Background and Motivation Understanding fluid motion is crucial for comprehension of our environment and our interactions with it in the field of physics. However, traditional fluid simulation methods face limitations in practical applications due to high computational demands. In recent years, physics-driven neural networks have emerged as a promi...

Currently, there are significant challenges in studying the statistical and geometrical properties of particles carried by the fluid in turbulence. Despite outstanding efforts in theory, numerical simulations, and experiments over the past 30 years, there is still a lack of models that can realistically reproduce the statistical and topological fea...