Physics-Aware Fluid Field Generation from User Sketches Using Helmholtz-Hodge Decomposition

Abstract: Fluid simulation techniques are widely used in various fields such as film production, but controlling complex fluid behaviors remains challenging. While recent generative models enable intuitive generation of vector fields from user sketches, they struggle to maintain physical properties such as incompressibility. To address these issues, this paper proposes a method for interactively designing 2D vector fields. Conventional generative models can intuitively generate vector fields from user sketches, but remain difficult to consider physical properties. Therefore, we add a simple editing process after generating the vector field. In the first stage, we use a latent diffusion model~(LDM) to automatically generate initial 2D vector fields from user sketches. In the second stage, we apply the Helmholtz-Hodge decomposition to locally extract physical properties such as incompressibility from the results generated by LDM and recompose them according to user intentions. Through multiple experiments, we demonstrate the effectiveness of our proposed method.