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arxiv: 2509.13571 · v2 · pith:CAX6AZJ4new · submitted 2025-09-16 · 🌌 astro-ph.SR

SuNeRF-CME: Physics-Informed Neural Radiance Fields for Tomographic Reconstruction of Coronal Mass Ejections

Robert Jarolim , Martin Sanner , Chia-Man Hung , Emma Stevenson , Hala Lamdouar , Josh Veitch-Michaelis , Ioanna Bouri , Anna Malanushenko
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Elena Provornikova V\'it R\r{u}\v{z}i\v{c}ka Carlos Urbina-Ortega
This is my paper

Pith reviewed 2026-05-18 15:25 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords coronal mass ejectionstomographic reconstructionneural radiance fieldsheliospheric plasmaThomson scattering3D reconstructionspace weatherphysics-informed neural networks
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The pith

Physics-informed neural radiance fields recover the full 3D structure and motion of coronal mass ejections from only two viewpoints.

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

The paper introduces SuNeRF-CME to create three-dimensional models of coronal mass ejections by fitting neural radiance fields to coronagraph images while enforcing physical rules on how the plasma flows. It combines ray-tracing that accounts for Thomson scattering with constraints on continuity, propagation direction, and speed so that limited viewing angles still produce consistent reconstructions. Tests on simulated CME data show the method recovers velocity to within roughly three percent and direction to within a few degrees even when only two viewpoints are available, and it reproduces the three-part structure plus internal density variations. This matters because accurate 3D knowledge of these eruptions improves forecasts of their arrival and strength at Earth. More viewpoints integrate directly to refine the plasma distribution further.

Core claim

SuNeRF-CME uses Neural Radiance Fields to estimate electron density in the heliosphere through a ray-tracing approach that accounts for Thomson scattering. The model is optimized by fitting time-dependent observational data while applying physical constraints on plasma continuity, propagation direction, and speed. On synthetic observations of a CME simulation the method estimates parameters from only two viewpoints with a mean velocity error of 3.01±1.94% and propagation direction errors of 3.39±1.94° in latitude and 1.76±0.79° in longitude. It also produces a full 3D reconstruction that correctly models the three-part structure, deformed CME front, and internal plasma variations, with extra

What carries the argument

SuNeRF-CME, a Neural Radiance Field framework that performs ray-tracing for Thomson scattering while enforcing continuity, propagation direction, and speed constraints on heliospheric plasma during time-dependent optimization.

If this is right

  • The reconstruction correctly captures the three-part structure of the CME along with its deformed front and internal plasma variations from two viewpoints.
  • Additional viewpoints integrate directly and improve the modeled plasma distribution without retraining the core framework.
  • The same physical constraints enable reliable parameter recovery even for complex or time-varying plasma distributions in the simulation.
  • The approach supports advanced space weather monitoring by providing dynamic 3D models of CMEs that can be updated as new observations arrive.

Where Pith is reading between the lines

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

  • The method could be applied to real multi-spacecraft coronagraph data to test how well the constraints handle instrument noise and calibration differences absent from simulations.
  • Similar continuity and speed constraints might extend the framework to reconstruct other large-scale heliospheric features such as solar wind streams from sparse viewpoints.
  • Coupling the density reconstruction with separate magnetic field models could yield testable predictions of CME arrival times and geoeffectiveness.

Load-bearing premise

The physical constraints on continuity, propagation direction, and speed of the heliospheric plasma are sufficient to overcome limitations from the sparse number of viewpoints and allow accurate reconstruction even when the underlying plasma distribution is complex or time-varying.

What would settle it

A direct comparison of the reconstructed CME velocity, propagation angles, and internal density structure against independent multi-viewpoint observations or in-situ measurements that shows errors much larger than the reported 3 percent and few-degree levels would indicate the constraints are insufficient.

