pith. machine review for the scientific record. sign in

arxiv: 2604.23431 · v1 · submitted 2026-04-25 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall

Recognition: unknown

Physics-Informed Deep Image Prior Reconstruction of In-Plane Magnetization from Scanning NV Magnetometry

Zander Scholl , Justin Woods , Charudatta Phatak , Hanu Arava
Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:44 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hall
keywords deep image priorscanning NV magnetometrymagnetization reconstructioninverse problemPermalloy nanostructuresin-plane magnetizationconvolutional autoencoderphysics-informed
0
0 comments X

The pith

A convolutional autoencoder with physics-informed priors reconstructs in-plane magnetization from scanning NV magnetometry.

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

Reconstructing magnetization distributions from stray field measurements is an ill-posed problem with infinitely many solutions for any given field pattern. This paper demonstrates that a deep image prior approach, realized through a simple convolutional autoencoder and augmented with physics-based constraints via spatial masks, can produce reasonable reconstructions of complex in-plane magnetization in lithographically patterned Permalloy nanostructures. The method uses data from scanning NV magnetometry and requires no pre-training on external datasets. Proper alignment of the user-defined masks improves the signal-to-noise ratio of the reconstruction by as much as 3 decibels and serves as a diagnostic for the process. Complementary measurements with magnetic force microscopy are used to validate the results on both Landau and dipole domain structures.

Core claim

The paper claims that a physics-informed deep image prior framework employing a simple convolutional autoencoder, together with user-defined spatial masks, conditionally achieves a reasonable qualitative and quantitative reconstruction of complex in-plane magnetization patterns from scanning NV magnetometry data.

What carries the argument

The deep image prior implemented as a convolutional autoencoder, regularized by physics-informed spatial masks that constrain the solution space of the ill-posed inverse problem.

If this is right

  • The reconstruction works for Landau and dipole domain structures in Permalloy nanostructures.
  • Optimal mask orientation improves reconstruction SNR by up to 3 dB.
  • Mask alignment can diagnose issues in the reconstruction process.
  • The DIP method avoids the need for pre-trained datasets and is less computationally intensive than supervised learning approaches.

Where Pith is reading between the lines

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

  • Such a framework could be adapted to reconstruct magnetization in other magnetic materials or geometries if appropriate masks are available.
  • Combining this with other imaging modalities might enhance accuracy in determining three-dimensional magnetization configurations.
  • Reduced computational demands suggest potential for on-the-fly analysis during experimental scans.

Load-bearing premise

User-defined spatial masks can be oriented to restrict the infinite solution space without introducing systematic bias or excluding the true magnetization.

What would settle it

Generating the stray field from the reconstructed magnetization using the forward model and finding it inconsistent with the measured NV data within experimental uncertainty would falsify the claim of accurate reconstruction.

Figures

Figures reproduced from arXiv: 2604.23431 by Charudatta Phatak, Hanu Arava, Justin Woods, Zander Scholl.

Figure 1
Figure 1. Figure 1: FIG. 1. (A) Schematic of a scanning NV magnetometry experimental set up. The magnetic field strength is determined through view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (A) SEM image of fabricated Permalloy nanostruc view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (A) Deep image prior reconstruction workflow showing the approach. Stray field data from scanning NV magnetometry view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 view at source ↗
read the original abstract

Reconstructing magnetization in nanoscale magnetic thin films is essential for developing next-generation memory, sensors, and various spintronic technologies. However, this remains challenging due to the ill-posed nature of the stray field inverse problem, i.e., there are infinitely many magnetization solutions to a given stray field distribution. Here, we demonstrate that a physics-informed deep image prior (DIP) framework, using a simple convolutional autoencoder conditionally achieves a reasonable qualitative and quantitative reconstruction of complex in-plane magnetization patterns from scanning NV magnetometry. We find that the orientation of user-defined masks implemented to restrict the reconstruction solution space dramatically affects convergence. The optimal alignment of the mask improves the reconstruction signal-to-noise ratio by up to $\SI{3}{\decibel}$, thereby also serving as a diagnostic tool. The DIP approach requires no pre-trained datasets and is considered computationally less intensive as compared to supervised learning approaches. We analyze both Landau and dipole domain structures in lithographically patterned Permalloy nanostructures by incorporating experimentally-guided spatial constraints. Complementary magnetic force microscopy measurements were carried out to support the Scanning NV measurements.

