Enhancing high-resolution reconstruction of flow fields using physics-informed diffusion model with probability flow sampling

The application of artificial intelligence (AI) technology in fluid dynamics is becoming increasingly prevalent, particularly in accelerating the solution of partial differential equations and predicting complex flow fields. Researchers have extensively explored deep learning algorithms for flow field super-resolution reconstruction. However, purely data-driven deep learning models in this domain face numerous challenges. These include susceptibility to variations in data distribution during model training and a lack of physical and mathematical interpretability in the predictions. These issues significantly impact the effectiveness of the models in practical applications, especially when input data exhibit irregular distributions and noise. In recent years, the rapid development of generative artificial intelligence and physics-informed deep learning algorithms has created significant opportunities for complex physical simulations. This paper proposes a novel approach that combines diffusion models with physical constraint information. By integrating physical equation constraints into the training process of diffusion models, this method achieves high-fidelity flow field reconstruction from low-resolution inputs. Thus, it not only leverages the advantages of diffusion models but also enhances the interpretability of the models. Experimental results demonstrate that, compared to traditional methods, our approach excels in generating high-resolution flow fields with enhanced detail and physical consistency. This advancement provides new insights into developing more accurate and generalized flow field reconstruction models.