SPIN4D: Spectropolarimetric Inversion in 4-Dimensions

Xudong Sun¹, Kai Yang¹, Jiayi Liu¹, Yannik Glaser¹, Lucas Tarr², Matthias Rempel³, Sarah Jaeggli², Tom Schad², S. C. Dodds¹, Peter Sadowski¹,

¹University of Hawaii Manoa ²National Solar Observatory ³High Altitude Observatory

Paper Supplementary

GitHub（2）

Data

arXiv（2）

Continuum emission at 500 nm from the SSD + 200 G case.

LOS Velocity of optical layer tau=1, of SSD + 200 G case.

LOS Magnetic Field of optical layer tau=1, of SSD + 200 G case.

Abstract

The National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multi-line spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our "SPIn4D" project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere based on DKIST observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the 4D MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes-profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Four cases with different mean vertical magnetic fields have been conducted; each case covers six solar-hours, totaling 64 TB in data volume. The simulation domain covers 25x25x8 Mm with 16x16x12 km spatial resolution, extending from the upper convection zone up to the temperature minimum. The outputs are generated at a 40 s cadence. We forward model the Stokes profile of two sets of Fe₁ lines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available.

Illustration of the SPIn4D model workflow. Our model, trained on an extensive library of MHD simulations, processes temporal sequences of Stokes profiles to exploit spatial/temporal coherence. It aims to estimate higher-level 4D parameters directly. On the left, we depict the time series of observed Stokes profiles data cube (I, Q, U, V) as the input for the DL model, predicting the photospheric time-varying 3D physical variables. The process on the right end indicates additional step for deriving other parameters such as vector velocity and Poynting flux. The dashed green box outlines the dataset generation and model training phases.

Example synthesized spectropolarimetric data computed for a single snapshot of the Case 5 MHD simulation at t=5.6 hrs, 3D data cubes show a subset of the output for both spectral line pairs and both forward modeling codes. The red box in panel (a) marks the source region of the subset in the continuum image. Panel (b) shows the continuum image of the zoom-in subset.

Poster

Paper II Abstract

Inferring the three-dimensional (3D) solar atmospheric structures from observations is a critical task for advancing our understanding of the magnetic fields and electric currents that drive solar activity. In this work, we introduce a novel, Physics-Informed Machine Learning method to reconstruct the 3D structure of the lower solar atmosphere based on the output of optical depth sampled spectropolarimetric inversions, wherein both the fully disambiguated vector magnetic fields and the geometric height associated with each optical depth are returned simultaneously. Traditional techniques typically resolve the 180-degree azimuthal ambiguity assuming a single layer, either ignoring the intrinsic non-planar physical geometry of constant optical-depth surfaces (e.g., the Wilson depression in sunspots), or correcting the effect as a post-processing step. In contrast, our approach simultaneously maps the optical depths to physical heights, and enforces the divergence-free condition for magnetic fields fully in 3D. Tests on magnetohydrodynamic simulations of quiet Sun, plage, and a sunspot demonstrate that our method reliably recovers the horizontal magnetic field orientation in locations with appreciable magnetic field strength. By coupling the resolutions of the azimuthal ambiguity and the geometric heights problems, we achieve a self-consistent reconstruction of the 3D vector magnetic fields and, by extension, the electric current density and Lorentz force. This physics-constrained, label-free training paradigm is a generalizable, physics-anchored framework that extends across solar magnetic environments while improving the understanding of various solar puzzles

Panel (a) shows the flowchart for training the model. The inputs are the 3D magnetic vector fields with azimuthal ambiguity, and an initial guess of the geometric heights associated with each optical-depth layer. The UNet3DB network predicts 3D vector magnetic field, and the UNet3DZ network provides the geometric heights. They are combined to compute a custom loss function with physics law encoded. Panel (b) shows the post-processing step that assembles the outputs from the neural networks (prediction) and the original input magnetic fields into the final output. Panel (c) shows an example of the 3D data, split with overlaps between nearby subfields. These individual subfields are used as the input for training. Panel (d) presents the UNet3D structure

Results for geometric heights for the Sunspot. Panels (a) and (b) present the true and predicted height values for the log10τ = −1 layer. Panels (c)–(f) show vertical cuts across the domain, along the dashed lines in (a). The colors represent the Bz distribution and span the optical depths from log10 τ = 0 to −3.1. The five dashed black curves indicate log10τ values of −0.5, −1, −1.5, −2.0, and −2.5 from bottom to top, respectively. Panels (c) and (e) display ground truth at vertical cuts X = 25.2 Mm and Y = 16.3 Mm, respectively, while (d) and (f) show the corresponding HDD results.

HDD Predicted 3D Vector Electric Current

2D histogram comparing the ground truth and the HDD output electric current density. Columns from left to right show the x-, y-, z-components, and absolute current magnitude, while rows from top to bottom represent results for the quiet Sun, plage region, and sunspot, with Pearson correlation coefficients specified for each case. Red and blue dashed lines denote the identity and the best-fit linear relation, respectively.

AAS 246 iPoster

BibTeX

@article{Yang_2024,
doi = {10.3847/1538-4357/ad865b},
url = {https://dx.doi.org/10.3847/1538-4357/ad865b},
year = {2024},
month = {nov},
publisher = {The American Astronomical Society},
volume = {976},
number = {2},
pages = {204},
author = {Kai E. Yang and Lucas A. Tarr and Matthias Rempel and S. Curt Dodds and Sarah A. Jaeggli and Peter Sadowski and Thomas A. Schad and Ian Cunnyngham and Jiayi Liu and Yannik Glaser and Xudong Sun},
title = {Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D). I. Overview, Magnetohydrodynamic Modeling, and Stokes Profile Synthesis},
journal = {The Astrophysical Journal},
abstract = {The National Science Foundation’s Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multiline spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our “SPIn4D” project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere from DKIST spectropolarimetric observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the four-dimensional MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Six cases with different mean magnetic fields have been explored; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least 25 × 25 × 8 Mm, with 16 × 16 × 12 km spatial resolution, extending from the upper convection zone up to the temperature minimum region. The outputs are stored at a 40 s cadence. We forward model the Stokes profile of two sets of Fe i lines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available, with 13.7 TB in the initial release.}
}

@article{Yang_2025,
       author = {{Yang}, Kai E. and {Sun}, Xudong and {Tarr}, Lucas A. and {Liu}, Jiayi and {Sadowski}, Peter and {Dodds}, S. Curt and {Rempel}, Matthias and {Jaeggli}, Sarah A. and {Schad}, Thomas A. and {Cunnyngham}, Ian and {Glaser}, Yannik and {Wolniewicz}, Linnea},
        title = "{Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction}",
      journal = {arXiv e-prints},
     keywords = {Solar and Stellar Astrophysics},
         year = 2025,
        month = oct,
          eid = {arXiv:2510.09967},
        pages = {arXiv:2510.09967},
archivePrefix = {arXiv},
       eprint = {2510.09967},
 primaryClass = {astro-ph.SR},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2025arXiv251009967Y},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}