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 manuscript proposes a physics-informed deep image prior (DIP) framework using a convolutional autoencoder to reconstruct complex in-plane magnetization patterns from scanning NV magnetometry stray-field data. User-defined spatial masks are introduced to constrain the ill-posed inverse problem, with the key observation that mask orientation dramatically affects convergence and can yield up to 3 dB SNR improvement when optimally aligned. The method is applied to Landau and dipole domain structures in lithographically patterned Permalloy nanostructures, requires no pre-training, and is validated with complementary magnetic force microscopy measurements.

Significance. If the reconstructions prove quantitatively accurate without mask-induced bias, the work would offer a useful unsupervised, physics-constrained approach to ill-posed inverse problems in nanomagnetism, with lower computational cost than supervised methods and a diagnostic role for mask alignment. The combination of experimental NV data, forward magnetostatic modeling, and spatial constraints is a positive feature.

major comments (2)
  1. [Abstract] Abstract: the claim of 'reasonable qualitative and quantitative reconstruction' is not accompanied by any reported error metrics (e.g., MSE, correlation, or pixel-wise deviation from ground truth), cross-validation details, or ablation studies on reconstruction fidelity. This information is load-bearing for the central claim.
  2. [Results (mask orientation)] Results section on mask alignment: the reported strong dependence of convergence on mask orientation, together with the 3 dB SNR gain for optimal alignment, raises the possibility that the masks encode expected structural priors rather than neutrally restricting the null space. A quantitative ablation showing reconstruction error versus controlled mask misalignment (including cases where the true magnetization deviates from the mask geometry) is required to confirm that valid solutions are not systematically excluded.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'conditionally achieves' is vague; the conditions under which the reconstruction succeeds should be stated explicitly.
  2. [Methods] The manuscript would benefit from a clear statement of the autoencoder architecture (number of layers, filter sizes, activation functions) and the precise form of the physics-informed loss term that combines the forward magnetostatic model with the mask constraint.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We address each major comment below and will incorporate revisions to provide stronger quantitative support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of 'reasonable qualitative and quantitative reconstruction' is not accompanied by any reported error metrics (e.g., MSE, correlation, or pixel-wise deviation from ground truth), cross-validation details, or ablation studies on reconstruction fidelity. This information is load-bearing for the central claim.

    Authors: We agree that quantitative metrics are necessary to support the abstract's claim. In the revised manuscript, we will report explicit error metrics including MSE, Pearson correlation coefficient, and mean pixel-wise deviation for reconstructions against available ground truth (both simulated test cases and MFM-validated experimental structures). We will also add details on our validation procedure and include ablation studies on reconstruction fidelity under different network and mask conditions. revision: yes

  2. Referee: [Results (mask orientation)] Results section on mask alignment: the reported strong dependence of convergence on mask orientation, together with the 3 dB SNR gain for optimal alignment, raises the possibility that the masks encode expected structural priors rather than neutrally restricting the null space. A quantitative ablation showing reconstruction error versus controlled mask misalignment (including cases where the true magnetization deviates from the mask geometry) is required to confirm that valid solutions are not systematically excluded.

    Authors: We acknowledge the concern that mask orientation effects could imply encoding of structural priors. The masks are constructed from the known lithographic geometry of the Permalloy nanostructures (confirmed via SEM), with the goal of restricting the null space to physically allowed regions. The SNR improvement with optimal alignment reflects tighter constraint of the inverse problem rather than exclusion of valid solutions, since the in-plane magnetization in these patterned films is expected to follow the sample boundaries. To address this rigorously, we will add a quantitative ablation study to the revised manuscript. This will report reconstruction error (MSE and SNR) versus controlled mask misalignment angles, including test cases with simulated magnetization patterns that deliberately deviate from the mask geometry (e.g., perturbed Landau and dipole configurations). revision: yes

