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

TL;DR

NeFTY introduces a differentiable physics-based neural network framework for accurate, label-free 3D inverse heat conduction imaging, outperforming existing methods in synthetic and real thermography data.

Contribution

NeFTY employs a hard-constrained neural field approach with differentiable PDE solving, enabling precise 3D thermal tomography without boundary labels.

Findings

NeFTY outperforms soft PINNs and voxel-baselines in synthetic benchmarks.

NeFTY achieves superior defect segmentation and depth estimation on real thermography data.

The framework enables efficient GPU-based 3D inverse heat conduction reconstruction.

Abstract

Inverse problems for stiff parabolic partial differential equations (PDEs), such as the inverse heat conduction problem (IHCP), are severely ill-posed: the forward map rapidly damps high-frequency interior structure before it reaches the boundary. Soft-constrained physics-informed neural networks (PINNs), which embed the PDE as a residual penalty, suffer from gradient pathology in this regime and tend to fit boundary measurements while leaving the interior field essentially untouched. We propose Neural Field Thermal Tomography (NeFTY), a hard-constrained neural field framework for label-free three-dimensional inverse heat conduction. NeFTY represents the unknown diffusivity as a continuous coordinate-based neural network, and at every optimization step passes the candidate field through a differentiable implicit-Euler heat solver with harmonic-mean interface flux, so that the governing PDE holds exactly on the discretization rather than as a soft penalty. Adjoint gradients propagate the surface reconstruction error back to the network weights at solver-level memory cost, making test-time inversion tractable on a single GPU. Across synthetic 3D benchmarks, NeFTY substantially outperforms soft-constrained PINN variants and a voxel-grid baseline on label-free volumetric recovery, and it transfers to real thermography data, surpassing classical signal-processing baselines in both defect segmentation and depth estimation. Additional details at https://cab-lab-princeton.github.io/nefty/