Fig 1. *Coronal Mass Ejections, or CMEs, refer to the significant releases of plasma and magnetic fields from the Sun’s outer atmosphere, also known as the corona. These powerful phenomena can propel enormous quantities of coronal substance into space and throw out an inherently intense magnetic field, which is stronger than the interplanetary magnetic field of the background solar wind. The speed at which these CMEs journey away from the Sun can vary widely, ranging from less than 250 kilometers per second to almost 3000 kilometers per second. Images that capture these events are provided by NASA, as well as the SOHO and STEREO missions.

Unveiling the Dynamic Universe with Neural Radiance Fields: Revolutionizing Solar Observations and Space-Weather Forecasting with SuNeRF

This story is the second article about Neural Radiance Fields and their applications in Astronomy. The first article is here. TLDR; The study discussed here leverages Solar Neural Radiance Fields (SuNeRF), a novel method for 3D reconstruction of the Sun’s corona, to enhance our understanding of solar activities and improve space-weather forecasting. By integrating principles from computer graphics and radiative transfer, SuNeRF produces high-resolution synthetic solar corona images, significantly surpassing the fidelity of traditional observation methods. This breakthrough in solar physics can help us better predict and prepare for disruptive solar events, like Coronal Mass Ejections, that could significantly impact our technology-dependent society.

Fig 2. DALL E 2 images for the prompt “The Solar Corona Using Simulated EUV Images and events like Carrington event from the Sun in the different spectrum.”

Electronics have become a vital part of our lives today. From the smartphones, we carry in our pockets to the satellite systems we depend on for communication and navigation, much of our modern existence hinges on these complex systems. Yet, these technological marvels we’ve grown accustomed to are vulnerable to forces emanating from our star, the Sun.

The Sun, in its fiery majesty, is not always calm. It undergoes periods of intense activity and sporadic outbursts known as solar storms or Coronal Mass Ejections (CMEs). These storms release powerful bursts of solar particles and electromagnetic radiation into space. When directed toward Earth, these solar storms can wreak havoc on our electronic infrastructure. Two such historical events, the Carrington Event of 1859 (> G5 event; CME) and the Miyake Event of 993 AD (>> G5 event; Solar Flares), provide a glimpse of the potential destruction with Carrington Event causing widespread disruption of telegraph systems across Europe and North America in 1859 CE and Miyake Event causing an outlying spike in carbon-14 levels in tree rings and ice cores in 993 CE. And the recent Carrington-like event (still a G2 event) in April 2023 only re-emphasizes their significance which was in a different direction from the Earth.

What are Solar flares?

Solar flares are sudden flashes of increased brightness on the Sun, often observed near its surface and magnetically active regions, and release a significant amount of high-energy particles and radiation into space. They are a product of the rapid release of magnetic energy stored in the Sun’s corona and can affect radiation conditions in near-Earth outer space. When observed through 3D reconstruction of the solar corona, they appear as bright, localized flashes often associated with sunspots and active regions.

What are CMEs?

CMEs are large expulsions of plasma and magnetic field from the Sun’s corona, ejecting billions of tons of coronal material and carrying an embedded magnetic field much stronger than the background solar wind interplanetary magnetic field (IMF) strength. These CMEs can trigger geomagnetic storms if their direction of propagation aligns with Earth. In 3D coronal reconstructions, the CMEs are large, expanding clouds of plasma and magnetic field structures erupting from the Sun and moving into interplanetary space.

What is Gn? How is it related to Solar flares and CMEs?

The G1 (minor)-G5 (major) classification (according to the NOAA Space Weather Scale for Geomagnetic Storms) refers to the intensity of geomagnetic storms, which are disturbances in Earth’s magnetosphere caused by solar activity, such as CMEs or solar flares. A G1 storm can cause weak power grid fluctuations with minor upsets in satellite operations and auroras visible at high latitudes. A G2 (moderate) storm can cause longer-lasting power grid fluctuations, increased drag on low-Earth orbit satellites, and more widespread auroras visible as far south as New York and Idaho. In Carrington Event, these auroras were visible as far as the Carribean.

Imagine, then, if a solar event of such magnitude happened today. The consequences could be disastrous, given our dependence on electronic systems for almost every aspect of our lives, from power grids and telecommunication systems to satellites and aviation. Massive blackouts, loss of communication, and severe disruption of transportation systems could follow, leading to significant economic and societal impacts.

