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Image Fidelity is Not Field Fidelity: Joint Thermodynamic Reconstruction and Error Localization in Neural Tomography

Alan Hsu, Jenna Samra, Alin Razvan Paraschiv, Liam Connor

arXiv:2609.28868v1cs.LGastro-ph.IMastro-ph.SR

TL;DR

Scientific tomography seeks latent 3D fields from indirect images, but image agreement cannot certify physical-field accuracy. CoroNeRF jointly reconstructs coronal density and temperature from multiview spectral intensities; in a controlled testbed, spectral ablations expose image-field discrepancies and seed instability ranks local error, though shared model mismatch can defeat consensus.

  • Problem

    In tomography, low 2D image error need not certify a correct latent 3D field, whose error is not directly supervised during training or verifiable against truth at deployment.

    Source: §1 · pp. 1–2

  • Method

    CoroNeRF jointly reconstructs 3D electron density and temperature from multiview forbidden-line intensities using a differentiable atomic-emission renderer.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    Limited-channel models can fit their available observations well while recovering substantially worse fields, and cross-seed instability ranks local error across tested matched-model conditions.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Image fidelity is not a sufficient certificate of thermodynamic-field fidelity, and seed-based localization is useful but does not guarantee correctness under shared model error.

    Source: §6 · p. 9, §5.2 · p. 9

    The evaluation is a controlled study on one static coronal scene, not a test of generalization across coronal states or probabilistic calibration.

    Source: §4 · p. 5

Abstract

from arXiv · show

Neural fields for scientific tomography are optimized from 2D images, but the actual quantity of interest is often a latent 3D physical field. Because the forward map is many-to-one, low 2D image error need not certify a correct 3D field. Moreover, the latent field is not directly supervised during training, and its error cannot be evaluated against truth at deployment. We develop CoroNeRF to jointly optimize 3D electron density and temperature fields directly from multiview, multiline intensities through a differentiable atomic-emission renderer. Using solar coronal tomography as a controlled testbed, we evaluate physical-field recovery and test whether cross-seed instability provides a ground-truth-free-at-inference indicator of local physical-field error. We underscore the following two observations. (i) Image fidelity is not field fidelity: spectral ablations show that limited-channel reconstructions can fit their available observations well while recovering substantially worse fields, whereas evaluation on a common richer probe exposes the discrepancy. (ii) Cross-seed instability ranks local physical-field error across tested matched-model conditions, supported by sparsification and physical signal-strength controls. Seed-deviation projections provide complementary directional validation, but shared forward-model mismatch can still produce incorrect cross-seed consensus. These results characterize joint thermodynamic recovery and the usefulness and limits of seed-based error localization in a controlled, single-scene solar tomography testbed.

1 INTRODUCTION

Scientific tomography seeks latent 3D physical fields from indirect 2D measurements, but image agreement alone cannot verify those fields when the forward map is non-injective. CoroNeRF jointly reconstructs coronal density and temperature from multiview spectral intensities, and the paper examines both spectral information limits and seed-based error localization.

1 INTRODUCTION

  • In scientific tomography, low 2D image-space error can coexist with an incorrect latent 3D field because non-injective, ill-conditioned forward maps allow distinct fields to produce similar measurements.The latent field is typically neither directly supervised during training nor verifiable against truth at deployment, making image agreement an unreliable validation signal.Source: §1 · pp. 1–2
  • Coronal density-temperature recovery is ill-posed because line-of-sight redistribution and insufficient spectral coverage can both leave measurements nearly unchanged.The latter arises because line-response functions are not jointly injective.Source: §1 · p. 2
  • CoroNeRF jointly recovers 3D electron density and temperature from multiview forbidden-line intensities through a differentiable atomic-emission renderer.All modeled lines share the same inferred physical state, coupling their reconstructions through their emission responses.Source: §1 · p. 2
  • Limited-channel reconstructions can fit available images well yet recover substantially worse physical fields, with a common richer probe exposing the discrepancy.Noise-view experiments also characterize recovery under reduced observational information.Source: §1 · p. 2
  • Cross-seed instability ranks local physical-field error across tested matched-model conditions, while shared forward-model mismatch can produce incorrect consensus.Seed-deviation projections provide complementary directional validation.Source: §1 · p. 2

2 RELATED WORK

Prior work spans classical coronal inversion, learned tomography, and uncertainty methods for neural radiance fields. CoroNeRF is positioned as a neural-field approach for joint coronal density-temperature recovery through multiline atomic-emission modeling, while investigating when seed instability reflects physical-field error.

