PEDM: A 3D Position Encoding Diffusion Model for Industrial Cracking Furnace Scalar Field Data Generation

Traditional computational fluid dynamics methods are time-consuming to obtain steady-state scalar fields by iteratively solving partial differential equations. Therefore, many scholars have adopted deep learning methods to construct data-driven surrogate models for more efficient generation of scalar fields. However, unlike the common image data usually used for deep learning modeling, the data used for the surrogate model are results of the computational fluid dynamics simulation models, which have irregular grids. Therefore, inputting the grid data into the deep learning model directly will cause difficulties in model training due to the unpreserved spatial location relationships. Auxiliary grids are traditionally used to pixelize the original irregular grid data and train the model. However, the resolution of the auxiliary grids is difficult to decide, which will result in either the information loss or the increase of computational complexity. In this paper, a 3D position encoding diffusion model (PEDM) is proposed to address the problem of the loss of spatial positional relationships in the grid data, by introducing the grid position encoding. The model uses U-net to learn feature information from the field data and utilizes spatial location within the original grids to encode the position of noised data through MultiLayer Perceptron, providing location information based on the global receptive field of the attention mechanism. This allows the network to learn the distribution of the field data better. Furthermore, the PEDM method is applied to an industrial cracking furnace for field data generation. The average normalized mean absolute error for the field data in the test data set is 0.1295%, indicating sufficient prediction accuracy. The method provides a promising avenue for generating 3D field data in industrial applications, facilitating visualization of reaction processes, virtual sensor deployment, and exploration of design and optimization spaces.