The Solar Dynamics Observatory has transformed solar science since its launch, delivering continuous, multi-wavelength monitoring of the Sun and generating roughly 1.5 terabytes of data every day. AIA captures the full solar disk in multiple extreme ultraviolet, ultraviolet, and visible channels, each sensitive to plasma at different temperatures and heights in the solar atmosphere, producing 57,600 images daily. HMI complements this view by measuring the photospheric magnetic field through spectropolarimetric observations, providing magnetograms, Dopplergrams, and continuum images. Together these instruments underpin real-time monitoring of solar flares and coronal mass ejections that can threaten power grids, GPS, and satellite communications. Yet despite this data abundance, analysis methods in solar physics have remained largely task-specific, relying on handcrafted features, curated event catalogs, or models trained independently for each objective, a fragmentation that motivated the search for shared, reusable representations.

Foundation models offer a way out of this fragmentation. Analogous to large language models or vision models trained on massive datasets, a foundation model learns broadly useful structure from unlabeled data and can then be adapted to many downstream tasks with lightweight task-specific heads or fine-tuning. SDO’s archive is uniquely suited to this paradigm because of its long-term continuity, consistent calibration, and multi-channel coverage, which allow self-supervised training without extensive manual labeling. SDOFMv2 builds on earlier efforts including SDOFMv1, the first masked-autoencoder-based foundation model for SDO imagery, as well as Solaris, a forecasting-centered transformer model, and Surya, a large-scale spatiotemporal model trained on native 4096 by 4096 resolution observations with roughly 366 million parameters.

At the heart of SDOFMv2 is a masked autoencoder built on a Vision Transformer backbone. During pretraining, a high fraction of image patches is hidden and the model must reconstruct the missing regions, forcing it to learn global spatial structure rather than local pixel interpolation. The team introduced several solar-specific innovations. A region-aware masking and reconstruction strategy explicitly distinguishes the inner solar disk, informative off-limb structures such as prominences, and nearly empty background regions, which can occupy roughly 20 percent of a square full-disk image. Background areas are strongly down-weighted in the reconstruction loss so the model concentrates its capacity on physically meaningful solar morphology rather than trivial black corners.

The loss function itself was redesigned around the physics of solar imagery. A weighted, region-aware objective balances reconstruction of the disk, prominences, and background, while a Huber loss provides robustness to the extreme statistical imbalance between the quiet Sun and intense, sparse active regions. Because magnetograms contain sparse, high-frequency magnetic structures with weaker spatial correlations than smooth EUV emission, the researchers added a denoising fine-tuning stage in which Gaussian noise is injected into inputs and the model learns to recover the clean signal. This stage, combined with a reduced masking ratio of 10 percent for magnetic data, substantially improved HMI reconstruction quality. A signum-logarithmic transformation was also applied to compress the enormous dynamic range of solar intensities and magnetic fields while preserving sign information.

The framework includes three configurations: an AIA-only model with approximately 114 million parameters, an HMI-only model with about 111 million, and a joint AIA+HMI model with 114 million. Notably, the models were trained on workstation-scale hardware, four compute nodes with a total of eight NVIDIA RTX 5090 GPUs, requiring roughly three weeks and an estimated 670 GPU-hours per model. The team found that data engineering mattered as much as raw compute: converting the dataset to the cloud-optimized Zarr format reduced image loading times from 20 to 40 seconds to under 100 milliseconds, and a RAID 0 array of NVMe SSDs achieving about 21 gigabytes per second kept the GPUs continuously fed. An interleaved monthly splitting strategy ensured that training, validation, and test sets each sampled the full range of solar activity across the cycle.

Qualitative and quantitative evaluations showed substantial improvements in reconstruction fidelity over SDOFMv1, with sharper intensity gradients, better preserved coronal loops, and faithful recovery of off-limb prominence emission that the earlier model largely omitted. Analyses of the learned latent space using principal component analysis revealed that the dominant modes of variation consistently highlight active regions, magnetic concentrations, and prominences, while attention maps from the transformer encoder showed that different attention heads specialize in complementary solar structures and adapt their focus as solar conditions change. Ablation studies indicated that modality-specific models remain strongest for pure reconstruction, and that among joint models the ViT-Base configuration offered the best balance of capacity and performance, with the larger ViT-L variant not surpassing it under equal training budgets.

