用可微分物理框架实现无标签三维热成像反演，精准还原内部缺陷。
Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation
- 将热导率建模为坐标驱动的神经场，通过可微隐式欧拉求解器硬约束满足热传导方程。
- 在合成3D数据上显著优于软约束PINN和体素基线，在真实热成像数据中提升缺陷分割与深度估计性能。
- 适合从事无损检测、逆问题求解与物理引导神经网络研究者参考。
对于刚性抛物型偏微分方程（PDE）的反问题，如逆热传导问题（IHCP），存在严重不适定性：前向映射在信号传播至边界前快速衰减高频内部结构。软约束物理信息神经网络（PINNs）通过残差惩罚嵌入PDE，在此场景下易出现梯度病态，倾向于拟合边界测量而忽略内部场。本文提出神经场热断层成像（NeFTY），一种用于无标签三维逆热传导的硬约束神经场框架。NeFTY将未知热扩散率表示为连续的坐标依赖神经网络，并在每一步优化中通过带有调和平均界面通量的可微隐式欧拉热求解器传递候选场，使控制PDE在离散化上精确成立，而非作为软惩罚。伴随梯度以求解器级内存开销将表面重建误差反传至网络权重，使得单个GPU上的测试时反演成为可能。在多个合成3D基准上，NeFTY显著优于软约束PINN变体和体素网格基线，在无标签体积恢复任务中表现优异；并成功迁移至真实热成像数据，在缺陷分割与深度估计上超越经典信号处理基线。
原文摘要 · Abstract (English)
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/
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