SuNeRF-CME: Physics-Informed CME Reconstruction

• The paper introduces a physics-informed neural radiance field that recovers the 3D structure of CMEs from multi-view solar data with high fidelity.
• It leverages a continuous 3D+time representation integrating radiative transfer and plasma physics to analyze eruptive dynamics in both EUV and white-light regimes.
• The method bridges low-coronal source diagnostics and heliospheric tomography, offering a unified alternative to traditional stereoscopy, DEMT, and forward shell modeling.

Searching arXiv for the cited SuNeRF and SuNeRF-CME papers to ground the article in the latest relevant work. [arXiv search] Query: id:(Jarolim et al., 16 Sep 2025) OR id:(Jarolim et al., 2024) OR id:(Bintsi et al., 2022) OR id:(Vemareddy et al., 2015) SuNeRF-CME denotes the extension of Sun Neural Radiance Fields from global extreme-ultraviolet reconstructions of the solar corona to the reconstruction and analysis of coronal mass ejections. In the low-coronal formulation, it uses a continuous 3D+time radiance field of wavelength-specific emission and absorption to represent eruptive source regions in EUV. In the heliospheric formulation, it becomes a physics-informed Neural Radiance Field that reconstructs time-dependent electron density and velocity from coronagraphic total- and polarized-brightness data using Thomson-scattering image formation. Across both usages, the defining idea is that CME-related observables are line-of-sight integrals through an optically thin plasma, and that sparse multi-viewpoint imaging can be inverted by a neural implicit representation constrained by solar geometry, radiative transfer, and, in the coronagraphic case, basic plasma-physics priors (Jarolim et al., 2024, Jarolim et al., 16 Sep 2025, Bintsi et al., 2022).

1. Genealogy and conceptual scope

SuNeRF originated as a solar adaptation of Neural Radiance Fields for reconstructing the EUV corona from a limited number of viewpoints. The 2022 validation study established the core premise on simulated 193 Å data: a learned 3D emissivity-and-absorption field, trained only on near-ecliptic views, could reconstruct non-ecliptic viewpoints with a peak signal-to-noise ratio of 43.3 dB and a mean absolute relative error of 0.3%, motivating the idea of a “virtual instrument” for arbitrary heliocentric viewpoints (Bintsi et al., 2022).

The 2024 EUV study generalized this static validation into a time-dependent, multi-channel formulation. SuNeRF was defined as a fully connected SIREN network with input $(x,y,z,t)$ and channel-specific outputs $\epsilon(x,y,z,t)$ and $\kappa(x,y,z,t)$, trained on simultaneous observations from SDO and STEREO to produce a complete 3D representation of the uppermost solar layer in EUV. Within that study, CME relevance was explicit: the learned radiance field was described as a continuous 3D+time representation of the low corona in which erupting filaments, flare ribbons, post-flare loops, coronal holes, and coronal mass ejections can be analyzed volumetrically rather than by point triangulation alone (Jarolim et al., 2024).

The term acquired a more specific meaning in 2025 with “SuNeRF-CME: Physics-Informed Neural Radiance Fields for Tomographic Reconstruction of Coronal Mass Ejections,” which shifted the target domain from the low-coronal EUV source region to the heliosphere observed in white light. That framework reconstructs the full 3D, time-dependent electron density and velocity field of CMEs and the surrounding solar wind from multi-viewpoint coronagraphic observations, coupling a Thomson-scattering forward model to a neural implicit representation regularized by continuity, propagation direction, and speed constraints (Jarolim et al., 16 Sep 2025).

A common misconception is to treat SuNeRF-CME as a generic NeRF applied unchanged to solar data. The solar formulations replace terrestrial “color + density” rendering with physically motivated emissivity, absorption, or electron-density fields and evaluate synthetic observations by line-of-sight integration in an optically thin medium. Another misconception is that the approach depends on assumed solar symmetry. In the EUV formulation, no assumption of solar symmetry is enforced; the geometry is fully 3D, although sparse ecliptic viewpoints constrain the model unevenly in latitude (Jarolim et al., 2024).

2. EUV radiance fields for CME source-region reconstruction

In the EUV implementation, SuNeRF models the corona as a wavelength-specific radiance field. For each channel, the network is a fully connected SIREN with 8 layers, 512 neurons each, and approximately 2M parameters. Its inputs are four coordinates $(x,y,z,t)$; its outputs are the emission and absorption coefficients

$\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$

Training is performed separately for 171, 193, 211, and 304 Å, using known spacecraft geometries and observed image sequences (Jarolim et al., 2024).

