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

arXiv: https://arxiv.org/abs/2603.11045 · HTML: https://mlsanity.com/paper/2603.11045/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 66 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [Discretize-Optimize vs. Optimize-Discretize for Time-Series Regression and Continuous Normalizing Flows](https://mlsanity.com/paper/2005.13420/) (2020)
- [Fast-Grasp'D: Dexterous Multi-finger Grasp Generation Through Differentiable Simulation](https://mlsanity.com/paper/2306.08132/) (2023)
- [Dual Cone Gradient Descent for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2409.18426/) (2024)
- [GAGrasp: Geometric Algebra Diffusion for Dexterous Grasping](https://mlsanity.com/paper/2503.04123/) (2025)
- [ProxNF: Neural Field Proximal Training for High-Resolution 4D Dynamic Image Reconstruction](https://mlsanity.com/paper/2403.03860/) (2024)
- [Differentiable programming across the PDE and Machine Learning barrier](https://mlsanity.com/paper/2409.06085/) (2024)
- [Integrating AI in NDE: Techniques, Trends, and Further Directions](https://mlsanity.com/paper/2404.03449/) (2024)

## Built on by (most cited first, 2 of 2)

- [Neural Fields for NV-Center Inverse Sensing](https://mlsanity.com/paper/2605.13988/) (2026)
- [Image Fidelity is Not Field Fidelity: Joint Thermodynamic Reconstruction and Error Localization in Neural Tomography](https://mlsanity.com/paper/2609.28868/) (2026)

## Abstract (arXiv)

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/