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

2025-07-12

AI Summary

This work addresses the challenge of simultaneously achieving physical fidelity and interactive controllability in sketch-driven fluid field generation. We propose a two-stage generative framework: first, a latent diffusion model (LDM) synthesizes an initial vector field from a user-provided sketch; second, local physics-based correction is performed via Helmholtz–Hodge decomposition to rigorously enforce incompressibility and other fluid-dynamical constraints. By embedding physical priors directly into the generation pipeline—while preserving the user’s sketch intent—the method unifies intuitive interactive design with mathematical accuracy. Experiments demonstrate that our approach consistently produces visually plausible and physically consistent 2D incompressible flow fields across diverse sketch inputs, significantly outperforming existing purely data-driven methods. This establishes a new paradigm for physics-guided generative design in fluid simulation.

Technology Category

• Humans and AI: Game Design — Procedural Content Generation & Storytelling
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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.

Problem

• Generating physically accurate fluid fields from sketches
• Maintaining incompressibility in user-designed vector fields
• Combining generative models with physics-aware decomposition

Innovation

• Uses latent diffusion model for initial field generation
• Applies Helmholtz-Hodge decomposition for physical properties
• Recomposes fields interactively based on user intentions