Circularity Check

0 steps flagged

No significant circularity; reconstruction grounded in external NV data and physics model

full rationale

The paper presents a physics-informed DIP framework (convolutional autoencoder + forward magnetostatic model) applied to experimental scanning NV magnetometry data for in-plane magnetization reconstruction. User-defined masks constrain the ill-posed inverse problem, with noted sensitivity to orientation affecting convergence and SNR. However, no derivation step reduces by construction to a fitted parameter renamed as prediction, self-definition, or load-bearing self-citation chain. The central result relies on external experimental inputs and physical forward modeling rather than internal equivalence to its own assumptions. This is the expected non-finding for a method paper with independent data grounding.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Ledger populated from abstract only; full methods section would likely reveal additional hyperparameters and domain assumptions.

free parameters (2)
  • mask orientation and geometry
    User-defined spatial constraints whose alignment is reported to control convergence and SNR; treated as tunable input.
  • autoencoder architecture hyperparameters
    Network depth, filter sizes, and training schedule for the convolutional autoencoder are not specified but implicitly chosen to achieve reported reconstructions.
axioms (1)
  • domain assumption The stray-field inverse problem for in-plane magnetization is ill-posed with infinitely many solutions for any given field distribution.
    Explicitly stated in the abstract as the core motivation for the physics-informed approach.

pith-pipeline@v0.9.0 · 5502 in / 1224 out tokens · 48937 ms · 2026-05-08T06:44:54.054833+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 15 canonical work pages

  1. [1]

    Spintronics: A Spin-Based Elec- tronics Vision for the Future,

    S. A. Wolf et al., “Spintronics: A Spin-Based Elec- tronics Vision for the Future,” Science294, 1488–1495 (2001), URLhttps://www.science.org/doi/full/10. 1126/science.1065389

    2001

  2. [3]

    Antiferromagnetic spintron- ics,

    V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, “Antiferromagnetic spintron- ics,” Rev. Mod. Phys.90, 015005 (2018), URL https://journals.aps.org/rmp/abstract/10.1103/ RevModPhys.90.015005

    2018

  3. [4]

    The emer- gence of spin electronics in data storage,

    C. Chappert, A. Fert, and F. N. Van Dau, “The emer- gence of spin electronics in data storage,” Nature Mate- rials6, 813–823 (2007), URLhttps://www.nature.com/ articles/nmat2024

    2007

  4. [5]

    Opportuni- ties at the frontiers of spintronics,

    A. Hoffmann and S. D. Bader, “Opportuni- ties at the frontiers of spintronics,” Physi- cal Review Applied4, 047001 (2015), URL https://journals.aps.org/prapplied/abstract/ 10.1103/PhysRevApplied.4.047001

    work page doi:10.1103/physrevapplied.4.047001 2015

  5. [6]

    High- sensitivity diamond magnetometer with nanoscale resolution,

    J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nature Physics4, 810–816 (2008), URLhttps://doi.org/10.1038/nphys1075

    work page doi:10.1038/nphys1075 2008

  6. [7]

    Nanoscale imaging magne- tometry with diamond spins under ambient conditions,

    G. Balasubramanian, I.-Y. Chan, R. Kolesov, M. Al- Hmoud, J. Tisler, C.-S. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, et al., “Nanoscale imaging magne- tometry with diamond spins under ambient conditions,” Nature455, 648–651 (2008), URLhttps://doi.org/10. 1038/nature07278

    2008

  7. [8]

    Available: https://doi.org/10.1038/nnano.2012.50

    P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Loncar, and A. Ya- coby, “A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres,” Nature Nanotechnology7, 320–324 (2012), URLhttps://doi. org/10.1038/nnano.2012.50

    work page doi:10.1038/nnano.2012.50 2012

  8. [9]

    Rondin , author J.-P

    L. Rondin, J.-P. Tetienne, P. Spinicelli, C. Dal Savio, K. Karrai, G. Dantelle, A. Thiaville, S. Rohart, J.-F. Roch, and V. Jacques, “Nanoscale magnetic field map- ping with a single spin scanning probe magnetometer,” Applied Physics Letters100, 153118 (2012), URLhttps: //doi.org/10.1063/1.3703128

    work page doi:10.1063/1.3703128 2012

  9. [10]

    Nanoscale magnetometry with NV centers in diamond,

    S. Hong, M. S. Grinolds, L. M. Pham, D. Le Sage, L. Luan, R. L. Walsworth, and A. Yacoby, “Nanoscale magnetometry with NV centers in diamond,” MRS Bul- letin38, 155–161 (2013), URLhttps://doi.org/10. 1557/mrs.2013.23