Figures

Figures reproduced from arXiv: 2509.13571 by Anna Malanushenko, Carlos Urbina-Ortega, Chia-Man Hung, Elena Provornikova, Emma Stevenson, Hala Lamdouar, Ioanna Bouri, Josh Veitch-Michaelis, Martin Sanner, Robert Jarolim, V\'it R\r{u}\v{z}i\v{c}ka.

Figure 1
Figure 1. Figure 1: Overview of the SuNeRF-CME method for tomo￾graphic reconstruction of coronal mass ejections (CMEs) us￾ing physics-informed Neural Radiance Fields. The approach leverages multi-viewpoint observations of total tB and polar￾ized pB brightness to estimate the electron density in the he￾liosphere. The tomographic reconstruction is performed via a ray-tracing approach (red): (1) Rays are traced per pixel into th… view at source ↗
Figure 2
Figure 2. Figure 2: shows sample input data from two view￾points, both in terms of total (top) and polarized (bot￾tom) brightness. From the corresponding 3D recon￾structions, we extract a longitudinal slice from the eclip￾tic plane (latitude=0◦ ; panel b) and latitudinal slice in the CME propagation direction (longitude=135◦ ; panel c). In addition, our approach intrinsically models the plasma velocity, by minimizing the cont… view at source ↗
Figure 3
Figure 3. Figure 3: Tomographic reconstruction of the full heliosphere from varying observer configurations. We compare ecliptic (top) and latitudinal slices at 135◦ longitude (bottom) for the ground truth and reconstructions using all available viewpoints, only ecliptic viewpoints, three ecliptic-plane observers, and a high-latitude configuration (polar). Observer positions are indicated by blue arrows. The results show that… view at source ↗
Figure 4
Figure 4. Figure 4: Evaluation of derived CME parameters across different observer configurations. (a) Errors in center-of-mass velocity (∆vCoM), shock front velocity (∆vFRT), latitudinal position (∆θ), longitudinal position (∆ϕ), and total CME mass (∆MCME). (b) Ecliptic slices of the reconstructed electron density for the ground truth, a three-viewpoint configuration, a halo-CME setup, two side-on viewpoints, and a far-side … view at source ↗
Figure 5
Figure 5. Figure 5: Tomographic reconstruction of a CME from three and two viewpoints. (a) Ground-truth electron density slices in the ecliptic plane and at 135◦ longitude; the blue dashed lines indicate the locations of the latitudinal slices. (b) Reconstructed slices from a three-viewpoint configuration and corresponding difference maps relative to the ground truth. (c) Same as (b), but for a two-viewpoint reconstruction. T… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of tomographic CME reconstructions with and without physics-based constraints. (a) Ecliptic slices of electron density over a 12.5-hour interval for the ground truth, the reconstruction with physics-informed losses, and the reconstruction without additional constraints. Both reconstructions are based on observations from two viewpoints, indicated by blue arrows. (b) Temporal evolution of key CME… view at source ↗
read the original abstract

Coronagraphic observations enable direct monitoring of coronal mass ejections (CMEs) through scattered light from free electrons, but determining the 3D plasma distribution from 2D imaging data is challenging due to the optically-thin plasma and the complex image formation processes. We introduce SuNeRF-CME, a framework for 3D tomographic reconstructions of the heliosphere using multi-viewpoint coronagraphic observations. The method leverages Neural Radiance Fields (NeRFs) to estimate the electron density in the heliosphere through a ray-tracing approach, while accounting for the underlying Thomson scattering of image formation. The model is optimized by iteratively fitting the time-dependent observational data. In addition, we apply physical constraints in terms of continuity, propagation direction, and speed of the heliospheric plasma to overcome limitations imposed by the sparse number of viewpoints. We utilize synthetic observations of a CME simulation to fully quantify the model's performance for different viewpoint configurations. The results demonstrate that our method can reliably estimate the CME parameters from only two viewpoints, with a mean velocity error of $3.01\pm1.94\%$ and propagation direction errors of $3.39\pm1.94^\circ$ in latitude and $1.76\pm0.79^\circ$ in longitude. We further show that our approach can achieve a full 3D reconstruction of the simulated CME from two viewpoints, where we correctly model the three-part structure, deformed CME front, and internal plasma variations. Additional viewpoints can be seamlessly integrated, directly enhancing the reconstruction of the plasma distribution in the heliosphere. This study underscores the value of physics-informed methods for reconstructing the heliospheric plasma distribution, paving the way for unraveling the dynamic 3D structure of CMEs and enabling advanced space weather monitoring.