The true test of a foundation model is transfer, and here SDOFMv2 was evaluated on three downstream tasks against SDOFMv1, Solaris, and Surya in one of the most comprehensive benchmarking studies of heliophysics foundation models to date. In regression of the F10.7 solar radio flux, a widely used ground-based proxy for solar EUV emission, Surya achieved the best overall performance with a coefficient of determination of 0.918, consistent with its high-resolution, forecasting-oriented pretraining, while SDOFMv2’s AIA-based variants remained competitive and outperformed Solaris on mean squared error and R-squared. In classification of solar wind phenomena into streamer belt, sector reversal, coronal hole, and ejecta categories using Parker Solar Probe in situ labels, fine-tuned SDOFMv2-AIA delivered the highest accuracy, precision, and F1-score, and all SDOFMv2 variants outperformed the corresponding SDOFMv1-based results. In missing-channel reconstruction, where an entire AIA wavelength must be inferred from the others, the AIA-only model achieved a mean R-squared of 0.96, improving on SDOFMv1’s 0.94 and exceeding both Solaris and Surya on agreement with ground truth.

The results carry a broader message about how machine learning is reshaping heliophysics. Modality-specific and joint foundation models exhibit complementary strengths, and accurate pixel-level reconstruction turns out not to be a strict prerequisite for useful downstream representations, as the HMI model achieved competitive solar wind classification despite lower reconstruction fidelity. The authors acknowledge limitations, including the reduced spatial resolution of the SDOML dataset, where each pixel corresponds to roughly 1,353 kilometers on the solar surface, and the absence of Dopplergrams and continuum intensity products, and they point toward temporal forecasting objectives and cross-modal alignment as future directions. By releasing model weights, training code, and a benchmark evaluation framework openly, the team has established strong, reproducible baselines that could accelerate space-weather research and lower the barrier to entry for smaller groups hoping to build on solar foundation models.

Subject of Research: A multi-instrument AI foundation model for the Solar Dynamics Observatory with transferable applications in solar physics and space weather

Article Title: SDOFMv2: A Multi-Instrument Foundation Model for the Solar Dynamics Observatory with Transferable Downstream Applications

Article References: Hong, J., Martin, D., & Gallego, J. (2026). SDOFMv2: A Multi-Instrument Foundation Model for the Solar Dynamics Observatory with Transferable Downstream Applications. Solar Physics, 301(9), Article 137. https://doi.org/10.1007/s11207-026-02740-z

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02740-z

Keywords: Solar Dynamics Observatory, foundation models, machine learning, solar physics, masked autoencoder, space weather, heliophysics, solar magnetic fields, solar wind, self-supervised learning, AIA, HMI

The two quantities at the heart of the study, magnetic helicity and magnetic energy, are central to nearly every modern theory of how the Sun stores and releases explosive energy. Magnetic energy, and in particular the free energy left over after subtracting the energy of the simplest potential field configuration, represents the fuel available to power solar flares and coronal mass ejections. Magnetic helicity, a measure of the twisting, linking, and shearing of magnetic field lines, quantifies the topological complexity of the field. First introduced into fluid dynamics by H.K. Moffatt in 1969 and extended to magnetized plasmas by Berger and Field in 1984, helicity is remarkable because it is approximately conserved even during rapid reconnection events. That conservation property means helicity can only escape the corona by being expelled wholesale in eruptions, making its accumulation a closely watched indicator of a region’s eruptive potential.

The difficulty has always been that neither quantity can be measured directly in three dimensions. Space- and ground-based instruments measure the vector magnetic field only at the photosphere, the Sun’s visible surface, and sometimes in the chromosphere just above it. Everything above must be reconstructed through a process called magnetic field extrapolation, in which a three-dimensional field is computed that matches the observed boundary data and satisfies certain physical assumptions. The most widely used assumption is that of a force-free field, in which electric currents flowing along the field lines mean that the Lorentz force vanishes and magnetic pressure dominates over gas pressure. Nonlinear force-free field, or NLFFF, extrapolations relax the simplifying assumption of a constant proportionality factor between current and field, allowing a realistic twisted coronal field to emerge from the numerical solution.

Here lies the problem the Chinese team set out to solve. Every extrapolation must be performed inside a finite computational box with a defined top boundary, and the choice of that height has traditionally been empirical—varied from study to study, often inherited from convention rather than from physics. Extrapolate too low, and the model truncates the extended, ballooning structures of the corona, discarding a non-negligible fraction of the helicity and energy budget. Extrapolate too high, and researchers pay a steep price in grid cells and computation time for volume that contributes almost nothing. Because statistical studies of helicity accumulation across many active regions and many solar cycles are increasingly in demand—particularly for testing models of the solar dynamo and the so-called hemispheric helicity rule—settling the question with physical criteria rather than habit has become an open problem in the field.