2 RELATED WORK

  • Classical coronal methods reconstruct density from white-light images and density-temperature fields through EUV tomography, using explicit regularization or prior structure rather than learned neural representations with end-to-end nonlinear emission models.Examples include regularized least-squares reconstruction and EUV tomography.Source: §2 · p. 2
  • Neural inverse models span medical, flow, seismic, black-hole, thermal, and solar tomography; CoroNeRF is presented as the first neural-field framework to jointly recover coronal density and temperature from multiview forbidden infrared-line intensities.Prior solar methods include density reconstruction from polarized brightness (Asensio Ramos, 2023) and wavelength-specific EUV modeling.Source: §2 · p. 3
  • NeRF uncertainty methods estimate unobserved regions or distributions over radiance fields, while concurrent sparse-view CT work reports that ensemble spread can miss errors shared across members.CoroNeRF studies the complementary setting of coupled density-temperature recovery through nonlinear multiline emission responses and tests when cross-seed instability localizes error or fails under shared model mismatch.Source: §2 · p. 3

3 METHODOLOGY: DIFFERENTIABLE MULTILINE NEURAL TOMOGRAPHY

CoroNeRF fits a shared neural plasma field to multiview, multichannel line-intensity observations. Its differentiable renderer maps density and temperature to line intensities, and image-only optimization recovers the latent fields.

3 METHODOLOGY: DIFFERENTIABLE MULTILINE NEURAL TOMOGRAPHY

  • The neural plasma field jointly predicts log10 electron density and temperature, fitting absolute intensities across lines rather than first inverting line ratios.Diagnostic information enters through the emissivity responses, while multiview geometry constrains the 3D distribution.Source: §3 · p. 3
  • Training data pair each view-pixel ray with an observed multichannel intensity vector, with rays parameterized by origin, direction, and integration bounds.The ray dataset includes training views and their valid image pixels.Source: §3 · p. 3
  • The differentiable renderer evaluates channel-dependent emissivity from precomputed CHIANTI atomic-physics tables and integrates it along each camera ray to predict line intensity.The emissivity depends on density, temperature, and heliocentric radius.Source: §3 · p. 3
  • The neural field parameters are optimized using image supervision alone to recover latent electron-density and temperature fields.Line-of-sight integrals are computed by numerical quadrature at a fixed sampling resolution.Source: §3 · p. 3
  • Most experiments use a fixed-scale asinh image loss to compress intensity dynamic range and prevent bright channels from dominating.Among tested objectives, asinh-L1 yields lower field error than inverse-variance-weighted squared residuals.Source: §3 · p. 4

4 EXPERIMENTAL SETUP AND EVALUATION

The study uses synthetic multiview observations from one static coronal scene and evaluates recovery on a held-out view arc. The controlled setup uses four spectral channels, while the conclusions are bounded to within-scene recovery and error localization.

