用物理约束提升木材热响应预测精度，兼顾准确与可解释性。
Physics-Informed Modeling for Wood Thermal Analysis and Prediction
- 将热传导方程作为先验嵌入神经网络，构建可解释的预测模型。
- 在三种真实木材样本上实现像素级热响应预测，误差低于传统数据驱动方法。
- 适合关注材料建模、物理增强深度学习的研究者与工程师。
木材材料具有复杂的空间异质性热属性，挑战了传统建筑中材料均质化的假设。尽管数据驱动方法可直接从木材RGB图像映射热响应，但其为不可解释的黑箱，易捕捉统计相关性而非热力学合理性，可能引入实验噪声。为此，我们提出融合偏微分方程（PDE）的物理信息深度学习框架，利用木材RGB图像和测温图预测空间异质木材的像素级热响应。具体采用两种方法：物理信息卷积神经网络（PICNNs），将归一化二维稳态热传导方程作为损失函数中的软约束；物理集成卷积神经网络（PInteCNNs），将解析近似-预测-校正求解器硬编码进CNN结构。基于杨木、大径向切片（Grandis-RC）及大横切片（Grandis-CC）三类真实木材样本构建多模态数据集进行验证。结果表明，引入物理归纳偏置能有效平衡预测精度、物理解释性与种内多样性，显著优于纯数据驱动方法，在复杂异质性处理与可解释参数提取方面表现更优。
原文摘要 · Abstract (English)
Wood materials exhibit complex, spatially varying thermal properties that challenge traditional architectural assumptions of material homogeneity. Although data-driven approaches can directly map wood RGB images to their corresponding thermal responses, they operate as uninterpretable black boxes that prioritize statistical correlation and may absorb experimental noise rather than thermodynamic plausibility. To address these limitations, we present physics-informed deep learning frameworks that integrate partial differential equations (PDEs) to predict pixel-level thermal responses of spatially heterogeneous wood materials using wood RGB images and testbed temperature maps. Specifically, we investigate two distinct approaches to enforcing a normalized 2D steady-state heat transfer equation derived from the general heat transfer equation: Physics-Informed Convolutional Neural Networks (PICNNs), which embed physics as a soft penalty term in the loss function, and Physics-Integrated Convolutional Neural Networks (PInteCNNs), which hard-code an analytical approximator-predictor-corrector solver directly into convolutional neural networks. To validate our proposed approaches, we collect three real-world multimodal datasets of Poplar, Grandis Cross-Cut (Grandis-CC), and Grandis Radial-Cut (Grandis-RC) wood samples. We further demonstrate that embedding physical inductive biases successfully balances predictive accuracy, physical interpretability, and intra-species diversity, outperforming data-driven approaches in handling complex wood material heterogeneity and enabling the extraction of interpretable physical parameters. Project: https://zekifayes.github.io/pim
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