The team, led by Hongyan Li with Shangbin Yang as corresponding author, approached the problem with an unusually rich dataset. They used observations from the Solar Magnetic Field Telescope, or SMFT, a vector magnetograph at the Huairou Solar Observing Station in Beijing whose operation stretches back to the 1980s. Spanning observations from 1988 to 2019, the dataset covers the declining phase of solar cycle 22, the entirety of cycles 23 and 24, and offers a rare four-decade record of vector magnetograms. The instrument’s polarization data require careful calibration, including statistical correction for Faraday rotation, an effect in which the Sun’s own magnetic environment rotates the polarization plane of light passing through it and distorts the inferred transverse field direction—corrections that the group has developed and refined in earlier work.

From this archive the researchers selected 150 active regions and grouped them according to their absolute magnetic flux, ensuring that the conclusions would not be skewed by a sample dominated by either small or large regions. For each region they performed NLFFF extrapolations using an optimization-based method of the kind introduced by Wheatland, Sturrock, and Roumeliotis in 2000 and refined by Wiegelmann and colleagues, in which a functional measuring the departure from both the force-free condition and the divergence-free condition is iteratively minimized. The vector magnetograms were preprocessed to remove instrumental and projection effects before being used as boundary conditions, following established procedures that bring the data into consistency with the force-free assumption.

With three-dimensional fields in hand for each region and for a series of extrapolation heights, the team computed the relative magnetic helicity using a finite volume method. This technique, codified in a widely cited 2016 review by Valori and collaborators, computes helicity inside a closed finite volume by splitting the magnetic field into two components—one closed, one open with respect to the volume boundary—and summing their self- and mutual helicities. The relative formulation sidesteps the ambiguity that absolute helicity suffers in open volumes, and its additivity properties across nested finite volumes were clarified in subsequent work, making it the standard tool for helicity estimates from extrapolated coronal fields. Magnetic energy was evaluated over the same volumes, allowing a direct, region-by-region comparison of how much helicity and energy is contained below each candidate top boundary.

The result was a consistent vertical profile across the entire sample. Magnetic helicity and magnetic energy both concentrate overwhelmingly in the lower corona: the fields of an active region are complex and current-carrying close to the surface, where the twisting driven by photospheric motions and flux emergence is strongest, and grow progressively simpler with height. By the time the computational volume reaches 81 megameters above the photosphere, the model retains 97 percent of the total helicity and energy regardless of the region’s size class. Above that height, the additional volume contributes diminishing returns, since the field becomes increasingly potential and the integrands of both quantities fall toward zero. The authors emphasize that this height constraint is derived from physical behavior of the quantities themselves—convergence of the helicity and energy integrals with height—rather than from an arbitrary numerical convention, addressing precisely the gap between physical and empirical criteria that had motivated the study.

The practical implications are considerable. Extrapolation cost scales steeply with the number of grid points, and for a three-dimensional box the burden grows roughly with volume. Trimming the vertical extent of the computational domain under the adopted grid configuration reduced computational costs by approximately 38 percent while sacrificing only 3 percent of the physically relevant helicity and energy. For a single calculation that saving is welcome; for long-term statistical programs that aim to process hundreds or thousands of magnetograms—each requiring a full nonlinear iterative solve—it is transformative. The authors position their result as providing important parameter constraints for exactly such long-term statistical studies of magnetic helicity in solar active regions, potentially enabling helicity-based eruptivity assessments across entire solar cycles at a fraction of the previous cost.

The broader scientific payoff touches several active frontiers in solar physics. Helicity budgets govern how the Sun sheds magnetic twist: because helicity is conserved under reconnection, active regions must either accumulate it until eruption becomes inevitable or shed it in bursts, and accurate bookkeeping of coronal helicity is essential to models of flux-rope formation and prominence eruption. Helicity is also a diagnostic window into the solar dynamo operating in the convection zone, where the sign and magnitude of helicity injected into emerging active regions reflect the interplay of large-scale differential rotation and small-scale turbulent effects. Recent modeling work has connected helicity fluxes to the hemispheric helicity rule, the empirical tendency for magnetic chirality to follow systematic patterns in the northern and southern hemispheres. A reliable, computationally efficient protocol for measuring helicity in the corona strengthens all of these lines of inquiry.

