Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D). II. A Physics-informed Machine Learning Method for 3D Solar Photosphere Reconstruction Article Swipe
Kai Yang
,
Xudong Sun
,
Lucas A. Tarr
,
Jiayi 嘉奕 Liu 刘
,
Peter Sadowski
,
S. Curt Dodds
,
M. Rempel
,
Sarah A. Jaeggli
,
Thomas A. Schad
,
Ian Cunnyngham
,
Yannik Glaser
,
Linnea M. Wolniewicz
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3847/1538-4357/ae12ef
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3847/1538-4357/ae12ef
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° azimuthal ambiguity assuming a single layer, either ignoring the intrinsic nonplanar physical geometry of constant optical-depth surfaces (e.g., the Wilson depression in sunspots) or correcting the effect as a postprocessing 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 height 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.
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- https://doi.org/10.3847/1538-4357/ae12ef
- OA Status
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- References
- 138
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https://openalex.org/W4417227315Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3847/1538-4357/ae12efDigital Object Identifier
- Title
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Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D). II. A Physics-informed Machine Learning Method for 3D Solar Photosphere ReconstructionWork title
- Type
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articleOpenAlex work type
- Publication year
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2025Year of publication
- Publication date
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2025-12-11Full publication date if available
- Authors
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Kai Yang, Xudong Sun, Lucas A. Tarr, Jiayi 嘉奕 Liu 刘, Peter Sadowski, S. Curt Dodds, M. Rempel, Sarah A. Jaeggli, Thomas A. Schad, Ian Cunnyngham, Yannik Glaser, Linnea M. WolniewiczList of authors in order
- Landing page
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https://doi.org/10.3847/1538-4357/ae12efPublisher landing page
- Open access
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.3847/1538-4357/ae12efDirect OA link when available
- Cited by
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0Total citation count in OpenAlex
- References (count)
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138Number of works referenced by this work
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| referenced_works | https://openalex.org/W3212037858, https://openalex.org/W4384201335, https://openalex.org/W2931086943, https://openalex.org/W2060189022, https://openalex.org/W2001948610, https://openalex.org/W3009258747, https://openalex.org/W2886509784, https://openalex.org/W2791540710, https://openalex.org/W2093586470, https://openalex.org/W4309188641, https://openalex.org/W2982600159, https://openalex.org/W3119808386, https://openalex.org/W4393852664, https://openalex.org/W2036821030, https://openalex.org/W1975032679, https://openalex.org/W4392737505, https://openalex.org/W2464708700, https://openalex.org/W4225986486, https://openalex.org/W2895921450, https://openalex.org/W4212865033, https://openalex.org/W2966895765, https://openalex.org/W2623792526, https://openalex.org/W4405103083, https://openalex.org/W2760972773, https://openalex.org/W2073863938, https://openalex.org/W4399727244, https://openalex.org/W2898329134, https://openalex.org/W2009618977, https://openalex.org/W1990324383, https://openalex.org/W1997386188, https://openalex.org/W4316661496, https://openalex.org/W3035965352, https://openalex.org/W3168386838, https://openalex.org/W3197319085, https://openalex.org/W3147526180, https://openalex.org/W1999016464, https://openalex.org/W2011301426, https://openalex.org/W3014974815, https://openalex.org/W2963073614, https://openalex.org/W4306885021, https://openalex.org/W2343822746, https://openalex.org/W4384132443, https://openalex.org/W4392099970, https://openalex.org/W4404373835, https://openalex.org/W2396787625, https://openalex.org/W2899823928, https://openalex.org/W3163993681, https://openalex.org/W3133294546, https://openalex.org/W2127460773, https://openalex.org/W4408824493, https://openalex.org/W4408132623, https://openalex.org/W4410548070, https://openalex.org/W3046832359, https://openalex.org/W2046513109, https://openalex.org/W2074648780, https://openalex.org/W2028278268, https://openalex.org/W1981038215, https://openalex.org/W2136306514, https://openalex.org/W1608169846, https://openalex.org/W2898212993, https://openalex.org/W1994075064, https://openalex.org/W2531003486, https://