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 introduces SuNeRF-CME, a physics-informed Neural Radiance Fields framework for 3D tomographic reconstruction of coronal mass ejections from coronagraphic observations. It models electron density via ray-tracing that accounts for Thomson scattering, optimizes the NeRF by fitting time-dependent multi-view data, and augments the loss with physical regularizers enforcing continuity, constant propagation direction, and constant speed of heliospheric plasma. Quantitative evaluation on synthetic CME simulation data shows that two viewpoints suffice to recover CME parameters with a reported mean velocity error of 3.01±1.94 % and direction errors of 3.39±1.94° (latitude) and 1.76±0.79° (longitude), while also reproducing the three-part structure, deformed front, and internal density variations.

Significance. If the central claims hold under broader testing, the work would be significant for heliospheric imaging and space-weather applications: it demonstrates that NeRFs augmented with domain-specific plasma constraints can mitigate the severe under-determination inherent in optically-thin line-of-sight integrals when only two viewpoints are available. The explicit quantitative error metrics on synthetic data and the seamless extensibility to additional viewpoints are clear strengths.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (synthetic validation): the reported velocity and direction errors are obtained exclusively on synthetic data generated from a simulation whose plasma evolution obeys the same constant-speed, constant-direction, and continuity assumptions used as regularizers. This matching of forward model and constraint set risks understating the tomographic ambiguity that would arise for real CMEs exhibiting variable speed, strong deformation, or internal flows; a load-bearing test would require at least one mismatched simulation or real-event case.
  2. [§3.2] §3.2 (physical constraints): the continuity, direction, and speed terms are introduced as weighted regularizers, yet no explicit functional form, weighting schedule, or ablation study is provided to show how these terms interact with the NeRF photometric loss to resolve the inverse problem. Without these details it is impossible to judge whether the constraints are sufficient to overcome the sparsity of two viewpoints or merely reproduce the simulation priors.
minor comments (2)
  1. [Figure captions and §4.2] Figure captions and §4.2 should explicitly state the number of synthetic viewpoints, the exact simulation code or reference, and the precise definition of the three-part structure used for visual comparison.
  2. [§2] Notation for the electron-density field and the Thomson-scattering integral should be introduced once in §2 and used consistently thereafter; several symbols appear without prior definition in the results section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their thorough review and valuable suggestions. We respond to each major comment in turn and indicate the changes we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (synthetic validation): the reported velocity and direction errors are obtained exclusively on synthetic data generated from a simulation whose plasma evolution obeys the same constant-speed, constant-direction, and continuity assumptions used as regularizers. This matching of forward model and constraint set risks understating the tomographic ambiguity that would arise for real CMEs exhibiting variable speed, strong deformation, or internal flows; a load-bearing test would require at least one mismatched simulation or real-event case.

    Authors: We acknowledge that the synthetic CME data follows the same physical assumptions encoded in the regularizers. This was a deliberate choice to enable quantitative error assessment against known ground truth while isolating the effect of viewpoint sparsity. The regularizers are implemented as soft penalties rather than hard constraints, allowing the photometric loss to drive recovery of deformed fronts and internal density variations. In the revised manuscript we will expand the discussion in §4 to explicitly address this limitation, including a qualitative assessment of expected performance under violated assumptions and a statement of planned future tests on simulations with variable speed. revision: partial

  2. Referee: [§3.2] §3.2 (physical constraints): the continuity, direction, and speed terms are introduced as weighted regularizers, yet no explicit functional form, weighting schedule, or ablation study is provided to show how these terms interact with the NeRF photometric loss to resolve the inverse problem. Without these details it is impossible to judge whether the constraints are sufficient to overcome the sparsity of two viewpoints or merely reproduce the simulation priors.

