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

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.