openalex.org/W1988318154, https://openalex.org/W2581773135, https://openalex.org/W2088758899, https://openalex.org/W2746431609, https://openalex.org/W2888024978, https://openalex.org/W3005745303, https://openalex.org/W3015479728, https://openalex.org/W3014009018, https://openalex.org/W2000460954, https://openalex.org/W2998366519, https://openalex.org/W4293763455, https://openalex.org/W2139191598, https://openalex.org/W1999951101, https://openalex.org/W1997076712, https://openalex.org/W1969843154, https://openalex.org/W2166632814, https://openalex.org/W2949159435, https://openalex.org/W1579563054, https://openalex.org/W4288079687, https://openalex.org/W4200573659, https://openalex.org/W2535388113, https://openalex.org/W4200134568, https://openalex.org/W2969795607, https://openalex.org/W2094483427, https://openalex.org/W2211637447, https://openalex.org/W4229443067, https://openalex.org/W3118502600, https://openalex.org/W2023546879, https://openalex.org/W2006760396, https://openalex.org/W4286586238, https://openalex.org/W2899283552, https://openalex.org/W2074599876, https://openalex.org/W1976882616, https://openalex.org/W2554273622, https://openalex.org/W3106791448, https://openalex.org/W4393991582, https://openalex.org/W1901129140, https://openalex.org/W1519784798, https://openalex.org/W4210401871, https://openalex.org/W1498436455, https://openalex.org/W2111078819, https://openalex.org/W2749028154, https://openalex.org/W2035485256, https://openalex.org/W1973960549, https://openalex.org/W2923172177, https://openalex.org/W3110567649, https://openalex.org/W2593715272, https://openalex.org/W2015857279, https://openalex.org/W2040960936, https://openalex.org/W2112866003, https://openalex.org/W4385409742, https://openalex.org/W4207000799, https://openalex.org/W2032894621, https://openalex.org/W3003257820, https://openalex.org/W4229036698, https://openalex.org/W2113753244, https://openalex.org/W190188485, https://openalex.org/W2149975687, https://openalex.org/W4236013985, https://openalex.org/W2084043060, https://openalex.org/W2106202136, https://openalex.org/W2886500195, https://openalex.org/W2144926424, https://openalex.org/W4206491814, https://openalex.org/W4237129014, https://openalex.org/W3046117255, https://openalex.org/W4400340432, https://openalex.org/W2779883228, https://openalex.org/W7083000387, https://openalex.org/W4404701120, https://openalex.org/W1849277567, https://openalex.org/W4224272812, https://openalex.org/W4392646515, https://openalex.org/W2887876507, https://openalex.org/W3015407441, https://openalex.org/W4387449199 |
| referenced_works_count | 138 |
| abstract_inverted_index.a | 11, 33, 86, 111, 146, 180, 205 |
| abstract_inverted_index.3D | 42, 185 |
| abstract_inverted_index.By | 165 |
| abstract_inverted_index.In | 28, 114 |
| abstract_inverted_index.as | 110 |
| abstract_inverted_index.by | 190 |
| abstract_inverted_index.in | 104, 135, 158 |
| abstract_inverted_index.is | 10, 204 |
| abstract_inverted_index.of | 18, 44, 53, 96, 141, 169, 183, 219 |
| abstract_inverted_index.on | 50, 138 |
| abstract_inverted_index.or | 106 |
| abstract_inverted_index.to | 39, 123 |
| abstract_inverted_index.we | 31, 178 |
| abstract_inverted_index.3D. | 136 |
| abstract_inverted_index.and | 21, 65, 126, 145, 173, 196 |
| abstract_inverted_index.are | 74 |
| abstract_inverted_index.for | 14, 131 |
| abstract_inverted_index.our | 16, 116, 150 |
| abstract_inverted_index.the | 2, 19, 41, 45, 51, 59, 66, 81, 91, 101, 108, 120, 128, 154, 167, 170, 174, 184, 192, 217 |
| abstract_inverted_index.(3D) | 4 |
| abstract_inverted_index.Sun, | 143 |
| abstract_inverted_index.This | 199 |
| abstract_inverted_index.and, | 189 |
| abstract_inverted_index.both | 58 |
| abstract_inverted_index.each | 71 |
| abstract_inverted_index.from | 8 |
| abstract_inverted_index.maps | 119 |
| abstract_inverted_index.task | 13 |
| abstract_inverted_index.that | 24, 149, 209 |
| abstract_inverted_index.this | 29 |
| abstract_inverted_index.with | 70, 160 |
| abstract_inverted_index.180° | 82 |
| abstract_inverted_index.Tests | 137 |
| abstract_inverted_index.based | 49 |
| abstract_inverted_index.depth | 73 |
| abstract_inverted_index.drive | 25 |
| abstract_inverted_index.field | 163 |
| abstract_inverted_index.fully | 60, 134 |
| abstract_inverted_index.lower | 46 |
| abstract_inverted_index.quiet | 142 |
| abstract_inverted_index.solar | 5, 26, 47, 212, 221 |
| abstract_inverted_index.step. | 113 |
| abstract_inverted_index.while | 215 |
| abstract_inverted_index.work, | 30 |
| abstract_inverted_index.(e.g., | 100 |
| abstract_inverted_index.Wilson | 102 |
| abstract_inverted_index.across | 211 |
| abstract_inverted_index.depths | 122 |