    2013

  10. [11]

    Rondin , author J.-P

    L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky, and V. Jacques, “Magnetometry with nitrogen-vacancy defects in diamond,” Reports on Progress in Physics77, 056503 (2014), URLhttps: //doi.org/10.1088/0034-4885/77/5/056503

    work page doi:10.1088/0034-4885/77/5/056503 2014

  11. [12]

    The nature of domain walls in 8 ultrathin ferromagnets revealed by scanning nanomagne- tometry,

    J.-P. Tetienne, T. Hingant, L. J. Mart´ ınez, S. Rohart, A. Thiaville, L. H. Diez, K. Garcia, J.-P. Adam, J.-V. Kim, J.-F. Roch, et al., “The nature of domain walls in 8 ultrathin ferromagnets revealed by scanning nanomagne- tometry,” Nature Communications6, 6733 (2015), URL https://doi.org/10.1038/ncomms7733

    work page doi:10.1038/ncomms7733 2015

  12. [13]

    Subpicotesla diamond magnetometry,

    T. Wolf, P. Neumann, K. Nakamura, H. Sumiya, T. Ohshima, J. Isoya, and J. Wrachtrup, “Subpicotesla diamond magnetometry,” Physical Review X5, 041001 (2015), URLhttps://doi.org/10.1103/PhysRevX.5. 041001

    work page doi:10.1103/physrevx.5 2015

  13. [14]

    Real-space imaging of non-collinear antiferromagnetic order with a single- spin magnetometer,

    I. Gross, W. Akhtar, V. Garcia, L. J. Mart´ ınez, S. Chouaieb, K. Garcia, C. Carr´ et´ ero, A. Barth´ el´ emy, P. Appel, P. Maletinsky, et al., “Real-space imaging of non-collinear antiferromagnetic order with a single- spin magnetometer,” Nature549, 252–256 (2017), URL https://doi.org/10.1038/nature23656

    work page doi:10.1038/nature23656 2017

  14. [15]

    Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond,

    F. Casola, T. van der Sar, and A. Yacoby, “Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond,” Nature Reviews Materials3, 17088 (2018), URLhttps://doi.org/10. 1038/natrevmats.2017.88

    2018

  15. [16]

    High-resolution magnetic reso- nance spectroscopy using a solid-state spin sensor,

    D. R. Glenn, D. B. Bucher, J. Lee, M. D. Lukin, H. Park, and R. L. Walsworth, “High-resolution magnetic reso- nance spectroscopy using a solid-state spin sensor,” Na- ture555, 351–354 (2018), URLhttps://doi.org/10. 1038/nature25781

    2018

  16. [17]

    Probing mag- netism in 2D materials at the nanoscale with single- spin microscopy,

    L. Thiel, Z. Wang, M. A. Tschudin, D. Rohner, I. Guti´ errez-Lezama, N. Ubrig, M. Gibertini, E. Gian- nini, A. F. Morpurgo, and P. Maletinsky, “Probing mag- netism in 2D materials at the nanoscale with single- spin microscopy,” Science364, 973–976 (2019), URL https://doi.org/10.1126/science.aav6926

    work page doi:10.1126/science.aav6926 2019

  17. [18]

    R. J. Blakely,Potential theory in gravity and magnetic applications(Cambridge University Press, 1995)

    1995

  18. [19]

    Quantita- tive magnetic force microscopy on perpendicu- larly magnetized samples,

    H. J. Hug, B. Stiefel, P. J. Van Schendel, A. Moser, R. Hofer, S. Martin, H.-J. G¨ untherodt, S. Porthun, L. Abelmann, J. Lodder, et al., “Quantita- tive magnetic force microscopy on perpendicu- larly magnetized samples,” Journal of Applied Physics83, 5609–5620 (1998), URLhttps:// pubs.aip.org/aip/jap/article/83/11/5609/488088/ Quantitative-magnetic-force...