    Authors: We agree that the current description in §3.2 lacks sufficient implementation detail. In the revised version we will add the explicit mathematical expressions for each regularizer term, the numerical weighting coefficients, and the schedule by which their relative strength is increased during optimization. We will also include a new ablation experiment that quantifies reconstruction error when each term is removed individually, thereby demonstrating their contribution to resolving the under-determined inverse problem with two viewpoints. revision: yes

Circularity Check

0 steps flagged

No significant circularity; reconstruction validated on independent synthetic benchmarks with standard physical regularizers.

full rationale

The paper optimizes a NeRF model via iterative fitting to time-dependent synthetic coronagraphic observations while adding physical constraints on plasma continuity, propagation direction, and speed as regularizers to address sparse viewpoints. Performance metrics (velocity error 3.01±1.94%, direction errors ~2-3°) are computed against ground-truth quantities from the CME simulation, which serves as an external benchmark rather than a self-derived input. No equations or steps reduce by construction to tautological definitions, fitted parameters renamed as predictions, or self-citation chains; the Thomson scattering ray-tracing and optimization are standard inverse-problem machinery applied to independent simulation data. The derivation chain remains self-contained against these benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard heliophysics assumptions about image formation and plasma dynamics plus the ability of the optimization to recover structure from sparse views; no new particles or forces are introduced.

free parameters (1)
  • constraint weights for continuity, direction, and speed
    Hyperparameters balancing the physical loss terms against the data-fitting loss during iterative optimization.
axioms (2)
  • domain assumption Image formation in coronagraphs is governed by Thomson scattering from free electrons in optically thin plasma
    Invoked to justify the ray-tracing forward model in the NeRF.
  • domain assumption Heliospheric plasma obeys continuity and propagates with consistent direction and speed
    Used as regularization to compensate for limited viewpoints.

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Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    A., et al

    Amerstorfer, T., Hinterreiter, J., Reiss, M. A., et al. 2021, Space Weather, 19, e02553, doi: 10.1029/2020SW002553

    work page doi:10.1029/2020sw002553 2021

  2. [2]

    2004, Journal of Atmospheric and Solar-Terrestrial Physics, 66, 1295

    Arge, C., Luhmann, J., Odstrcil, D., Schrijver, C., & Li, Y. 2004, Journal of Atmospheric and Solar-Terrestrial Physics, 66, 1295

    work page 2004

  3. [3]

    Aschwanden, M. J. 2011, Living Reviews in Solar Physics, 8, 5, doi: 10.12942/lrsp-2011-5 Asensio Ramos, A. 2023, SoPh, 298, 135, doi: 10.1007/s11207-023-02226-2 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ...

    work page doi:10.12942/lrsp-2011-5 2011

  4. [4]

    T., Bobra, M

    Barnes, W. T., Bobra, M. G., Christe, S. D., et al. 2020, The Astrophysical Journal, 890, 68

    work page 2020

  5. [5]

    2021, Space Weather, 19, e02873, doi: 10.1029/2021SW002873

    Bauer, M., Amerstorfer, T., Hinterreiter, J., et al. 2021, Space Weather, 19, e02873, doi: 10.1029/2021SW002873

    work page doi:10.1029/2021sw002873 2021

  6. [6]

    Billings, D. E. 1966, A guide to the solar corona

    work page 1966

  7. [7]

    E., Howard, R

    Brueckner, G. E., Howard, R. A., Koomen, M. J., et al. 1995, SoPh, 162, 357, doi: 10.1007/BF00733434

    work page doi:10.1007/bf00733434 1995

  8. [8]