For each image pixel, a ray is constructed from the observer position and viewing angle and traced through a coronal volume normalized to $1\,R_\odot$. The sampling range is from $-1.3$ to $+1.3\,R_\odot$ relative to Sun center, while rays intersecting the solar surface stop at $1.0\,R_\odot$ to enforce an opaque photosphere. Two-level sampling is used: a coarse network samples 64 points uniformly along the ray, and a fine network samples 128 additional points according to a probability distribution derived from coarse emission, plus the original 64 points (Jarolim et al., 2024).

The rendering model is a discrete radiative-transfer scheme appropriate for optically thin EUV emission with possible localized absorption: $$E = \epsilon \cdot ds, \qquad A = \exp(-\kappa \cdot ds),$$

$\epsilon(x,y,z,t)$0

Here $\epsilon(x,y,z,t)$1 is the spacing between sampled points, $\epsilon(x,y,z,t)$2, and the first point is fully transmitted. This formulation retains the line-of-sight integral structure that is central to solar EUV imaging and is particularly relevant for 304 Å, where filament and prominence plasma can introduce localized absorption (Jarolim et al., 2024).

To prevent bright active regions and flares from dominating optimization, intensities are scaled by

$\epsilon(x,y,z,t)$3

and the core loss is MSE between predicted and observed scaled pixels. A regularization term,

$\epsilon(x,y,z,t)$4

penalizes strong absorption above $\epsilon(x,y,z,t)$5 during full-disk training, suppressing spurious high-altitude dark structures. Global reconstructions use 14-day sequences at 1-hour cadence and typically $\epsilon(x,y,z,t)$6 iterations; CME analysis starts from a pre-trained global model and fine-tunes on a localized subframe at 1-minute cadence. This explicit temporal conditioning is central to the source-region version of SuNeRF-CME, because it allows the network to learn smooth evolution over both days and eruption-scale minutes (Jarolim et al., 2024).

The observational geometry is sparse in latitude. Synthetic tests use 32 ecliptic viewpoints with $\epsilon(x,y,z,t)$7 for training and 224 non-ecliptic viewpoints for testing; real data use SDO/AIA and STEREO/EUVI observations with approximately $\epsilon(x,y,z,t)$8 to $\epsilon(x,y,z,t)$9 latitude coverage but full $\kappa(x,y,z,t)$0 longitude coverage through spacecraft separation and solar rotation. This implies that the method is best constrained where rays from the available viewpoints traverse the volume, especially near the ecliptic (Jarolim et al., 2024).

3. CME source-region diagnostics in the 2012-08-31 eruption

The canonical EUV SuNeRF-CME case study is the 304 Å reconstruction of the filament eruption on 2012-08-31. The workflow is two-stage. First, a global 304 Å SuNeRF is trained on 14 days of multi-viewpoint data to establish a baseline 3D corona. Second, the model is cropped to a $\kappa(x,y,z,t)$1 subframe centered on the erupting filament at Carrington longitude $\kappa(x,y,z,t)$2 and latitude $\kappa(x,y,z,t)$3, the cadence is increased to 1 minute starting at 2012-08-31 19:30 UT, and the network is fine-tuned for an additional 100,000 iterations, approximately 4 epochs (Jarolim et al., 2024).

This reconstruction yields several CME-source diagnostics. SuNeRF-rendered images at the SDO viewpoint show the slow rise of the filament/prominence, rapid ejection into interplanetary space, and the formation of flare ribbons close to the solar surface together with post-flare loops. Height maps are obtained by computing the average distance from the solar center for all sample points along a ray, using channel-specific emission as a weight. In these maps, flare ribbons remain close to $\kappa(x,y,z,t)$4, while post-flare loops extend to about

$\kappa(x,y,z,t)$5

The same model also renders “total absorption” along each ray. Before eruption, the filament appears as a region of strong absorption; during eruption, the absorbing structure rises and then clears, indicating the ejection of dense plasma from the low corona (Jarolim et al., 2024).

Radial slices through the atmosphere provide an additional diagnostic representation. By extracting 2D slices along a fixed longitude crossing the erupting filament, the model displays emission versus height and absorption versus height as functions of time. These slices reveal post-flare loop evolution and track the rise and escape of absorbing filament material. The profiles show motion of the absorption ridge with height and time; this suggests that velocities of the rising plasma can be estimated from the reconstructed slices, although they were not explicitly quantified in the paper (Jarolim et al., 2024).

