AION: Physics-informed machine learning advances forecasting of high-dimensional ionospheric spatiotemporal states

Jiayu Ma; Haiyang Fu; Yuhong Liu; Chaoshi Shang; Yeying Dai; Yaqiu Jin

doi:10.59717/j.xinn-inform.2026.100037

The Innovation Informatics > 2026 Vol. 2 > No. 2 > 100037

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AION: Physics-informed machine learning advances forecasting of high-dimensional ionospheric spatiotemporal states

1.
Key Laboratory for Information Science of Electromagnetic Waves (MoE), School of Information Science and Engineering, Fudan University, Shanghai 200433, China
2.
College of Future Information Technology, Fudan University, Shanghai 200433, China
3.
These authors contributed equally

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Corresponding author: haiyang_fu@fudan.edu.cn
Received Date: October 08, 2025

Accepted Date: April 14, 2026

Published Online: April 16, 2026

The Innovation Informatics 2(2), https://doi.org/10.59717/j.xinn-inform.2026.100037 | Cite this article

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PUBLIC SUMMARY

PUBLIC SUMMARY
1. We propose AION, an innovation-informatics framework uniting data and physics for ionosphere modeling.
  
  Built on deep operator network (DeepONet), it learns mappings between drivers and ionospheric states.
  
  A pretrained closure model encodes plasma transport and heating knowledge within the system.
  
  This enables electron temperature equation to be embedded directly into the assimilation process.
  
  AION achieves 54.5% error reduction versus International Reference Ionosphere, benefiting satellite safety.

ABSTRACT

ABSTRACT

Modeling the Earth’s ionosphere (50–5000 km) remains a fundamental challenge due to sparse and heterogeneous observations and incomplete physical representations of plasma energy transfer. Existing empirical and physics-based approaches lack a unified mechanism to integrate data-driven learning with first-principles knowledge. We present AION, an innovation-informatics–driven framework that establishes a unified representation of observational data, physical knowledge, and system dynamics for ionospheric modeling. Built upon the deep operator network (DeepONet) architecture, AION learns functional mappings between external drivers and ionospheric states while enforcing physical consistency through differentiable governing equations. A pretrained closure model serves as an explicit representation of plasma transport and heating knowledge, enabling the electron temperature equation to be embedded directly within the assimilation process across varying solar conditions. Across diverse solar activity regimes, AION achieves 24-h electron-temperature forecast errors of 387–413 K, corresponding to a 54.5% improvement over the International Reference Ionosphere, together with a 38.2% enhancement in electron-density prediction. The framework efficiently generates full four-dimensional ionospheric states for complex geometries, demonstrating a scalable and transferable informatics paradigm for data–physics integrated intelligent modeling of complex space environments, with implications for satellite communications, navigation, and spacecraft safety.
- Ionospheric forecasting /
- Physics-informed deep learning /
- Multi-source data fusion /
- Electron density/temperature /
- Pretrained closure model.