    C., & Seiden, J

    Cyr, O. C., & Seiden, J. A. 2004, Journal of Geophysical Research (Space Physics), 109, A03103, doi: 10.1029/2003JA010149

    work page doi:10.1029/2003ja010149 2004

  9. [9]

    Cargill, P. J. 2004, SoPh, 221, 135, doi: 10.1023/B:SOLA.0000033366.10725.a2

    work page doi:10.1023/b:sola.0000033366.10725.a2 2004

  10. [10]

    C., & Vourlidas, A

    Colaninno, R. C., & Vourlidas, A. 2009, ApJ, 698, 852, doi: 10.1088/0004-637X/698/1/852 de Koning, C. A., & Pizzo, V. J. 2011, Space Weather, 9, 03001, doi: 10.1029/2010SW000595 de Koning, C. A., Pizzo, V. J., & Biesecker, D. A. 2009, SoPh, 256, 167, doi: 10.1007/s11207-009-9344-7

    work page doi:10.1088/0004-637x/698/1/852 2009

  11. [11]

    CPEG: A Convex Predictor-corrector Entry Guidance Algorithm,

    Deforest, C., Killough, R., Gibson, S., et al. 2022, in 2022 IEEE Aerospace Conference, 1–11, doi: 10.1109/AERO53065.2022.9843340

    work page doi:10.1109/aero53065.2022.9843340 2022

  12. [12]

    E., de Koning, C

    DeForest, C. E., de Koning, C. A., & Elliott, H. A. 2017, ApJ, 850, 130, doi: 10.3847/1538-4357/aa94ca

    work page doi:10.3847/1538-4357/aa94ca 2017

  13. [13]

    E., Howard, T

    DeForest, C. E., Howard, T. A., & Tappin, S. J. 2013, ApJ, 765, 44, doi: 10.1088/0004-637X/765/1/44 D´ ıaz Baso, C. J., Asensio Ramos, A., de la Cruz Rodr´ ıguez, J., da Silva Santos, J. M., & Rouppe van der Voort, L. 2025, A&A, 693, A170, doi: 10.1051/0004-6361/202452172 16

    work page doi:10.1088/0004-637x/765/1/44 2013

  14. [14]

    R., Hudson, H

    Fletcher, L., Dennis, B. R., Hudson, H. S., et al. 2011, SSRv, 159, 19, doi: 10.1007/s11214-010-9701-8

    work page doi:10.1007/s11214-010-9701-8 2011

  15. [15]

    G., Linker, J

    Forbes, T. G., Linker, J. A., Chen, J., et al. 2006, SSRv, 123, 251, doi: 10.1007/s11214-006-9019-8

    work page doi:10.1007/s11214-006-9019-8 2006

  16. [16]

    A., & Kamalabadi, F

    Frazin, R. A., & Kamalabadi, F. 2005, ApJ, 628, 1061, doi: 10.1086/430846

    work page doi:10.1086/430846 2005

  17. [17]

    E., & Low, B

    Gibson, S. E., & Low, B. C. 1998, ApJ, 493, 460, doi: 10.1086/305107

    work page doi:10.1086/305107 1998

  18. [18]

    Howard, T. A. 2015, Journal of Space Weather and Space Climate, 5, A22, doi: 10.1051/swsc/2015024

    work page doi:10.1051/swsc/2015024 2015

  19. [19]

    A., & Tappin, S

    Howard, T. A., & Tappin, S. J. 2009, SSRv, 147, 31, doi: 10.1007/s11214-009-9542-5

    work page doi:10.1007/s11214-009-9542-5 2009

  20. [20]

    2006, Journal of Geophysical Research (Space Physics), 111, A04S91, doi: 10.1029/2004JA010942