The study also carries a message about the value of long-arcade observational records. The SMFT dataset, calibrated consistently across four decades, allowed the team to sample active regions spanning a wide dynamic range of flux and complexity—something no single modern mission-era snapshot could provide. By demonstrating that a well-defined extrapolation height suffices to capture the helicity and energy content of the corona, the work turns what was once a source of systematic uncertainty into a controlled, quantified parameter. For researchers planning large statistical studies with current instruments such as the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager or upcoming facilities, the result offers a concrete, physics-based rule of thumb: you do not need to model the Sun’s magnetic field to the edge of the heliosphere to understand what makes it explode—you need barely more than 81,000 kilometers above the surface, and the numbers show that is enough.

The MURaM code stands as a pinnacle of computational astrophysics, uniquely designed to capture the physics spanning the solar photosphere, chromosphere, and corona in three dimensions. At its core, it solves the non-ideal MHD equations—conservation laws of mass, momentum, energy, and magnetic field evolution—within a Cartesian framework, integrating crucial effects such as gravity, resistive and radiative heating, Spitzer thermal conduction, and semi-relativistic corrections to circumvent stringent time-step constraints. This multiphysics approach is vital to replicate the harsh solar environment where magnetic forces and radiative processes dominate.

One of the key aspects of MURaM is its treatment of thermal conduction along magnetic field lines, modeled through an evolutionary Spitzer heat flux that incorporates saturation effects to prevent nonphysical overconduction at steep temperature gradients. The code also employs a hyperbolic divergence cleaning technique to enforce the divergence-free condition of magnetic fields, ensuring numerical stability. Notably, the Lorentz force—a crucial player governing magnetic pressure and tension—is carefully computed with a velocity-limiting factor to suppress artificially high Alfvén speeds that could bottleneck simulation time steps, utilizing a semi-relativistic approach adapted from Boris corrections.

To simulate the solar atmosphere with realism, MURaM leverages two versions: a coronal extension (MURaM-CE) that captures optically thin radiative losses and LTE radiation, and a chromospheric extension (MURaM-ChE) that adds non-LTE physics crucial in the chromosphere. The chromospheric mode integrates time-dependent hydrogen ionization, sophisticated radiative transfer with scattering, and detailed line emissions of elements such as hydrogen, magnesium, and calcium. These advances permit intricate modeling of radiative heating and cooling, including back-heating effects from extreme ultraviolet radiation, rendering a more nuanced simulation of chromospheric dynamics than ever before.

The simulations underpinning this study utilized 3D boxes spanning 80 Mm horizontally and up to 34 Mm vertically, capturing both the convection zone and atmospheric layers up to the corona. The grid resolution amounted to roughly 80 km horizontally and 50 km vertically, balancing physical fidelity and computational feasibility. Initial conditions were generated from evolved 2D simulations exhibiting dipped magnetic field structures, extended into three dimensions with stochastic perturbations to avoid artificial symmetries. These dipped magnetic arcades constitute the fundamental magnetic skeleton capable of supporting dense, cool prominence plasma against gravity.

Two primary simulation runs, distinct in magnetic field configurations and bottom boundary treatments, were explored alongside a sheared configuration derived from one of these runs. Run I features six narrow magnetic flux columns that create a nuanced multipolar structure, while Run II employs four wider flux columns resulting in stronger magnetic fields. These vertical flux concentrations were fixed deep in the convection zone to anchor the evolved field configurations, stabilizing the magnetic dips critical for prominence formation. The magnetic topology deliberately lacks an initial horizontal component, diverging from typical in-situ observed prominence fields but enabling controlled study of prominence onset and evolution.

Boundary conditions play a pivotal role in simulating solar physics accurately. The bottom boundary allowed open flows in Run I but suppressed flows within magnetic columns in Run II through asymmetric velocity constraints, reflecting different physical regimes below the photosphere. Horizontally periodic boundaries ensured seamless plasma dynamics, while an open, potential-field top boundary allowed outflows and realistic magnetic field extension into the corona. Notably, the sheared set-up implemented velocity drivers that imparted horizontal shear to the central magnetic flux regions, mimicking shear often inferred in solar active regions and allowing exploration of shear’s effects on prominence morphology.