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REFERENCES

[1]	Minnis C.M. (1958). Solar activity and the ionosphere. Nature 181:543−544. DOI:10.1038/181543a0 View in Article CrossRef Google Scholar
[2]	Markson R. (1978). Solar modulation of atmospheric electrification and possible implications for the Sun–weather relationship. Nature 273:103−109. DOI:10.1038/273103a0 View in Article CrossRef Google Scholar
[3]	Minnis C. (1954). The ionosphere during the solar eclipse of February 25, 1952. Nature 174:1137−1138. DOI:0.1038/1741137a0. DOI:10.1038/1741137a0 View in Article CrossRef Google Scholar
[4]	Cole K. (1976). Physical argument and hypothesis for Sun–weather relationships. Nature 260:229−230. DOI:10.1038/260229a0 View in Article CrossRef Google Scholar
[5]	Lotko W., Smith R.H., Zhang B., et al. (2014). Ionospheric control of magnetotail reconnection. Science 345:184−187. DOI:10.1126/science.1252907 View in Article CrossRef Google Scholar
[6]	Kelly M.C. (2009). The Earth's ionosphere: Plasma physics and electrodynamics, Second Edition. Academic Press. DOI:10.1016/C2009-0-01818-9 View in Article Google Scholar
[7]	Munro G.H. (1961). Possible solar flare effects in the F region of the ionosphere. Nature 192:347−347. DOI:10.1038/192347a0 View in Article CrossRef Google Scholar
[8]	Kitchen F.A. and Joy W.R.R. (1958). Some effects of the fine structure of the ionosphere on transmissions received from the Russian Earth satellite 1958δ. Nature 181:1759−1761. DOI:10.1038/1811759a0 View in Article CrossRef Google Scholar
[9]	Baker D.N. J.S. (2002). How to cope with space weather. Science 297:1486−1487. DOI:10.1126/science.1074956 View in Article CrossRef Google Scholar
[10]	Huba J.D., Joyce G. and Fedder J.A. (2000). SAMI2 is another model of the ionosphere (SAMI2): A new low-latitude ionosphere model. J. Geophys. Res. Space Phys. 105:23035−23053. DOI:10.1029/2000ja000035 View in Article CrossRef Google Scholar
[11]	Huba J.D., Joyce G. and Krall J.J.G.R.L. (2008). Three-dimensional equatorial spread F modeling. Geophys. Res. Lett. 35:L10102. DOI:10.1029/2008gl033509 View in Article CrossRef Google Scholar
[12]	Ridley A.J., Deng Y. and Tóth G. (2006). The global ionosphere-thermosphere model. J. Atmos. Sol.-Terr. Phys. 68:839−864. DOI:10.1016/j.jastp.2006.01.008 View in Article CrossRef Google Scholar
[13]	Roble R.G., Ridley E.C., Richmond A.D., et al. (2012). A coupled thermosphere/ionosphere general circulation model. Geophys. Res. Lett. 15:1325−1328. DOI:10.1029/GL015i012p01325 View in Article CrossRef Google Scholar
[14]	Wang W., Killeen T.L., Burns A.G., et al. (1999). A high-resolution, three-dimensional, time dependent, nested grid model of the coupled thermosphere–ionosphere. J. Atmos. Sol.-Terr. Phys. 61:385−397. DOI:10.1016/S1364-6826(98)00079-0 View in Article CrossRef Google Scholar
[15]	Bilitza D. (2018). IRI the international standard for the ionosphere. Adv. Radio Sci. 16:1−11. DOI:10.5194/ars-16-1-2018 View in Article CrossRef Google Scholar
[16]	Nava B., Coïsson P. and Radicella S.M. (2008). A new version of the NeQuick ionosphere electron density model. J. Atmos. Sol.-Terr. Phys. 70:1856−1862. DOI:10.1016/j.jastp.2008.01.015 View in Article CrossRef Google Scholar
[17]	He J., Yue X., Wang W., et al. (2019). EnKF ionosphere and thermosphere data assimilation algorithm through a sparse matrix method. J. Geophys. Res. Space Phys. 124:7356−7365. DOI:10.1029/2019JA026554 View in Article CrossRef Google Scholar
[18]	Scherliess L., Schunk R.W., Sojka J.J., et al. (2006). Utah State University global assimilation of ionospheric measurements Gauss-Markov Kalman filter model of the ionosphere: model description and validation. J. Geophys. Res. Space Phys. 111:A11S11. DOI:10.1029/2006JA011712 View in Article CrossRef Google Scholar
[19]	Yue X., Wan W., Ning B., et al. (2022). An active phased array radar in China. Nature Astronomy 6:619−619. DOI:10.1038/s41550-022-01684-1 View in Article CrossRef Google Scholar
