Three-Dimensional Thermal Tomography with Physics-Informed Neural Networks

Background: Accurate reconstruction of internal temperature fields from surface temperature data is critical for applications such as non-invasive thermal imaging, particularly in scenarios involving small temperature gradients, like those in the human body. Methods: In this study, we employed 3D convolutional neural networks (CNNs) to predict internal temperature fields. The network's performance was evaluated under both ideal and non-ideal conditions, incorporating noise and background temperature variations. A physics-informed loss function embedding the heat equation was used in conjunction with statistical uncertainty during training to simulate realistic scenarios. Results: The CNN achieved high accuracy for small phantoms (e.g., 10 cm in diameter). However, under non-ideal conditions, the network's predictive capacity diminished in larger domains, particularly in regions distant from the surface. The introduction of physical constraints in the training processes improved the model's robustness in noisy environments, enabling accurate reconstruction of hot-spots in deeper regions where traditional CNNs struggled. Conclusions: Combining deep learning with physical constraints provides a robust framework for non-invasive thermal imaging and other applications requiring high-precision temperature field reconstruction, particularly under non-ideal conditions.