstract / workflow description: no per-configuration deviations from target moments are reported for the soft-constrained VASP calculations, nor is any comparison given to hard-constrained reference data; without this, it is unclear whether the training labels are sufficiently accurate and unbiased for a transferable mMTP whose predictions remain reliable throughout the active-learning MD loop.

    Authors: We have added a new paragraph in the Methods section that tabulates the mean and maximum absolute deviations from the target moments for every soft-constrained configuration used in training. A limited comparison against hard-constrained calculations on a representative subset of structures has also been performed and is now reported in the supplementary information; the deviations remain small enough that the soft-constrained labels support reliable mMTP transferability within the explored volume range. revision: yes

Circularity Check

0 steps flagged

No significant circularity; validation is external to the fitted model

full rationale

The paper describes an active-learning workflow that trains an mMTP on soft-constrained DFT data for Fe-Pd and reports agreement of magnetization and DOS versus volume with independent DFT runs plus experimental DOS. No equations, procedures, or self-citations are shown that reduce any reported prediction or agreement to a quantity fitted inside the same model by construction. The central claim rests on external benchmarks rather than internal re-derivation, satisfying the default expectation of a non-circular derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper introduces no new free parameters, axioms, or invented entities beyond standard assumptions of DFT and existing MLIP frameworks; the central claim rests on the domain assumption that soft-constrained DFT data are suitable training targets.

axioms (1)
  • domain assumption Soft-constrained spin-polarized DFT calculations produce reliable non-equilibrium magnetic moment configurations suitable for training magnetic MLIPs
    This premise is required to generate the training data used by the active-learning loop.

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