Within the source-region interpretation of SuNeRF-CME, the principal observables are therefore 3D emission morphology, emission-weighted height estimates, integrated absorption, and time-resolved radial slices. The method extends 2D EUV imaging by providing a volumetric, time-dependent representation of the low-coronal environment in which CME initiation occurs, while explicitly coupling emissive and absorbing plasma rather than reducing the event to sparse stereoscopic correspondences (Jarolim et al., 2024).

4. Physics-informed coronagraphic SuNeRF-CME

The 2025 framework reformulates SuNeRF-CME for coronagraphic white-light tomography. Instead of learning EUV emissivity and absorption, the network represents the log electron density and plasma velocity field: $\kappa(x,y,z,t)$6 The architecture is again a SIREN with 8 hidden layers and 512 neurons per layer. The raw outputs are post-processed to impose a radial background profile,

$\kappa(x,y,z,t)$7

and

$\kappa(x,y,z,t)$8

so that the learned field captures deviations from an $\kappa(x,y,z,t)$9 density falloff and nominal radial solar-wind outflow (Jarolim et al., 16 Sep 2025).

Image formation is based on Thomson scattering. For a line of sight $(x,y,z,t)$0, the polarized and total brightness are

$(x,y,z,t)$1

$(x,y,z,t)$2

with $(x,y,z,t)$3 the scattering angle and $(x,y,z,t)$4, $(x,y,z,t)$5 geometry- and limb-darkening-dependent functions. The discretized renderer uses 64 stratified samples and 128 hierarchical samples along each ray, with the additional samples concentrated where preliminary brightness estimates are large. This is the white-light analogue of NeRF-style coarse-to-fine rendering, but the radiometric kernel is the Thomson-scattering LOS integral rather than generic volume opacity (Jarolim et al., 16 Sep 2025).

The total loss combines image fidelity and physics-informed regularization. Data terms include a log-intensity MSE for total and polarized brightness and a loss on the polarization ratio $(x,y,z,t)$6. Physics terms impose the continuity equation,

$(x,y,z,t)$7

equivalently

$(x,y,z,t)$8

a radial-flow regularization

$(x,y,z,t)$9

and a velocity-range penalty that constrains $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$0 to a plausible solar-wind/CME range. The reported loss weights are $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$1, $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$2, and $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$3 (Jarolim et al., 16 Sep 2025).

The synthetic training set is derived from a GAMERA-Helio MHD simulation with a Gibson–Low CME, using the public CME challenge dataset associated with PUNCH mission test data. Observers are placed at 1 AU, at latitudes $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$4, $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$5, and $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$6, with longitudes every $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$7, yielding 54 viewpoints. The network is trained on all 75 timesteps of a $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$8 day interval. Each iteration samples 2048 rays for image rendering and 4096 random 3D points for physics losses, and a model trained from scratch converges in approximately 40 epochs or about 12 hours on four NVIDIA A100 GPUs (Jarolim et al., 16 Sep 2025).

5. Validation, performance, and uncertainty

The methodological lineage begins with simulated non-ecliptic reconstruction. The precursor validation study reported PSNR $\epsilon(x,y,z,t), \quad \kappa(x,y,z,t).$9 dB, SSIM $1\,R_\odot$0, MAE $1\,R_\odot$1, and ME $1\,R_\odot$2 for non-ecliptic viewpoints reconstructed from near-ecliptic training data. In the later multi-channel formulation, synthetic tests based on a PSI MHD simulation used 32 ecliptic viewpoints for training and 224 non-ecliptic viewpoints for evaluation, yielding averaged metrics across channels of PSNR $1\,R_\odot$3, SSIM $1\,R_\odot$4, MAE $1\,R_\odot$5, and ME up to $1\,R_\odot$6. The reported qualitative result was that simulated polar reconstructions were “almost identical” to ground truth, with the largest discrepancies near the limb and in highly structured active regions (Bintsi et al., 2022, Jarolim et al., 2024).

In the EUV formulation, uncertainty is estimated with deep ensembles. Five independent SuNeRF models with different random initial weights are trained, and the pixel-wise standard deviation of their rendered outputs is used as an uncertainty map. On synthetic data, this standard deviation correlates with the actual reconstruction error, with Pearson correlation $1\,R_\odot$7 and Spearman $1\,R_\odot$8. For real observations, uncertainty is larger, especially near the limb, in highly structured active regions, and in polar regions that are poorly constrained by ecliptic viewpoints. This is significant for CME source-region analysis because the same regions often host the most rapid topological changes (Jarolim et al., 2024).

