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 green line at 530.3 nanometers is the brightest emission line in the solar corona, produced by highly ionized iron atoms, Fe XIV, stripped of thirteen of their electrons by the extreme coronal temperatures of roughly two million kelvin. Unlike the photospheric surface we see with the naked eye, the corona traces magnetic structures that arch high above active regions, and its emission intensity varies with the strength and distribution of the underlying magnetic field. Because ground-based observatories, coordinated through networks that produced the green corona database and the coronal index of solar activity, have monitored this emission consistently since the mid-twentieth century, the green line provides an exceptionally long and homogeneous record of large-scale coronal behavior that modern space-based instruments simply cannot match in duration.

On the sunspot side, the study departs from tradition in a crucial way. Conventional analyses of the solar cycle often rely on the sunspot number or the total sunspot area, both of which collapse the entire two-dimensional distribution of spottedness into a single scalar per day. Takalo instead constructed a Gaussian representation of the sunspot activity field, built from the individual areas and latitudes of every recorded sunspot group. This activity-field model preserves where on the solar disk the magnetic flux emerges, capturing the characteristic equatorward migration of sunspot belts as each cycle progresses and the poleward drift of its remnants. The result is a mathematical description of the large-scale spatial organization of solar magnetic activity that is far more realistic than any single-number index.

The central discovery of the study is a remarkably stable, double-peaked correlation structure in latitude. When coronal green-line emission at each latitude band is correlated against the modeled sunspot activity field at the same latitude, the correlation profile shows two strong maxima that track the well-known active-region belts on either side of the solar equator. These peaks, typically centered in the low and mid-latitudes where sunspot groups preferentially emerge, remain strikingly similar in shape and position from one cycle to the next. Even between weak cycles and strong cycles, and between even-numbered and odd-numbered cycles with their differing amplitudes and parity, the latitude profiles of the corona–sunspot relationship barely change, indicating that the large-scale coupling between photospheric activity and coronal emission is largely independent of how vigorous any particular cycle happens to be.

This finding carries weight because solar cycles are far from identical twins. Cycle 19, which peaked in the late 1950s, was the most active in the observational record, while Cycle 24 was notably feeble, and the even–odd alternation in cycle strength, sometimes called the Gnevyshev–Ohl rule, hints at deep-seated differences in the solar dynamo from one cycle to the next. Yet the corona appears to respond to the sunspot engine in a nearly invariant geometric pattern. The double-peaked structure is a direct signature of the fact that green coronal emission is strongest not randomly across the disk but precisely where active-region magnetic fields cluster, confirming quantitatively what decades of qualitative observation have suggested: the corona is, in a very real sense, a magnetic portrait of the activity belts painted in glowing iron light.

Perhaps the most subtle part of the analysis concerns timing. Using lag-correlation techniques, the study finds that the strongest correlations between the coronal emission and the sunspot activity field generally occur at positive lags, which would naively suggest that the corona follows the sunspots with a specific, measurable delay. But here the author applied a rigorous statistical safeguard. Surrogate-data tests, in which the temporal ordering of one record is scrambled while its statistical properties are preserved, show that these formal lag maxima are usually not statistically distinguishable from the correlations at neighboring lag values. The lag-correlation profiles instead display broad, flat positive-lag plateaus, meaning the apparent delay is not a sharply defined physical delay at all.

What the plateaus do reveal is something arguably more interesting: temporal persistence and memory in the large-scale coronal magnetic structures. Rather than the corona slavishly tracking each new burst of sunspot emergence after a fixed interval, the green-line emission behaves like a slowly evolving reservoir that integrates and smooths the photospheric activity underneath it. Magnetic fields introduced into the corona by emerging active regions persist, relax, and redistribute over extended timescales, so the coronal response is broad and smeared rather than impulsive. This interpretation aligns with a growing body of work emphasizing that the large-scale distribution of magnetic flux, spanning scales far beyond individual sunspots, governs the evolution of the corona as a global system.

The comparison between modeling approaches proved decisive in this regard. When the Gaussian activity-field representation was used as the predictor of coronal emission, it produced substantially stronger and more coherent correlations than conventional sunspot number or sunspot area measures ever achieved. In other words, knowing not just how many sunspots exist but where they sit on the disk at any moment allows a far better reconstruction of the green-line corona’s behavior. This supports the central physical conclusion of the paper: that it is the large-scale spatial distribution of magnetic activity, rather than the presence of individual sunspots alone, that controls the evolution of the large-scale corona. For modelers of the solar atmosphere, this is an invitation to move beyond scalar activity indices toward genuinely two-dimensional descriptions of the emerging flux.

The practical implications extend beyond pure solar physics. The green corona has long served as a proxy for solar activity in space-weather and solar-terrestrial research, and the coronal index built from it has been used to study everything from geomagnetic disturbance to long-term solar variability. Establishing that the corona’s response to sunspot activity is stable in latitude, amplitude-independent, and temporally diffuse strengthens confidence in using coronal records to extend our knowledge of solar behavior backward in time and, potentially, to refine reconstructions of past solar cycles. It also cautions against overinterpreting any single lag measurement as a physical delay mechanism, a lesson in statistical humility that applies across solar-terrestrial science.

Spanning seven decades and seven solar cycles, this analysis demonstrates that beneath the Sun’s famously variable surface behavior lies an unexpectedly disciplined architecture. The green-line corona and the sunspot belts are locked together in a latitude-dependent partnership whose geometry survives even the wildest swings in cycle strength, while their timing relationship reflects the lingering memory of magnetic structures rather than any simple cause-and-effect delay. As the Sun progresses through Cycle 25 and observers accumulate fresh coronal data, the stable patterns documented here provide a robust baseline against which any genuine, long-term change in solar behavior can be recognized. In the quiet green glow of iron atoms two million degrees hot, the Sun has written down, cycle after cycle, a remarkably consistent record of its own magnetic heartbeat.

Subject of Research: Latitude-dependent relationships between green-line coronal emission and sunspot activity across Solar Cycles 18–24

Article Title: Large-Scale Latitude-Time Relationships Between the Green-Line Corona and Sunspot Activity During Solar Cycles 18 – 24

Article References: Large-Scale Latitude-Time Relationships Between the Green-Line Corona and Sunspot Activity During Solar Cycles 18 – 24. (n.d.). https://doi.org/10.1007/s11207-026-02729-8

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02729-8

Keywords: solar corona, green coronal line, sunspots, solar cycle, solar magnetic fields, activity belts, lag correlation, surrogate data, solar physics, coronal index, solar dynamo, space weather

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.