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Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation

NeurIPS 2026 · Probabilistic and scientific modeling › Differential equations and PDEs · approach: Physics-informed neural network training · 0 citations (OpenAlex)

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Proposes NeFTY, a hard-constrained neural-field framework that inverts a 3D implicit-Euler heat solver with adjoint gradients to recover thermal diffusivity from surface-only thermography, outperforming soft-constrained PINNs on synthetic data and classical methods on real PVC data.

Problem

Label-free volumetric inverse heat conduction (IHCP) from surface temperature sequences is severely ill-posed, and soft-constrained PINNs fit boundary data while failing to recover the interior diffusivity field.

Approach

Represent diffusivity as a bounded coordinate MLP with Fourier features and frequency annealing, pass it through a differentiable implicit-Euler finite-volume heat solver with harmonic-mean interface flux so the PDE holds as a hard constraint, and compute gradients with a discrete adjoint at constant memory in time.

Key results

• On the synthetic homogeneous setting NeFTY reaches volumetric IoU 0.45 and PSNR 18.48 dB, while PINN variants stay near IoU 0.02 or below.
• On real PVC data NeFTY achieves 0.431 IoU and 0.597 Dice for 2D segmentation and 0.465 Abs Rel for 2.5D depth, the best label-free result on every metric.
• The discrete adjoint reduces peak GPU memory from 18.63 GB (autograd) to 21.9 MB on a 64x64x16 sample with matched simulation error.

Surprising findings

• Soft-constrained PINN variants fit surface data to high PSNR (~63 dB) yet recover near-zero volumetric IoU, showing low surface error does not imply correct interior recovery.
• The supervised Swin-UNETR collapses under synthetic-to-real domain shift.

Limitations

• Per-specimen test-time optimization is slower than supervised feedforward inversion.
• Quantitative recovery is attenuated inside very high-contrast voids.
• Real-data evaluation relies on projected 2D and 2.5D labels because no public 3D ground truth exists.

Experimental setup

Datasets: PhiFlow synthetic 3D diffusivity benchmark (1,000 samples) PVC-Infrared PVC-Depth

Benchmarks: Synthetic 3D benchmark (homogeneous and layered) PVC-Infrared PVC-Depth

Metrics: MSE PSNR SSIM IoU Dice Abs Rel RMSE delta < 1.25 Edge F1

Baselines: PINN SPINN Causal-PINN DCGD Grid Opt. U-Net (Sound-Only) PPT TSR Swin-UNETR

Builds on: PINN SIREN NeRF GradNorm DCGD

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