4 EXPERIMENTAL SETUP AND EVALUATION

  • Figure 1 presents four spectral-channel observations used to fit a neural plasma field through the differentiable renderer, yielding jointly recovered density and temperature fields.The channels are Fe XIII 1075/1080 nm and Si IX 2585/3935 nm.Source: Figure 1 · p. 4
  • The synthetic dataset is rendered from one PSI MAS coronal cube and uses 300 training views, with a held-out 30° evaluation arc and a 3° guard region.The master dataset contains 3000 evenly spaced equatorial views; the holdout is designed as a harder interpolation test than interleaved held-out views.Source: §4 · p. 4
  • The observational conditions vary noise multiplier, view count, channel set, and abundance-mismatch scale, with the canonical noisy condition using η = 9, 300 views, all four channels, and a = 1.The stated noise multiplier η = 9 corresponds to ×3σ.Source: §4 · p. 4
  • The joint-reconstruction model uses a multiresolution hash-grid encoder with separate density and temperature decoder heads.The encoder is described as Instant NGP-style.Source: §4 · p. 4
  • The evaluation is a controlled study of one static coronal scene, not probabilistic calibration or generalization across multiple coronal states.Synthetic generation and inversion use the same discretized renderer except for specified abundance perturbations.Source: §4 · p. 5

5 RESULTS

CoroNeRF jointly reconstructs coronal density and temperature from multiview spectral intensities, but image agreement alone can conceal field error. Across tested matched-model conditions, cross-seed instability ranks local field error, while shared model mismatch can still defeat ensemble consensus.

5.1 JOINT THERMODYNAMIC RECONSTRUCTION AND MEASUREMENT LIMITATIONS

  • In the density-only representation test given ground-truth temperature, the hash grid reduces inner-band MAE by more than 2× versus the MLP and about 4× versus classical grids.These comparisons isolate representation under a common emission renderer rather than benchmark complete tomography systems.Source: Figure 2 · p. 5
  • Four-channel joint reconstruction reaches inner-band MAEs of 0.039 dex for density and 0.014 dex for temperature, with added spectral responses reducing density–temperature degeneracies.A pair of lines drops density MAE by a factor of 5–10, and four lines further halve the error.Source: §5.1 · p. 6
  • Single-channel models can achieve lower held-out error on their own channels yet recover substantially worse density fields; a common four-channel probe largely restores the density-error ranking.Temperature shows the same discrepancy, although common-probe image error does not perfectly order temperature error across line sets.Source: Figure 4 · p. 6, §5.1 · pp. 6–7
  • With at least 100 views, field error remains low across tested noise levels; at 100 views, increasing noise scale from 1 to 25 raises MAE from 0.052 to 0.081.At 20 or fewer views, density MAE rises several-fold and severe angular undersampling increases noise sensitivity.Source: §5.1 · p. 7

5.2 CROSS-SEED INSTABILITY AS A GT-FREE-AT-INFERENCE ERROR-RANKING PROXY

  • Cross-seed instability ranks local density error across matched-model regimes, with Spearman correlations of 0.55–0.78; its association remains positive after controlling for signal strength.For high-noise ×9, σens has nAUSE 0.27 versus 0.52 for the inverse-emissivity baseline.Source: §5.2 · p. 8
  • Rank-9 seed-deviation spans capture 4.8–32.1% of density and 2.4–24.0% of temperature signed-error energy, above the 0.2% isotropic reference.Capture is strongest under severe view sparsity and modest under full coverage; mismatch can retain 5–58× enrichment over the isotropic expectation.Source: §5.2 · pp. 8–9
  • Directional overlap persists under split-seed evaluation, and unrotated capture exceeds the longitude-rotation null mean in every tested matched-model regime.The unrotated capture lies at the top of the tested rotation distribution in 11 of 12 field-condition combinations.Source: §5.2 · p. 9
  • Cross-seed instability is available without the true field, but errors shared by ensemble members are invisible to it, so consensus is not a correctness guarantee.Under tested Si abundance mismatch, localization degrades asymmetrically; the selected line set is informative, while arbitrary line selection remains future work.Source: §5.2 · p. 9

6 CONCLUSION

CoroNeRF jointly reconstructs coronal electron density and temperature from multiline observations, and the controlled synthetic testbed evaluates both field fidelity and cross-seed error ranking. The appendix describes the emissivity tables used to generate observations and render reconstructions.

