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The papers

The series has two published papers so far. Both solve an inverse problem of scientific sensing without training data: a coordinate neural field is optimized for one measurement through a differentiable model of the instrument. They differ in the instrument, in the geometry of the unknown, and therefore in the representation that works.

NeTMY NeFTY
paper Neural Fields for NV-Center Inverse Sensing Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation
arXiv 2605.13988 2603.11045
instrument widefield NV-center array reading magnetic-noise spectra infrared camera after a laser flash (pulsed thermography)
unknown spin density ρ ≥ 0 and Larmor field ωL (2-D) thermal diffusivity α ∈ [αmin, αmax] (3-D)
geometry of the unknown sparse point-like sources piecewise-constant defects in a (layered) bulk
physics FFT convolution with tensor power-summed dipolar kernels × Lorentzian (F2) implicit-Euler finite volumes, harmonic-mean faces, discrete adjoint
representation gated softplus head, support-masked Larmor head, annealed Fourier features, two-stage multiscale bounded sigmoid head, annealed Fourier features, isotropic TV
failure it explains center collapse of free-density solvers PINNs fit the surface data but not the interior
nefi instance nv_relaxometry thermal_tomography

NeTMY — Neural Fields for NV-Center Inverse Sensing

Zhixuan Zhao, Tao Zhong, Yixun Hu, Nathalie P. de Leon, Christine Allen-Blanchette. arXiv:2605.13988, 2026.

A nitrogen-vacancy (NV) center in diamond senses the magnetic noise of nearby fluctuating spins; a widefield array turns that into a noise spectrum at every pixel. Recovering the sparse spin sources and their local Larmor frequencies from those spectra is nonlinear, spectrally coupled and strongly blurred. NeTMY shows that replacing the common scalar (coherent) forward approximation with a tensor power-summed dipolar operator changes the inverse landscape and exposes a center-collapse failure of free-density optimization, and it solves the problem with an amortization-free coordinate neural field: annealed positional encoding, multiscale optimization, a sparsity gate and spectrum-fidelity losses. Its mechanism analysis shows that the parameterization does not execute the raw density-space gradient — it smooths and redistributes updates, which is exactly what defeats the collapse.

In nefi: the F1 / F2 operators and the F3 direct simulator (nefi.instances.nv_relaxometry), the gated softplus and support-masked heads (nefi.fields.heads), log-MSE on normalized maps and the direct-density term (nefi.losses), the energy-anchored scale correction (post-processing), the eight scene classes and the localization metrics (Hungarian F1, sliced Wasserstein, GMSD); the center-collapse diagnostics (iter-0 gradient, energy barrier, filter-kernel rows) are general functions in nefi.diagnostics. configs/nv_relaxometry_paper.yaml holds Tables 5–7.

@article{zhao2026netmy,
  title   = {Neural Fields for {NV}-Center Inverse Sensing},
  author  = {Zhao, Zhixuan and Zhong, Tao and Hu, Yixun and de Leon, Nathalie P. and
             Allen-Blanchette, Christine},
  journal = {arXiv preprint arXiv:2605.13988},
  year    = {2026}
}

NeFTY — Neural Field Thermal Tomography

Tao Zhong, Yixun Hu, Dongzhe Zheng, Aditya Sood, Christine Allen-Blanchette. arXiv:2603.11045, 2026.

Inverse heat conduction is severely ill-posed: the forward map damps interior structure before it reaches the surface. Physics-informed networks that put the PDE into a soft residual penalty fit the boundary measurements while leaving the interior essentially untouched. NeFTY keeps the PDE exact on the discretization: at every step the candidate diffusivity field passes through a differentiable implicit-Euler heat solver with harmonic-mean interface fluxes, and adjoint gradients carry the surface error back to the network at solver-level memory cost. On synthetic 3-D benchmarks it outperforms soft-constrained PINNs and a voxel grid, and it transfers to real thermography data, where it beats classical signal-processing baselines in defect segmentation and depth estimation.

In nefi: the finite-volume stencil, the inner solvers and the discrete adjoint (nefi/operators/pde/, see Heat equation), the explicit substepped data simulator, the bounded head and isotropic TV, the soft-PINN, PPT and TSR baselines, the segmentation / depth metrics and the 2-D / 2.5-D projections of the real-data protocol. configs/thermal_tomography_paper.yaml holds Table 5.

@article{zhong2026nefty,
  title   = {Neural Field Thermal Tomography: A Differentiable Physics Framework for
             Non-Destructive Evaluation},
  author  = {Zhong, Tao and Hu, Yixun and Zheng, Dongzhe and Sood, Aditya and
             Allen-Blanchette, Christine},
  journal = {arXiv preprint arXiv:2603.11045},
  year    = {2026}
}

One recipe

Put side by side, the two methods are the same five pieces with different settings: field → hard physics → losses → curriculum → solver. nefi makes each piece a swappable component and adds the parts both papers needed but did not package — diagnostics that explain a result, a benchmark protocol with confidence intervals and an inverse-crime guard, and a representation layer that treats geometry as a design axis (The representation is the prior).

  • Reproduce: the server runbook lists the exact commands for the headline tables, their cost and the caveats to check first.
  • Trace: Paper → code mapping maps every equation, proposition and table to the code.
  • Caveats: Limitations and caveats lists the model-error floor, seed variation and the other effects to account for when comparing numbers.