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

Nondestructive evaluation (NDE) technologies are crucial in industrial and engineering fields, particularly for detecting defects in complex material structures. Traditional thermographic techniques often rely on 1D pixel-wise approximations that neglect lateral diffusion, leading to significant errors in estimating the size and depth of low-aspect-ratio defects. In recent years, with the rapid development of computer vision and scientific machine learning, implicit neural representations (such as NeRF) have shown great potential in solving physical inverse problems. However, existing Physics-Informed Neural Networks (PINNs) often struggle to converge in transient diffusion scenarios due to gradient stiffness issues. Therefore, combining neural fields with differentiable physics to achieve high-resolution 3D thermal diffusion reconstruction has become a hot research topic.

Accurately reconstructing the 3D thermal diffusion field in complex material structures is a core problem in nondestructive evaluation. Traditional thermographic techniques often rely on 1D pixel-wise approximations that neglect lateral diffusion, leading to significant errors in estimating the size and depth of low-aspect-ratio defects. Additionally, existing Physics-Informed Neural Networks (PINNs) often struggle to converge in transient diffusion scenarios due to gradient stiffness issues. These challenges make it particularly difficult to achieve high-resolution nondestructive evaluation in complex geometries and material structures.

NeFTY's core innovations lie in its integration of implicit neural representations with differentiable physics to solve the 3D inverse heat conduction problem. First, NeFTY parameterizes the 3D diffusivity field as a continuous neural field optimized through a rigorous numerical solver, enforcing thermodynamic laws as hard constraints. Second, NeFTY employs a discretize-then-optimize paradigm to effectively mitigate spectral bias and ill-posedness in inverse heat conduction. Additionally, NeFTY incorporates techniques such as positional encoding, frequency annealing, and harmonic mean to significantly improve model physical plausibility and defect boundary sharpness. These innovations allow NeFTY to generalize to novel geometries and materials without requiring large labeled datasets.

• �� NeFTY parameterizes the 3D diffusivity field as a continuous neural field optimized through a rigorous numerical solver, enforcing thermodynamic laws as hard constraints.

• �� NeFTY employs a discretize-then-optimize paradigm to effectively mitigate spectral bias and ill-posedness in inverse heat conduction.

• �� NeFTY incorporates techniques such as positional encoding, frequency annealing, and harmonic mean to significantly improve model physical plausibility and defect boundary sharpness.

• �� NeFTY's differentiable physics solver enforces thermodynamic laws during optimization, ensuring physical consistency of the results.

Experimental validation demonstrates that NeFTY significantly improves the accuracy of subsurface defect localization over baselines. Specifically, NeFTY achieves superior accuracy in recovering subsurface defect geometry through unsupervised test-time optimization, enabling generalization to novel geometries and materials without the need for labeled training data. The synthetic dataset used in the experiments includes samples with different geometries and material structures, ensuring the broad applicability of the experimental results. Ablation studies were also conducted to verify the impact of techniques such as positional encoding, frequency annealing, and harmonic mean on model performance.

NeFTY significantly improves the accuracy of subsurface defect localization over baselines. Specifically, NeFTY achieves superior accuracy in recovering subsurface defect geometry through unsupervised test-time optimization, enabling generalization to novel geometries and materials without the need for labeled training data. Compared to traditional Physics-Informed Neural Networks (PINNs), NeFTY addresses optimization pathologies by enforcing strict thermodynamic constraints, significantly enhancing defect localization accuracy. In experiments, NeFTY's defect localization accuracy (IoU) surpasses PINN by approximately 0.45.

NeFTY has broad application prospects in the field of nondestructive evaluation, particularly in high-resolution inspection of complex geometries and material structures. By parameterizing the 3D diffusivity field as a neural field, NeFTY can effectively identify and locate defects in materials, suitable for industries such as aerospace and automotive manufacturing. Additionally, NeFTY's differentiable physics solver enforces thermodynamic laws during optimization, ensuring physical consistency of the results, providing new technological pathways for industrial nondestructive evaluation.

NeFTY may face limitations in handling very deep or complex defects due to memory and computational resource constraints, as it requires high-resolution parameterization and optimization of the 3D diffusivity field. While NeFTY performs well on synthetic data, further validation is needed to ensure its robustness across different materials and geometries in real-world applications. Additionally, NeFTY's optimization process depends on the choice of initial parameters, which may affect convergence speed and result accuracy. Future research directions include applying NeFTY to more practical NDE scenarios to validate its robustness across different materials and geometries.