| abstract_inverted_index.effect | 109 |
| abstract_inverted_index.either | 89 |
| abstract_inverted_index.fields | 64, 133, 188 |
| abstract_inverted_index.force. | 198 |
| abstract_inverted_index.height | 68, 176 |
| abstract_inverted_index.layer, | 88 |
| abstract_inverted_index.method | 38, 151 |
| abstract_inverted_index.novel, | 34 |
| abstract_inverted_index.output | 52 |
| abstract_inverted_index.plage, | 144 |
| abstract_inverted_index.single | 87 |
| abstract_inverted_index.vector | 62, 186 |
| abstract_inverted_index.Lorentz | 197 |
| abstract_inverted_index.achieve | 179 |
| abstract_inverted_index.current | 194 |
| abstract_inverted_index.density | 195 |
| abstract_inverted_index.extends | 210 |
| abstract_inverted_index.machine | 36 |
| abstract_inverted_index.optical | 72, 121 |
| abstract_inverted_index.resolve | 80 |
| abstract_inverted_index.sunspot | 147 |
| abstract_inverted_index.various | 220 |
| abstract_inverted_index.wherein | 57 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.approach | 117 |
| abstract_inverted_index.assuming | 85 |
| abstract_inverted_index.constant | 97 |
| abstract_inverted_index.coupling | 166 |
| abstract_inverted_index.critical | 12 |
| abstract_inverted_index.currents | 23 |
| abstract_inverted_index.electric | 22, 193 |
| abstract_inverted_index.enforces | 127 |
| abstract_inverted_index.geometry | 95 |
| abstract_inverted_index.heights, | 125 |
| abstract_inverted_index.ignoring | 90 |
| abstract_inverted_index.learning | 37 |
| abstract_inverted_index.magnetic | 63, 132, 162, 187, 213 |
| abstract_inverted_index.paradigm | 203 |
| abstract_inverted_index.physical | 94, 124 |
| abstract_inverted_index.puzzles. | 222 |
| abstract_inverted_index.recovers | 153 |
| abstract_inverted_index.reliably | 152 |
| abstract_inverted_index.returned | 75 |
| abstract_inverted_index.surfaces | 99 |
| abstract_inverted_index.training | 202 |
| abstract_inverted_index.Inferring | 1 |
| abstract_inverted_index.activity. | 27 |
| abstract_inverted_index.advancing | 15 |
| abstract_inverted_index.ambiguity | 84, 172 |
| abstract_inverted_index.azimuthal | 83, 171 |
| abstract_inverted_index.condition | 130 |
| abstract_inverted_index.contrast, | 115 |
| abstract_inverted_index.framework | 208 |
| abstract_inverted_index.geometric | 67, 175 |
| abstract_inverted_index.improving | 216 |
| abstract_inverted_index.intrinsic | 92 |
| abstract_inverted_index.introduce | 32 |
| abstract_inverted_index.locations | 159 |
| abstract_inverted_index.nonplanar | 93 |
| abstract_inverted_index.problems, | 177 |
| abstract_inverted_index.strength. | 164 |
| abstract_inverted_index.structure | 43 |
| abstract_inverted_index.sunspots) | 105 |
| abstract_inverted_index.typically | 79 |
| abstract_inverted_index.associated | 69 |
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| abstract_inverted_index.correcting | 107 |
| abstract_inverted_index.depression | 103 |
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| abstract_inverted_index.horizontal | 155 |
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| abstract_inverted_index.Traditional | 77 |
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| abstract_inverted_index.inversions, | 56 |
| abstract_inverted_index.orientation | 157 |
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| abstract_inverted_index.magnetic-field | 156 |
| abstract_inverted_index.postprocessing | 112 |
| abstract_inverted_index.reconstruction | 182 |
| abstract_inverted_index.simultaneously | 118 |
| abstract_inverted_index.divergence-free | 129 |
| abstract_inverted_index.magnetic-fields | 20 |
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| abstract_inverted_index.simultaneously. | 76 |
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| abstract_inverted_index.physics-informed | 35 |
| abstract_inverted_index.three-dimensional | 3 |
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| abstract_inverted_index.spectropolarimetric | 55 |
| abstract_inverted_index.physics-constrained, | 200 |
| abstract_inverted_index.optical-depth-sampled | 54 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5044362811, https://openalex.org/A5046732648, https://openalex.org/A5036167083, https://openalex.org/A5052428131, https://openalex.org/A5014750155, https://openalex.org/A5051354155, https://openalex.org/A5083550114, https://openalex.org/A5078271069, https://openalex.org/A5020101263 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 12 |
| corresponding_institution_ids | https://openalex.org/I107766831, https://openalex.org/I115194318, https://openalex.org/I117965899, https://openalex.org/I4210088762 |
| citation_normalized_percentile |