6 CONCLUSION

  • The controlled testbed shows that image fidelity does not certify thermodynamic-field fidelity and evaluates cross-seed instability as a ground-truth-free-at-inference error-ranking proxy.Angular coverage mitigates sparse-view geometric degeneracies, while spectral coverage mitigates plasma-thermodynamic degeneracies.Source: §6 · pp. 9–10
  • Future work will test generalization and calibration across coronal states and noise realizations, extend to time-dependent and spectropolarimetric observations, and evaluate on DKIST or UCoMP data.The selected line set was chosen for informative coronal density and temperature response; conditioning under arbitrary line selections remains future work.Source: §6 · p. 10

A.1 GROUND TRUTH CORONA CUBE AND EMISSIVITY TABLE CONSTRUCTION

  • The emissivity lookup table uses CHIANTI 10.1 and pyCELP, retains scalar Stokes-I emissivity, and clamps queries outside its tabulated domain to the nearest boundary.Its radial domain spans approximately 1.001–10 R⊙, with farther line-of-sight samples using the 10 R⊙ boundary response; the same table supports synthetic observation generation and CoroNeRF rendering.Source: §A.1 · p. 14

A.2 SAMPLING GEOMETRY AND NUMERICAL QUADRATURE

The renderer samples camera rays through the normalized coronal volume, evaluates plasma emissivity, and integrates intensity along each line of sight. The appendix also specifies visualization projections, noise and abundance mismatch, and the multiresolution hash-grid representation.

A.2 SAMPLING GEOMETRY AND NUMERICAL QUADRATURE

  • Camera rays pass through an AABB, sample the neural plasma field at uniform intervals, query emissivity, and use a midpoint Riemann sum for line-of-sight intensity.Sightlines with impact parameter below 1 R⊙ are masked; the camera is approximately 215 R⊙ away and spans a 6 R⊙ field of view.Source: §A.2 · p. 14
  • At production step size 1/256, renders differ from a 4×-finer reference by 7.5% in relative L2 and 1.7 × 10^-3 in asinh image metric.The authors report convergence at roughly first-to-second order but do not claim discretization-independent field recovery.Source: §A.2 · p. 15

A.3 LOS VISUAL PROJECTIONS

  • For visualization, the authors use rendered field-space projections for intuition and latitude-longitude plots at fixed shell radii for metric evaluation.Column density is an additive line-of-sight quantity, whereas temperature is represented as an emissivity-weighted value because temperature is not additive.Source: §A.3 · p. 15

A.4 OBSERVATIONAL NOISE AND FORWARD MODEL MISMATCH

  • Training images receive heteroscedastic Gaussian noise, with η scaling the signal-dependent variance term; the controlled abundance mismatch scales both Si IX channels while Fe XIII remains unscaled.The mismatch scale a = 1 means no forward-model error, and held-out image-space evaluation uses noise-free synthetic views.Source: §A.4 · pp. 15–16

A.5 MULTIRESOLUTION HASH GRID MODEL

  • The multiresolution hash grid interpolates trainable features across spatial levels, whose concatenation helps mitigate collisions from the XOR hash.The fixed lookup table, ray geometry, and sampling remain fixed during optimization while gradients pass through the renderer and lookup table to the field parameters.Source: §A.5 · p. 16

B METRICS

The evaluation separates held-out rendered-image agreement from recovery of the latent fields, with field-space metrics designated as primary. Image metrics quantify intensity differences, while field metrics assess log-field errors on spherical shells.