The evolution from 2D snapshots to fully fledged 3D simulations was essential to capture realistic prominence dynamics. Randomized perturbations prevented artificial coherence, generating a three-dimensional dipped arcade resembling observed structures. Intriguingly, the sheared runs demonstrated how introducing horizontal velocity components selectively at the prominent magnetic columns induced localized shear that diminishes with height, closely replicating the naturally tapered shear profiles expected in the solar atmosphere. This nuanced shearing dynamics allowed the study of how realistic magnetic configurations influence prominence stability and evolution.

Magnetic field profiles extracted from the simulations reveal compelling insights. While the photospheric magnetic strength hits several hundred Gauss, the field in the prominence dips falls to tens of Gauss, matching observationally inferred strengths. The sheared configuration displayed a dominance of the horizontal field component aligned along the polarity inversion line, confirming that localized shear correlates with enhanced horizontal magnetic structuring. These findings bear directly on how magnetic support and confinement mechanisms operate in suspended prominence plasma and the balance of magnetic and plasma pressures.

Simulation physics included two treatments of the equation of state: a straightforward LTE model and a more sophisticated non-LTE approach that resolved hydrogen ionization and molecular hydrogen kinetics in time-dependent detail near the photosphere and chromosphere. The combined use of these EoS treatments enabled more accurate modeling of thermodynamics under varying optical depths and ionization states, critical for tracking prominence formation and thermal balance. The non-LTE runs also employed improved radiative loss functions that accounted for chromospheric line emission, vital for reproducing realistic energetics in the simulated prominence plasma.

These simulations mark a notable advance in prominence research by integrating multi-physics components into self-consistent, large-scale 3D models, bridging the photosphere-corona transition that is pivotal for understanding prominence mass loading and stability. They suggest that stable dipped magnetic configurations, seeded in subsurface flux bundles and evolving through naturally occurring flows and shear, can indeed support prominence plasma for extended periods. Furthermore, the sheared runs underscore the role of magnetic shear in shaping prominence geometry, offering fresh pathways to relate magnetic field measurements to prominence morphology.

Remarkably, the simulations handle extreme disparities in plasma parameter scales, such as transitioning from dense, cool chromospheric plasma to hot, tenuous coronal plasma, without resorting to non-physical approximations that could obscure essential dynamics. This is achieved through advanced numerical treatments like slope-limited diffusion, fourth-order hyperdiffusion, and careful energy equation partitioning to minimize numerical artifacts. The inclusion of resistive and viscous heating components emerging from numerical schemes ensures that dissipative energy conversions are physically meaningful within the simulated environment.

The computational demands of such simulations remain formidable. To balance this, initial prominence formation was modeled under LTE assumptions, speeding simulations, while the more computationally intensive NLTE runs were initiated from pre-formed prominence states. Future work aspires to push grid resolution beyond the current 50 km to better resolve fine-scale dynamics, turbulence, and instabilities within prominence plasma, which are essential for connecting simulation results with high-resolution solar observations.

This pioneering research synthesized complex physics, cutting-edge numerical methods, and advanced computational resources to create a comprehensive model for solar prominence formation and dynamics. The results open avenues for deeper investigation into solar activity phenomena, including prominence eruptions and their role in coronal mass ejections. They also lay foundations for improved understanding of magnetic energy storage and release in the solar corona, with direct relevance for space weather modeling and prediction.

By meticulously linking boundary conditions, magnetic field configurations, radiative transfer, and plasma thermodynamics, this work sets a new standard for self-consistent numerical simulations of solar prominences. Its clarity and detail provide researchers a robust platform to interrogate fundamental solar physics questions, ultimately advancing our mastery of Sun–Earth connections. As observational capabilities evolve, these simulation frameworks promise to be indispensable tools to interpret and predict solar behavior at multiple scales.

In sum, the merging of MURaM’s sophisticated code capabilities with a carefully crafted simulation setup has yielded transformative insights into the fundamental physics of solar prominences. The emergent magnetic dips and plasma condensations elucidated here offer a realistic path toward understanding one of solar physics’ enduring puzzles, propelling the field into a new era of modeling precision and physical fidelity.

Subject of Research: Numerical simulations of solar prominences and their formation, dynamics, and magnetic configurations using radiative magnetohydrodynamic modeling.

Article Title: Self-consistent numerical simulations for the formation and dynamics of solar prominences.

Article References:
Zessner, L.M., Cameron, R.H., Solanki, S.K. et al. Self-consistent numerical simulations for the formation and dynamics of solar prominences. Nat Astron (2026). https://doi.org/10.1038/s41550-026-02840-7

Image Credits: AI Generated

DOI: https://doi.org/10.1038/s41550-026-02840-7