[20]	Wang C., Xu J., Chen Z., et al. (2024). China's ground‐based space environment monitoring network—Chinese Meridian Project (CMP). Space Weather 22:e2024SW003972. DOI:10.1029/2024SW003972 View in Article CrossRef Google Scholar
[21]	Bain H.M., Steenburgh R.A., Onsager T.G., et al. (2021). A summary of National Oceanic and Atmospheric Administration Space Weather Prediction Center proton event forecast performance and skill. Space Weather 19:e2020SW002670. DOI:10.1029/2020SW002670 View in Article CrossRef Google Scholar
[22]	Smith J., Kast A., Geraschenko A., et al. (2024). Mapping the ionosphere with millions of phones. Nature 635:365−369. DOI:10.1038/s41586-024-08520-8 View in Article CrossRef Google Scholar
[23]	Vance T.C., Huang T. and Butler K.A. (2024). Big data in Earth science: Emerging practice and promise. Science 383:1193−1193. DOI:10.1126/science.adh9607 View in Article CrossRef Google Scholar
[24]	Yuval J. and O'Gorman P.A. (2020). Stable machine-learning parameterization of subgrid processes for climate modeling at a range of resolutions. Nat. Commun. 11:3295. DOI:10.1038/s41467-020-17142-3 View in Article CrossRef Google Scholar
[25]	Camps-Valls G., Fernández-Torres M.-A., Cohrs K.H., et al. (2025). Artificial intelligence for modeling and understanding extreme weather and climate events. Nat. Commun. 16:1919. DOI:10.1038/s41467-025-56573-8 View in Article CrossRef Google Scholar
[26]	Dax M., Green S.R., Gair J., et al. (2025). Real-time inference for binary neutron star mergers using machine learning. Nature 639:49−53. DOI:10.1038/s41586-025-08593-z View in Article CrossRef Google Scholar
[27]	Degrave J., Felici F., Buchli J., et al. (2022). Magnetic control of tokamak plasmas through deep reinforcement learning. Nature 602:414−419. DOI:10.1038/s41586-021-04301-9 View in Article CrossRef Google Scholar
[28]	Brunton S.L. and Kutz J.N. (2024). Promising directions of machine learning for partial differential equations. Nat. Comput. Sci. 4:483−494. DOI:10.1038/s43588-024-00643-2 View in Article CrossRef Google Scholar
[29]	Solera-Rico A., Sanmiguel Vila C., Gómez-López M., et al. (2024). β-variational autoencoders and transformers for reduced-order modelling of fluid flows. Nat. Commun. 15:1361. DOI:10.1038/s41467-024-45578-4 View in Article CrossRef Google Scholar
[30]	Karniadakis G.E., Kevrekidis I.G., Lu L., et al. (2021). Physics-informed machine learning. Nat. Rev. Phys. 3:422−440. DOI:10.1038/s42254-021-00314-5 View in Article CrossRef Google Scholar
[31]	Ham Y.G., Joo Y.S., Kim J.H., et al. (2024). Partial-convolution-implemented generative adversarial network for global oceanic data assimilation. Nat. Mach. Intell. 6:834−843. DOI:10.1038/s42256-024-00867-x View in Article CrossRef Google Scholar
[32]	Cheng S., Quilodrán-Casas C., Ouala S., et al. (2023). Machine learning with data assimilation and uncertainty quantification for dynamical systems: A review. IEEE/CAA J. Autom. Sin. 10:1361−1387. DOI:10.1109/JAS.2023.123537 View in Article CrossRef Google Scholar
[33]	Vinuesa R. and Brunton S.L. (2022). Enhancing computational fluid dynamics with machine learning. Nat. Comput. Sci. 2:358−366. DOI:10.1038/s43588-022-00264-7 View in Article CrossRef Google Scholar
[34]	Lu L., Jin P., Pang G., et al. (2021). Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3:218−229. DOI:10.1038/s42256-021-00302-5 View in Article CrossRef Google Scholar
[35]	Wang S., Wang H. and Perdikaris P. (2021). Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Sci. Adv. 7:eabi8605. DOI:10.1126/sciadv.abi8605 View in Article CrossRef Google Scholar
[36]	Kurth T., Subramanian S., Harrington P., et al. (2022). FourCastNet: Accelerating global high-resolution weather forecasting using adaptive Fourier neural operators. PASC Conf. Proc. 1:1−11. DOI:10.1145/3592979.3593412 View in Article CrossRef Google Scholar
[37]	Hao Z., Wang Z., Su H., et al. (2023). GNOT: A general neural operator transformer for operator learning. Proc. 40th Int. Conf. Mach. Learn. PMLR. DOI:10.48550/arXiv.2302.14376 View in Article Google Scholar
