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Physics-Informed Video Diffusion for Shallow Water Equations

MCML Authors

Yang Bai

→ Group Gitta Kutyniok
Mathematical Foundations of Artificial Intelligence

Gitta Kutyniok

Prof. Dr.

Principal Investigator

Mathematical Foundations of Artificial Intelligence

Abstract

Traditional fluid dynamics simulation pipelines combine numerical solvers with rendering, producing highly realistic results but at considerable computational cost. Diffusion-based generative video models offer a faster alternative, yet often ignore physical laws and thus fail to capture consistent dynamics. We propose a physics-informed video diffusion framework that jointly generates visual outputs and physical states. Unlike prior two-stage approaches that first simulate the physical variables and then render, we directly integrate physics constraints into the generative process, enabling simultaneous prediction of physical states and realistic videos without a separate rendering step. Built on the two-dimensional shallow water equations with terrain topography, our method produces temporally coherent water flow while maintaining physical plausibility. Experiments show that it outperforms purely data-driven video diffusion baselines in both realism and physical fidelity, while generating videos significantly faster than traditional simulation-plus-rendering pipelines.

inproceedings BEL+26