Physics-Informed Modeling for Wood Thermal Analysis and Prediction

2026-06-22

AI Summary

This study addresses the limitations of traditional building models that assume homogeneous thermal properties of wood, failing to capture its inherent spatial heterogeneity, as well as purely data-driven approaches that lack physical interpretability and are sensitive to noise. To overcome these challenges, the authors propose a novel paradigm integrating physical priors with deep learning, leveraging RGB images and thermal maps of wood samples. They embed the normalized two-dimensional steady-state heat conduction equation directly into the network architecture to enable pixel-level thermal response prediction. Two physics-informed architectures are introduced: PICNN, which incorporates physical constraints as soft penalty terms, and PInteCNN, which hard-codes an analytical heat conduction solver into its convolutional structure, thereby balancing accuracy, interpretability, and intra-species variability. Experiments on three real-world wood datasets—Poplar, Grandis-CC, and Grandis-RC—demonstrate that the proposed approach significantly outperforms purely data-driven models in both predictive accuracy and the extraction of physically meaningful parameters.

Abstract

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

Problem

• wood thermal analysis
• material heterogeneity
• physics-informed modeling
• thermal response prediction
• interpretable machine learning

Innovation

• Physics-Informed Neural Networks
• Thermal Property Prediction
• Wood Heterogeneity
• PDE-Constrained Learning
• Interpretable Deep Learning