The coronagraphic SuNeRF-CME study reports volumetric density-reconstruction metrics over snapshots 10–39. With all 54 viewpoints, the cross-correlation coefficient is $1\,R_\odot$9 and the relative MAE is $-1.3$0; with 19 ecliptic viewpoints, the values are $-1.3$1 and $-1.3$2; with three ecliptic viewpoints, $-1.3$3 and $-1.3$4; and with three polar-distributed viewpoints, $-1.3$5 and $-1.3$6. Even in sparse-view settings, the method reconstructs the three-part CME structure, deformed front, and internal plasma variations, while the most persistent errors concern background streamer placement and the outer shock-front edge (Jarolim et al., 16 Sep 2025).

For CME parameter estimation from two viewpoints with at least one observer within $-1.3$7 of the CME direction, the reported errors are $-1.3$8 in latitude, $-1.3$9 in longitude, $+1.3\,R_\odot$0 for shock-front velocity, $+1.3\,R_\odot$1 for center-of-mass velocity, and $+1.3\,R_\odot$2 for total mass. For far-side configurations, performance degrades, with velocity errors exceeding $+1.3\,R_\odot$3 and latitudinal errors exceeding $+1.3\,R_\odot$4, although propagation direction remains recoverable within about $+1.3\,R_\odot$5 longitude and $+1.3\,R_\odot$6 latitude. These results delimit the regime in which sparse-view SuNeRF-CME is reliable: the method remains informative with two viewpoints, but directional coverage relative to the CME trajectory matters strongly (Jarolim et al., 16 Sep 2025).

6. Relation to classical CME reconstruction and current limitations

SuNeRF-CME is positioned against three established classes of CME reconstruction. First, stereoscopy and triangulation, associated in the EUV context with Aschwanden, Inhester, Liewer, and Bemporad, require feature correspondence across images and are effective for localized loops or prominence features but struggle when a pixel integrates multiple structures along the same line of sight. Second, rotational tomography and DEMT, associated with Frazin, Vasquez, Franzin, and Cho, are powerful for quiescent coronal structure but have typically a temporal resolution of about 14 days and are not suited to regions characterized by fast dynamics. Third, forward shell modeling such as the Graduated Cylindrical Shell model of Thernisien et al. provides parametric CME morphology in coronagraph data; representative Sun–Earth applications couple such geometry to drag-based propagation, as in an Earth-directed magnetic-flux-rope study that used GCS fitting and DBM to relate source-region structure, 3D kinematics, and magnetic-cloud arrival at 1 AU (Jarolim et al., 2024, Vemareddy et al., 2015).

Relative to these methods, the EUV source-region version of SuNeRF-CME treats the whole emitting and absorbing volume rather than isolated points, while the coronagraphic version reconstructs a continuous 4D density-and-velocity field instead of fitting a predefined shell. The explicit use of line-of-sight radiative transfer in EUV and Thomson scattering in white light is a methodological distinction: the observation model is not an afterthought but the core of the inversion. This is why the approach can render arbitrary viewpoints once the neural field has been learned and why it can, in principle, bridge low-coronal source-region structure and heliospheric propagation within one representational framework (Jarolim et al., 2024, Jarolim et al., 16 Sep 2025).

Its limitations are equally explicit. In the EUV regime, training from scratch for a 14-day sequence requires days on multiple GPUs; the 2M-parameter network cannot capture all fine-scale structures perfectly; sparse latitude coverage leaves polar and far-off-plane morphology less constrained; height estimates are emission-weighted and can therefore misplace dark structures; and there is no explicit density/temperature inversion yet. In the heliospheric regime, background solar-wind reconstruction remains difficult with short time spans and limited viewpoints; event-specific training is computationally intensive; real-instrument effects such as vignetting, stray light, stars, noise, and cosmic rays remain to be incorporated; and very sparse coverage can still produce ambiguity for complex events (Jarolim et al., 2024, Jarolim et al., 16 Sep 2025).

The development trajectory is correspondingly clear. The EUV study proposed extension to coronagraph data, DEM-based density and temperature reconstruction, a continuous operational training scheme in which new frames are added and old ones truncated, and integration of additional non-ecliptic viewpoints such as Solar Orbiter/EUI. The later coronagraphic study identified application to real data, longer temporal sequences, solar-rotation constraints, and extensions from continuity to fuller MHD constraints as next steps. Taken together, these works define SuNeRF-CME not as a single fixed algorithm but as a research program: a physically informed neural-field approach to CME reconstruction that spans low-coronal initiation, volumetric source-region diagnostics, and heliospheric white-light tomography, with the long-term aim of advanced space-weather monitoring (Jarolim et al., 2024, Jarolim et al., 16 Sep 2025).