Fig 3. Overview of the SuNeRF model. A neural network represents the simulation volume and maps each coordinate point (x, y, z) to the corresponding emission and absorption coefficient (ε, κ). This approach sample rays from the volume and compute the total intensity using radiative transfer principles for each pixel. [IMAGE: [1]]

In light of this, the recent groundbreaking study led by Kyriaki-Margarita Bintsi et al. becomes of significant interest. This research team’s pioneering work on 3D corona reconstruction using an innovative technique known as Sun (or Solar) Neural Radiance Fields (SuNeRF) [1] holds promise to revolutionize our understanding of the Sun, its dynamics and our ability to predict space weather events. Earlier state-of-the-art maps combined simultaneous images from different observers to generate a synchronic map of the corona [3] by reprojecting different viewpoints onto a spherical surface. This synchronous approach was under the assumption that the observed intensity originated from a single plane without considering the 3D solar corona. On the other hand, the SuNeRF model is a powerful approach that adapts standard NeRF [4] to “match the reality of the Sun,” providing unprecedented insights into the Sun’s behavior and potentially revolutionizing how we predict space weather events.

The researchers introduced radiative transfer and geometric sampling of NeRFs, a technology initially developed for computer graphics and computer vision, and applied it to Solar Corona Reconstruction. By training a deep neural network on a vast dataset of solar observations, this approach was able to generate high-resolution synthetic images of the corona. These synthetically-generated images closely resemble the actual solar corona observation and can allow researchers to study the Sun’s dynamics in greater detail and with better precision than ever before. For evaluating the generated images, the authors used MagnetoHydroDynamics (MHD) simulations of the solar corona for forecasting the solar atmosphere state before July 2019 total solar eclipse and simulated images of the Sun in the EUV for the non-existing observations (from non-ecliptic of the Sun).

Fig 4. (a) Satellite image of the Sun at 193Å that was captured from the ecliptic on 2019–07–02 at 20:41:08 (UT). (b) Simulated image of the satellite viewpoint (offset), extracted from a 3D model of the Sun. © The 3D model is used to extract the positions of the 256 viewpoints. The color coding indicates the viewpoints used for the training set (magenta) and the test set (green) [IMAGE: [1]].

What is MHD?

MagnetoHydroDynamic (MHD) simulations involve mathematical techniques to model the behavior of electrically conducting fluids, such as plasma, under the influence of magnetic and electric fields. It unifies principles from electromagnetism and fluid dynamics to investigate a wide range of natural and artificial systems. The simulations are powerful tools for studying complex phenomena like the flow of plasma in stars, the behavior of liquid metal in a dynamo, or the plasma environment around planets, giving us an understanding of how electromagnetic forces interact with fluid flows and affect the overall system behavior.

How can MHD be used to forecast the solar atmosphere and estimate the 3D distribution of plasma parameters and magnetic fields?

When applied to the solar corona, MagnetoHydroDynamic simulations can forecast the state of the solar atmosphere and provide a comprehensive 3D distribution of plasma parameters and the magnetic field. Using observational data from the Sun’s photosphere as initial conditions, these simulations model the large-scale structure and dynamics of the solar corona, including solar winds, coronal mass ejections, and other solar activities. These plasma parameters and magnetic field distributions allow scientists to predict space weather and can disturb satellite operations, communication systems, and navigation on Earth. As such, MHD simulations of the solar corona are essential in ongoing efforts to understand and forecast solar activities.

The core idea behind this optimal performance was the replacement of color and density predictions in standard NeRFs with emission and absorption as pixel values in solar corona images integrate emitting and absorbing plasma elements along line-of-sight. So, this network predicted emission and absorption coefficients (ε, κ) at each point (x, y, z). Hence, Hence, the equation at the core of the SuNeRF model was as follows:

I(ε, κ) = ∑ₖ Iₖ ∗ ∏ᵢ→ₖ₋₁ Aᵢ

Here, Iₖ is the emission per point (x, y, z) multiplied with κ (emission coefficient) with a discrete spacing of sampled ray ds, absorption per point A is scaled between 0 and 1 (total and no absorption, resp.) using A(x, y, z) = exp (−κ ds), and indices refer to the sampled points along the ray. For the final pixel value, we use an a*sinh stretching to optimize the value range for training. The NeRF sample rays ranged from [-1.3, 1.3] solar radii from the Sun to adapt the NeRF model to the geometry of the Sun. This equation allowed the researchers to account for the complex interplay of light and matter in the solar atmosphere, enabling the model to generate synthetic images that closely resembled solar observations. The ray endpoints passing through the Sun are fixed to the surface (i.e., no emission from the interior) to account for the opaqueness of the solar surface (i.e., the transition to an optically thick medium).