[38]	Sui Y., Fu H., Dai Y., et al. (2025). Global ionospheric 4-D tomography and forecast based on multisource DMD data assimilation. IEEE Trans. Geosci. Remote Sens. 63:1−10. DOI:10.1109/TGRS.2025.363370 View in Article CrossRef Google Scholar
[39]	Ma J., Fu H., Huba J., et al. (2024). A novel ionospheric inversion model: PINN‐SAMI3 (physics informed neural network based on SAMI3). Space Weather 22:e2023SW003823. DOI:10.1029/2023SW003823 View in Article CrossRef Google Scholar
[40]	Hammett G.W. and Perkins F.W. (1990). Fluid moment models for Landau damping with application to the ion-temperature-gradient instability. Phys. Rev. Lett. 64:3019−3022. DOI:10.1103/PhysRevLett.64.3019 View in Article CrossRef Google Scholar
[41]	Daughton W., Roytershteyn V., Karimabadi H., et al. (2011). Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nat. Phys. 7:539−542. DOI:10.1038/nphys1965 View in Article CrossRef Google Scholar
[42]	Huang Z., Tóth G., van der Holst B., et al. (2019). A six-moment multi-fluid plasma model. J. Comput. Phys. 387:134−153. DOI:10.1016/j.jcp.2019.02.023 View in Article CrossRef Google Scholar
[43]	Qin Y., Ma J., Jiang M., et al. (2023). Data-driven modeling of Landau damping by physics-informed neural networks. Phys. Rev. Res. 5:033079. DOI:10.1103/physrevresearch.5.033079 View in Article CrossRef Google Scholar
[44]	Cheng W., Fu H., Wang L., et al. (2022). Data-driven, multi-moment fluid modeling of Landau damping. Comput. Phys. Commun 282:108538. DOI:10.1016/j.cpc.2022.108538 View in Article CrossRef Google Scholar
[45]	Vlachas P.R., Arampatzis G., Uhler C., et al. (2022). Multiscale simulations of complex systems by learning their effective dynamics. Nat. Mach. Intell. 4:359−366. DOI:10.1038/s42256-022-00478-4 View in Article CrossRef Google Scholar
[46]	Gunnarson P., Mandralis I., Novati G., et al. (2021). Learning efficient navigation in vortical flow fields. Nat. Commun. 12:7143. DOI:10.1038/s41467-021-27015-8 View in Article CrossRef Google Scholar
[47]	Kochkov D., Yuval J., Langmore I., et al. (2024). Neural general circulation models for weather and climate. Nature 632:1060−1066. DOI:10.1038/s41586-024-07744-y View in Article CrossRef Google Scholar
[48]	Allen A., Markou S., Tebbutt W., et al. (2025). End-to-end data-driven weather prediction. Nature 641:1172−1179. DOI:10.1038/s41586-025-08897-0 View in Article CrossRef Google Scholar
[49]	Schreiner W.S., Weiss J., Anthes R.A., et al. (2020). COSMIC‐2 radio occultation constellation: First results. Geophys. Res. Lett. 47:e2019GL086841. DOI:10.1029/2019GL086841 View in Article CrossRef Google Scholar
[50]	Compagnucci R.H., Araneo D. and Canziani P.O. (2001). Principal sequence pattern analysis: A new approach to classifying the evolution of atmospheric systems. Int. J. Climatol. 21:1465−1482. DOI:10.1002/joc.601 View in Article CrossRef Google Scholar
[51]	Li C., Fang H., Cao X., et al. (2024). A new method for reconstruction of regional three‐dimensional electron density distributions using AI‐based data assimilation method and incoherent scatter radar measurements. Geophys. Res. Lett. 51:e2024GL112352. DOI:10.1029/2024GL112352 View in Article CrossRef Google Scholar
[52]	Liu Y., Fu H., Wang L., et al. (2025). Data-driven modeling of electrostatic turbulence by physics-informed Fourier neural operator. Mach. Learn. Sci. Technol. 6:045050. DOI:10.1088/2632-2153/ae19cd View in Article CrossRef Google Scholar

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Ma J., Fu H., Liu Y., et al. (2026). AION: Physics-informed machine learning advances forecasting of high-dimensional ionospheric spatiotemporal states. The Innovation Informatics 2:100037. https://doi.org/10.59717/j.xinn-inform.2026.100037

Ma J., Fu H., Liu Y., et al. (2026). AION: Physics-informed machine learning advances forecasting of high-dimensional ionospheric spatiotemporal states. The Innovation Informatics 2:100037. https://doi.org/10.59717/j.xinn-inform.2026.100037

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AION: Physics-informed machine learning advances forecasting of high-dimensional ionospheric spatiotemporal states

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