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 this https URL
| Comments: | 37 pages, 19 figures |
| Subjects: | Machine Learning (cs.LG); Materials Science (cond-mat.mtrl-sci); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Instrumentation and Detectors (physics.ins-det) |
| Cite as: | arXiv:2603.11045 [cs.LG] |
| (or arXiv:2603.11045v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.11045 arXiv-issued DOI via DataCite |
Submission history
From: Tao Zhong [view email]
[v1]
Wed, 11 Mar 2026 17:59:42 UTC (10,114 KB)
[v2]
Wed, 13 May 2026 18:32:32 UTC (13,500 KB)