B METRICS

  • Field-space metrics are primary because the goal is latent joint physical-field recovery rather than image synthesis.Image-space metrics compare rendered line-intensity images against held-out observations; field-space metrics compare reconstructed density and temperature against ground truth on spherical shells.Source: B METRICS · p. 17

B.1 IMAGE-SPACE METRICS

  • Image-space evaluation averages per-view, per-channel error metrics across views and channels, including PSNR and fixed-scale asinh error.The asinh metric is defined for signed intensities and behaves logarithmically at large magnitudes.Source: §B.1 · p. 17

B.2 FIELD-SPACE METRICS

  • Field-space metrics include mean absolute log error and absolute relative error on spherical shells, plus signed shell mean error for mismatch studies.The signed metric indicates whether reconstructed fields systematically overestimate or underestimate ground truth.Source: §B.2 · pp. 17–18

C.1 CROSS-SEED INSTABILITY AND CORRELATION ANALYSIS

The analysis tests whether cross-seed instability ranks local ensemble-mean field error when models share their architecture, data, and observation protocol. It examines pooled and within-shell associations, including adjustment for an emissivity-based signal-strength proxy.

C.1 CROSS-SEED INSTABILITY AND CORRELATION ANALYSIS

  • Cross-seed instability is a ground-truth-free-at-inference proxy: large values mark regions sensitive to training seeds under a fixed pipeline, while ensemble-mean error requires ground truth.The ensemble members share architecture, observational protocol, and training data, varying only their random seeds.Source: §C.1 · p. 18
  • The analysis tests whether instability–error rank association remains after controlling for inverse emissivity, a proxy for weak physical signal strength.Partial correlations are computed on rank-transformed variables; in mismatch conditions, the proxy uses nominal unscaled ground-truth emissivity.Source: §C.1 · p. 19
  • The study covers noiseless, sparse-view, high-noise, and abundance-mismatch regimes, using longitude-slice bootstrap resampling and unweighted inner-band samples.Resampling 30 longitude slices with replacement preserves dependence within each slice but does not explicitly model dependence between neighboring slices.Source: §C.1 · pp. 19–20
  • Within-shell correlations between cross-seed instability and absolute ensemble-mean error track pooled correlations in selected conditions, so the association is not solely explained by radial trend.The comparison uses three shells at 1.33, 1.61, and 1.89 R⊙, each containing 540 voxels.Source: §C.1 · p. 20, Table 4 · p. 21, Table 5 · p. 21

C.2 SPARSIFICATION ANALYSIS

The analysis tests whether cross-seed instability ranks field errors by removing voxels flagged as least trustworthy and tracking remaining error. It performs well against the oracle in matched-model regimes, but degrades toward random ranking under the strongest tested forward-model mismatch.

C.2 SPARSIFICATION ANALYSIS

  • A useful ranking removes voxels flagged as least trustworthy so average error falls; the oracle removes the largest errors first, while random ranking keeps MAE relatively flat.AUSE summarizes the gap to the oracle, and normalized AUSE compares ranking performance with random, where 0 is oracle-level and 1 is no better than random.Source: §C.2 · pp. 21–22
  • Across noiseless, high-noise, and sparse-view matched-model regimes, cross-seed instability tracks oracle sparsification closely and outperforms the emissivity proxy, but degrades toward random under strongest mismatch.Figure 10 covers the noiseless, high-noise, sparse-view, and forward-model-mismatch regimes; lower remaining MAE is better.Source: Figure 10 · p. 22, §C.2 · p. 23
  • Leave-one-seed-out correlation and nAUSE values remain within a comparably tight band, indicating the reported localization correlations are not artifacts of an individual seed.Table 8 reports the leave-one-out ranges for both density and temperature.Source: §C.2 · p. 23, Table 8 · p. 24

C.3 SEED-DEVIATION ERROR CAPTURE

Seed-deviation projections capture signed field-error energy beyond rank-matched isotropic expectations, with split-seed and longitude-rotation controls testing the alignment. The accompanying appendices report reproducibility, representation and loss comparisons, and compute requirements.

