标题： 使用傅里叶变换的热扩散波场使神经网络理解内部传热 显示英文标题

标题： Making neural networks understand internal heat transfer using Fourier-transformed thermal diffusion wave fields

摘要： 热传播由声子相互作用控制，并用偏微分方程（PDEs）进行数学描述，这些方程将热传输与材料的固有特性联系起来。传统的实验技术基于表面辐射来推断热响应，限制了它们全面解析地下结构和内部热分布的能力。此外，现有的热层析技术只能从每一层中拍摄一帧图像。物理信息神经网络（PINNs）最近作为解决传热中反问题的强大工具出现，通过将观测数据与物理约束相结合。然而，标准的PINNs主要专注于拟合给定的外部温度数据，而没有对未知的内部温度分布的明确了解。在本研究中，我们引入了一种赫姆霍兹信息神经网络（HINN），以预测内部温度分布，而无需内部测量。时域热扩散方程被转换到频域并成为伪赫姆霍兹方程。HINN将这个伪赫姆霍兹方程嵌入学习框架中，利用热场的真实和虚部。最后，逆傅里叶变换将真实部分和虚部带回时域，并可用于映射具有内部缺陷的三维热场。此外，进行了截断操作以提高计算效率，并采用了共轭对称性原理来修复被丢弃的数据。这种方法显著提高了预测精度和计算效率。我们的结果表明，HINN优于最先进的PINNs和反向热求解器，为材料科学、生物医学诊断和无损评估等应用中的非侵入式热成像提供了一种新解决方案。 显示英文摘要

摘要： Heat propagation is governed by phonon interactions and mathematically described by partial differential equations (PDEs), which link thermal transport to the intrinsic properties of materials. Conventional experimental techniques infer thermal responses based on surface emissions, limiting their ability to fully resolve subsurface structures and internal heat distribution. Additionally, existing thermal tomographic techniques can only shoot one frame from each layer. Physics-informed neural networks (PINNs) have recently emerged as powerful tools for solving inverse problems in heat transfer by integrating observational data with physical constraints. However, standard PINNs are primarily focused on fitting the given external temperature data, without explicit knowledge of the unknown internal temperature distribution. In this study, we introduce a Helmholtz-informed neural network (HINN) to predict internal temperature distributions without requiring internal measurements. The time-domain heat diffusion equation was converted to the frequency-domain and becomes the pseudo-Helmholtz equation. HINN embeds this pseudo-Helmholtz equation into the learning framework, leveraging both real and imaginary components of the thermal field. Finally, an inverse Fourier transform brings real-part and imagery-part back to the time-domain and can be used to map 3D thermal fields with interior defects. Furthermore, a truncated operation was conducted to improve computational efficiency, and the principle of conjugate symmetry was employed for repairing the discarded data. This approach significantly enhances predictive accuracy and computational efficiency. Our results demonstrate that HINN outperforms state-of-the-art PINNs and inverse heat solvers, offering a novel solution for non-invasive thermography in applications spanning materials science, biomedical diagnostics, and nondestructive evaluation.