# Physics-Informed Modeling for Wood Thermal Analysis and Prediction

arXiv: https://arxiv.org/abs/2606.23402 · HTML: https://mlsanity.com/paper/2606.23402/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 58 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics](https://mlsanity.com/paper/2205.03990/) (2022)
- [Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs](https://mlsanity.com/paper/2109.07143/) (2021)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networks](https://mlsanity.com/paper/2505.10949/) (2025)
- [Thermal Spread Functions (TSF): Physics-guided Material Classification](https://mlsanity.com/paper/2304.00696/) (2023)
- [A Multimodal Physics-Informed Neural Network Approach for Mean Radiant Temperature Modeling](https://mlsanity.com/paper/2503.08482/) (2025)
- [Deep Convolutional Ritz Method: Parametric PDE surrogates without labeled data](https://mlsanity.com/paper/2206.04675/) (2022)
- [Deep Thermal Imaging: Proximate Material Type Recognition in the Wild through Deep Learning of Spatial Surface Temperature Patterns](https://mlsanity.com/paper/1803.02310/) (2018)
- [Fully Differentiable Lagrangian Convolutional Neural Network for Physics-Informed Precipitation Nowcasting](https://mlsanity.com/paper/2402.10747/) (2024)
- [Deep Learning methodology for the identification of wood species using high-resolution macroscopic images](https://mlsanity.com/paper/2406.11772/) (2024)
- [Automated machine learning for physics-informed convolutional neural networks](https://mlsanity.com/paper/2407.06151/) (2024)
- [MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations](https://mlsanity.com/paper/2209.03151/) (2022)

## Built on by (most cited first, 1 of 1)

- [Seeing the Heat: Synthesizing High-Resolution Wood Thermal Responses from Optical Imagery](https://mlsanity.com/paper/2609.31737/) (2026)

## Abstract (arXiv)

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