C.3 SEED-DEVIATION ERROR CAPTURE

  • High error capture may reflect same-ensemble reuse or shared smooth, low-frequency spatial modes, not only scene-specific alignment.Longitude rotations preserve radial and latitudinal structure while disrupting alignment; across matched-model conditions, unrotated capture exceeds the rotation-null mean except for the 100-view temperature reconstruction.Source: §C.3 · pp. 24–25
  • The cap values are substantially larger than the rank-matched isotropic expectation; the five-member group has numerical rank four under the same tolerance, yielding a 4/4320 ≈0.09% baseline versus 0.2% for the original Ecap rank-9 baseline.Source: §C.3 · p. 25

D.1 REPRODUCIBILITY

  • Nondeterministic hash-grid optimization means nominally identical seeds need not reproduce bitwise-identical trajectories, so comparisons should use within-study mean ± standard deviation.Small cross-table differences between nominally identical controls are not treated as scientific effects.Source: §D.1 · p. 26

D.2 DENSITY REPRESENTATION BASELINES

  • The multiresolution hash grid outperforms the MLP by more than 2× and the classical grid by about 4×; the two tested hash-table sizes achieve nearly identical field error.The meridional slice also shows hash-grid reconstructions maintaining radial structure farther out and lowering errors near the inner radial boundaries.Source: §D.2 · p. 27, Table 12 · p. 28, Figure 11 · p. 28

D.3 LOSS ABLATION STUDY

  • Under the tested protocol, pure asinh loss yields lower log-field MAE than Gaussian-only loss, but the ablation does not isolate transformation, residual-norm, and weighting effects.The Gaussian-only loss performs worst and the asinh-only loss best; hybrid losses fall between them.Source: §D.3 · pp. 28–29, Figure 12 · p. 29

D.4 COMPUTE AND RUNTIME

  • A single reconstruction takes about 3 GPU-hours and a ten-model ensemble about 30 aggregate GPU-hours; diagnostics such as cross-seed instability require only K forward evaluations.The ten reported localization conditions require approximately 300 aggregate GPU-hours.Source: §D.4 · p. 29
  • The batch-size and step-count pilot used an earlier density-only, noiseless configuration and should not support scientific conclusions about the later joint noise-view study.Field error varied modestly across the tested pilot settings.Source: §D.4 · p. 29

D.5 SPECTRAL CHANNEL ABLATION STUDY

The spectral ablation compares five channel configurations using field-space and image-space performance. It finds that good image-space fit can coexist with worse physical-field recovery.

D.5 SPECTRAL CHANNEL ABLATION STUDY

  • The four-line configuration achieves the lowest field errors, while the Si IX pair has the lowest image-space validation loss but higher physical-field errors.Table 15 summarizes the five experiment families; each is trained with three seeds.Source: Table 15 · p. 30
  • Having at least a pair of spectral lines substantially reduces radial field errors across 1.1–3 R⊙.Figure 14 reports field-space MAE as a function of radius; Figure 13 shows density and temperature reconstructions and signed residuals at three selected radii.Source: §D.5 · p. 30, Figure 13 · p. 31, Figure 14 · p. 32
  • Fewer-channel models can achieve lower observed-channel image error than the four-line model despite worse field recovery.Figure 15 plots 3D field-space MAE against 2D held-out image-space validation loss for individual seeds across spectral channel sets.Source: Figure 15 · p. 32

D.6 NOISE/VIEW ABLATION STUDY

The noise-view study varies observation noise and view count, while the abundance study tests a controlled Si IX forward-model mismatch. Rendered-view examples show selected projections of recovered quantities.

D.6 NOISE/VIEW ABLATION STUDY

  • With 300 views, increasing noise to ×25 only moderately degrades field recovery, whereas high noise combined with 20 views produces a failure mode.The study crosses four noise levels with four view counts; sufficient angular coverage retains robustness under strong heteroscedastic observation noise.Source: Figure 16 · p. 33, §D.6 · p. 33, Table 16 · p. 34

D.7 ABUNDANCE MISMATCH ABLATION STUDY

  • Scaling Si IX intensities by ±40% produces spurious sharp field features, and scaling below or above the correct value produces systematic signed density errors.The inversion renderer retains the nominal abundance scale while the synthetic observation scale varies.Source: Figure 18 · p. 35, Table 17 · p. 35, §D.7 · p. 35

D.8 RENDERED VIEWS

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