This model’s performance was evaluated against the state-of-the-art in solar observation techniques [3], and the results were impressive. The SuNeRF model reproduced solar observations with remarkable fidelity and achieved higher resolution against traditional methods using only limited viewpoints captured from the ecliptic to reflect on the limitations of current space-based observations. The evaluation results by the authors are as follows.

Result 1. Metrics of performance for a synchronic map (baseline) and a SuNeRF applied to the test dataset (non-ecliptic viewpoints), including the Peak Signal-to-Noise-Ratio (PSNR), Structural Similarity Index (SSIM), Mean Absolute relative Errors (MAE), and Mean relative Errors (ME).

As the SuNeRF model gains more traction in the scientific community, it will become a vital tool for furthering our understanding of the Sun’s behavior. The model’s impressive ability to reproduce solar observations can not only facilitate the study of existing data but also opens up doors to new possibilities in scenarios not yet observed. This capability would be crucial for researchers aiming to explore and anticipate the impacts of extreme space weather events like the Carrington-like event (directed away from the Sun) of April 2023.

Fig 5. Extreme ultraviolet composite image of the Sun (red: 21.1 nm, green: 19.3 nm, blue: 17.1 nm) taken by the Solar Dynamics Observatory on August 1, 2010, showing a solar flare and coronal mass ejection. [IMAGE: https://www.nist.gov/image/1280px-sun-august12010jpg]

The SuNeRF model’s success in simulating solar observations can also open new avenues for interdisciplinary research. By bridging the gap between computer graphics and solar physics, this approach encourages collaboration between researchers from diverse fields, such as computer vision, astrophysics, and climate science. This convergence of expertise can accelerate the development of novel techniques and models, propelling solar research into uncharted territories.

Fig 6. Evaluation of the SuNeRF using forward-modeled data of the EUV Sun at 193Å. (a) PSNR and SSIM are calculated at 256 viewpoints and represented by points at the corresponding latitudes and longitudes. The color indicates the quality of the reconstruction, with larger values indicating a better agreement with the ground truth. Red dashed lines at ±7◦ latitudes mark the separation between the training and test viewpoints. (b) Qualitative comparison between the baseline method (spherical reprojection; first row), the simulation data (ground truth; second row), and the SuNeRF reconstruction (third row) at different latitudes. Difference maps (fourth row) identify regions where this method deviates from the ground truth. Uncertainty estimates (fifth row) are in agreement with the errors [IMAGE: [1]].

In conclusion, the Sun Neural Radiance Fields (SuNeRF) model represents a significant breakthrough in solar observation and space-weather forecasting. Its ability to generate high-resolution synthetic images of the solar atmosphere is a powerful tool for understanding the Sun’s dynamics and predicting solar activity. Moreover, the model’s open-source nature and interdisciplinary applications foster a vibrant community of researchers dedicated to unraveling the mysteries of the Sun. As the world continues to grapple with the possible consequences of the Carrington and Miyake events, the SuNeRF model offered a beacon of hope and a pathway toward a more prepared and resilient future.

TLDR was written using ChatGPT-4 for convenience of summarization.

REFERENCES

[1] Bintsi, K. M., Jarolim, R., Tremblay, B., Santos, M., Jungbluth, A., Mason, J. P., … & Jaramillo, A. M. (2022). SuNeRF: Validation of a 3D Global Reconstruction of the Solar Corona Using Simulated EUV Images. arXiv preprint arXiv:2211.14879.

[2] SPACE WEATHER PREDICTION CENTER NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION. (2023, March 17). G2 (moderate) storm levels reached 15 March, 2023. G2 (Moderate) Storm Levels Reached 15 March, 2023 | NOAA / NWS Space Weather Prediction Center. https://www.swpc.noaa.gov/news/g2-moderate-storm-levels-reached-15-march-2023

[3] Caplan, R. M., Downs, C., & Linker, J. A. (2016). Synchronic coronal hole mapping using multi-instrument EUV images: data preparation and detection method. The Astrophysical Journal, 823(1), 53.

[4] Mildenhall, B., Srinivasan, P. P., Tancik, M., Barron, J. T., Ramamoorthi, R., & Ng, R. (2021). Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1), 99–106.