3D dataset for thermal tomography

In this study, we explore the use of 3D convolutional neural networks (CNNs) for predicting internal temperature fields from the surface temperature, with a focus on applications where small temperature gradients, similar to those in the human body, are present. The network accuracy was evaluated under both ideal and non-ideal conditions which include noise and background temperature effects. In non-ideal scenarios, the network accurately reconstructed the 3D temperature field for small phantoms (e.g., 10 cm in diameter). However, as the size of the domain increased, the network's predictive capacity diminished, particularly in regions far from the surface. To address this limitation, we introduced statistical uncertainty during training, simulating non-ideal conditions, in combination with a physics-informed loss function which embed the heat equation directly into the training process. This combination can improve the model's performance, particularly in noisy environments, where traditional CNN architectures failed to reconstruct hot-spots in deeper regions. Our results suggest that combining deep learning with physical constraints offers a robust framework for non-invasive thermal imaging and other applications requiring high-precision temperature field reconstruction.To generate synthetic data for thermal tomography, we solve the heat equation within a cylindrical region representing a phantom. The phantom consists of a medium with conductivity similar to that of the human body, containing cylindrical hotspots, which simulate regions of varying thermal activity. The boundary conditions applied to the cylindrical phantom are convective boundary conditions. At the boundary, the heat flux is proportional to the temperature difference between the surface of the phantom and the surrounding ambient air. The value of the thermal conductivity of the medium was chosen to be 0.5 W/(mk) and the heat convection (used in the boundary condition-cooling from air) = 7.5 W/(m$^2$K).The dataset provided is composed of the training, validation and testing sets. Files x_train, x_validation and x_test provide the input to the CNN which is a representation of the 3D surface temperature of a cylindrical phantom. Equivalently the y_train, y_validation and y_test is the actual 3D temperature field resulting from the solution of the heat equation.