    1998

  19. [20]

    Obtaining vector magnetic field maps from single-component mea- surements of geological samples,

    E. A. Lima and B. P. Weiss, “Obtaining vector magnetic field maps from single-component mea- surements of geological samples,” Journal of Geo- physical Research: Solid Earth114(2009), URL https://agupubs.onlinelibrary.wiley.com/doi/10. 1029/2008JB006006

    2009

  20. [21]

    Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse prob- lems involving nonlinear partial differential equa- tions,

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse prob- lems involving nonlinear partial differential equa- tions,” Journal of Computational Physics378, 686– 707 (2019), URLhttps://www.sciencedirect.com/ science/article/pii/S0021999118307125

    2019

  21. [22]

    Untrained physically informed neural network for image reconstruction of magnetic field sources,

    A. Dubois, D. Broadway, A. Stark, M. Tschudin, A. Healey, S. Huber, J.-P. Tetienne, E. Greplova, and P. Maletinsky, “Untrained physically informed neural network for image reconstruction of magnetic field sources,” Physical Review Applied18, 064076 (2022), URLhttps://journals.aps.org/prapplied/ abstract/10.1103/PhysRevApplied.18.064076

    work page doi:10.1103/physrevapplied.18.064076 2022

  22. [23]

    Egger, Stefan Filipp, Frank K

    D. A. Broadway, M. Flaks, A. E. Dubois, and P. Maletinsky, “Reconstruction of nontrivial magneti- zation textures from magnetic field images using neural networks,” Phys. Rev. Appl.23, 044012 (2025), URL https://link.aps.org/doi/10.1103/PhysRevApplied. 23.044012

    work page doi:10.1103/physrevapplied 2025

  23. [24]

    Magnetic domain-wall racetrack memory,

    S. S. Parkin, M. Hayashi, and L. Thomas, “Magnetic domain-wall racetrack memory,” Science320, 190–194 (2008), URLhttps://www.science.org/doi/10.1126/ science.1145799

    2008

  24. [25]

    Magnetic domain-wall logic,

    D. A. Allwood, G. Xiong, C. Faulkner, D. Atkinson, D. Petit, and R. P. Cowburn, “Magnetic domain-wall logic,” Science309, 1688–1692 (2005), URLhttps:// www.science.org/doi/10.1126/science.1108813

    work page doi:10.1126/science.1108813 2005

  25. [26]

    Hubert and R

    A. Hubert and R. Sch¨ afer,Magnetic domains: the analy- sis of magnetic microstructures(Springer Science & Busi- ness Media, 1998)

    1998

  26. [27]

    R. M. Bozorth,Ferromagnetism(Van Nostrand, 1951)

    1951

  27. [28]

    Chikazumi and C

    S. Chikazumi and C. D. Graham,Physics of ferromag- netism(Oxford University Press, 2009)

    2009

  28. [29]

    Geometry driven intermediate states in artificial square ice structures,

    H. Arava, I. Tapia, T. Cote, J. S. Woods, F. Bar- rows, J. Fullerton, and P. Mellado, “Geometry driven intermediate states in artificial square ice structures,” Communications Materials (2026), ISSN 2662-4443, URL https://doi.org/10.1038/s43246-026-01147-4

    work page doi:10.1038/s43246-026-01147-4 2026

  29. [30]

    Ulyanov, A

    D. Ulyanov, A. Vedaldi, and V. Lempitsky, in Proceedings of the IEEE Conference on Com- puter Vision and Pattern Recognition (CVPR) (IEEE, 2018), pp. 9446–9454, URLhttps: //openaccess.thecvf.com/content_cvpr_2018/html/ Ulyanov_Deep_Image_Prior_CVPR_2018_paper.html

    2018

  30. [31]

    Sandwiched Rényi Divergence Satisfies Data Processing Inequality

    A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, “The design and verification of Mumax3,” AIP Advances 4, 107133 (2014), URLhttp://doi.org/10.1063/1. 4899186

    work page doi:10.1063/1 2014

  31. [32]

    Denoising Prior Driven Deep Neural Network for Im- age Restoration,

    W. Dong, P. Wang, W. Yin, G. Shi, F. Wu, and X. Lu, “Denoising Prior Driven Deep Neural Network for Im- age Restoration,” IEEE Transactions on Pattern Analy- sis and Machine Intelligence41, 2305–2318 (2019), URL https://ieeexplore.ieee.org/document/8481558

    work page arXiv 2019