    Webb, D. 2006, Journal of Geophysical Research (Space Physics), 111, A04S91, doi: 10.1029/2004JA010942

    work page doi:10.1029/2004ja010942 2006

  21. [21]

    V., Hick, P

    Jackson, B. V., Hick, P. P., Buffington, A., et al. 2011, Journal of Atmospheric and Solar-Terrestrial Physics, 73, 1214, doi: 10.1016/j.jastp.2010.10.007

    work page doi:10.1016/j.jastp.2010.10.007 2011

  22. [22]

    E., Tremblay , B., Centeno , R., and Rempel , M

    Rempel, M. 2025, ApJL, 985, L7, doi: 10.48550/arXiv.2502.13924

    work page doi:10.48550/arxiv.2502.13924 2025

  23. [23]

    2023, Nature Astronomy, doi: 10.1038/s41550-023-02030-9

    Podladchikova, T. 2023, Nature Astronomy, doi: 10.1038/s41550-023-02030-9

    work page doi:10.1038/s41550-023-02030-9 2023

  24. [24]

    2024a, ApJL, 963, L21, doi: 10.3847/2041-8213/ad2450

    Jarolim, R., Tremblay, B., Rempel, M., et al. 2024a, ApJL, 963, L21, doi: 10.3847/2041-8213/ad2450

    work page doi:10.3847/2041-8213/ad2450 2041

  25. [25]

    2024b, ApJL, 961, L31, doi: 10.3847/2041-8213/ad12d2

    Jarolim, R., Tremblay, B., Mu˜ noz-Jaramillo, A., et al. 2024b, ApJL, 961, L31, doi: 10.3847/2041-8213/ad12d2

    work page doi:10.3847/2041-8213/ad12d2 2041

  26. [26]

    L., Kucera, T

    Kaiser, M. L., Kucera, T. A., Davila, J. M., et al. 2008, SSRv, 136, 5, doi: 10.1007/s11214-007-9277-0

    work page doi:10.1007/s11214-007-9277-0 2008

  27. [27]

    Keller, C. U. 2025, ApJ, 989, 92, doi: 10.3847/1538-4357/add6a9

    work page doi:10.3847/1538-4357/add6a9 2025

  28. [28]

    G., & Luntama, J

    Kraft, S., Puschmann, K. G., & Luntama, J. P. 2017, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10562, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 105620F, doi: 10.1117/12.2296100

    work page doi:10.1117/12.2296100 2017

  29. [29]

    P., Tancik, M., et al

    Mildenhall, B., Srinivasan, P. P., Tancik, M., et al. 2021, Communications of the ACM, 65, 99 M¨ ostl, C., Rollett, T., Frahm, R. A., et al. 2015, Nature Communications, 6, 7135, doi: 10.1038/ncomms8135

    work page doi:10.1038/ncomms8135 2021

  30. [30]

    J., Christe, S., Freij, N., et al

    Mumford, S. J., Christe, S., Freij, N., et al. 2020, SunPy, v1.1.4, Zenodo, doi: 10.5281/zenodo.3871057

    work page doi:10.5281/zenodo.3871057 2020

  31. [31]

    2003, Advances in Space Research, 32, 497, doi: 10.1016/S0273-1177(03)00332-6

    Odstrcil, D. 2003, Advances in Space Research, 32, 497, doi: 10.1016/S0273-1177(03)00332-6

    work page doi:10.1016/s0273-1177(03)00332-6 2003

  32. [32]

    2019, in Advances in Neural Information Processing Systems 32, ed

    Paszke, A., Gross, S., Massa, F., et al. 2019, in Advances in Neural Information Processing Systems 32, ed. H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alch´ e-Buc, E. Fox, & R. Garnett (Curran

    work page 2019

  33. [33]

    2018, Journal of Space Weather and Space Climate, 8, A35, doi: 10.1051/swsc/2018020

    Pomoell, J., & Poedts, S. 2018, Journal of Space Weather and Space Climate, 8, A35, doi: 10.1051/swsc/2018020

    work page doi:10.1051/swsc/2018020 2018

  34. [34]

    G., Vourlidas, A., et al

    Provornikova, E., Merkin, V. G., Vourlidas, A., et al. 2024, ApJ, 977, 106, doi: 10.3847/1538-4357/ad83b1

    work page doi:10.3847/1538-4357/ad83b1 2024

  35. [35]

    Raissi, M., Perdikaris, P., & Karniadakis, G. E. 2019, Journal of Computational Physics, 378, 686, doi: 10.1016/j.jcp.2018.10.045

    work page doi:10.1016/j.jcp.2018.10.045 2019

  36. [36]

    2020, Advances in Neural Information Processing Systems, 33, 7462

    Wetzstein, G. 2020, Advances in Neural Information Processing Systems, 33, 7462

    work page 2020

  37. [37]

    2016, ApJ, 830, 58, doi: 10.3847/0004-637X/830/2/58

    Susino, R., & Bemporad, A. 2016, ApJ, 830, 58, doi: 10.3847/0004-637X/830/2/58

    work page doi:10.3847/0004-637x/830/2/58 2016

  38. [38]

    2021, Living Reviews in Solar Physics, 18, 4, doi: 10.1007/s41116-021-00030-3

    Temmer, M. 2021, Living Reviews in Solar Physics, 18, 4, doi: 10.1007/s41116-021-00030-3

    work page doi:10.1007/s41116-021-00030-3 2021

  39. [39]

    Temmer, M., Preiss, S., & Veronig, A. M. 2009, SoPh, 256, 183, doi: 10.1007/s11207-009-9336-7

    work page doi:10.1007/s11207-009-9336-7 2009

  40. [40]

    G., et al

    Temmer, M., Scolini, C., Richardson, I. G., et al. 2023, arXiv e-prints, arXiv:2308.04851, doi: 10.48550/arXiv.2308.04851

    work page doi:10.48550/arxiv.2308.04851 2023

  41. [41]

    2011, ApJS, 194, 33, doi: 10.1088/0067-0049/194/2/33

    Thernisien, A. 2011, ApJS, 194, 33, doi: 10.1088/0067-0049/194/2/33

    work page doi:10.1088/0067-0049/194/2/33 2011

  42. [42]

    Thernisien, A. F. R., Howard, R. A., & Vourlidas, A. 2006, ApJ, 652, 763, doi: 10.1086/508254 V´ asquez, A. M., Frazin, R. A., Hayashi, K., et al. 2008, ApJ, 682, 1328, doi: 10.1086/589682

    work page doi:10.1086/508254 2006

  43. [43]

    L., Kay, C., et al

    Verbeke, C., Mays, M. L., Kay, C., et al. 2023, Advances in Space Research, 72, 5243, doi: 10.1016/j.asr.2022.08.056

    work page doi:10.1016/j.asr.2022.08.056 2023

  44. [44]

    Vourlidas, A., & Howard, R. A. 2006, ApJ, 642, 1216, doi: 10.1086/501122 Vrˇ snak, B., Sudar, D., Ruˇ zdjak, D., &ˇZic, T. 2007, A&A, 469, 339, doi: 10.1051/0004-6361:20077175 Vrˇ snak, B.,ˇZic, T., Vrbanec, D., et al. 2013, SoPh, 285, 295, doi: 10.1007/s11207-012-0035-4

    work page doi:10.1086/501122 2006

  45. [45]

    F., & Howard, T

    Webb, D. F., & Howard, T. A. 2012, Living Reviews in Solar Physics, 9, 1

    work page 2012

  46. [46]

    K., & Solanki, S

    Wiegelmann, T., Thalmann, J. K., & Solanki, S. K. 2014, A&A Rv, 22, 78, doi: 10.1007/s00159-014-0078-7

    work page doi:10.1007/s00159-014-0078-7 2014