Fast Subspace Fluid Simulation with a Temporally-Aware Basis SIGGRAPH North America 2025

Siyuan Chen1,2, Yixin Chen1, Jonathan Panuelos1, Otman Benchekroun1, Yue Chang1, Eitan Grinspun1, Zhecheng Wang1

1University of Toronto, 2Shanghai Jiao Tong University

Abstract

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of both spatial reduced order models (ROMs) as well as spectral decompositions.

We adapt DMD for graphics applications by reducing computational overhead, incorporating user-defined force inputs, and optimizing memory usage with randomized SVD. The integration of OptDMD and DMD with Control (DMDc) facilitates noise-robust reconstruction and real-time user interaction. We demonstrate the technique's robustness across diverse simulation scenarios, including artistic editing, time-reversal, and super-resolution.

Through experimental validation on challenging scenarios, such as colliding vortex rings and boundary-interacting plumes, our method also exhibits superior performance and fidelity with significantly fewer basis functions compared to existing spatial ROMs. Leveraging the inherent linearity of the DMD formulation, we demonstrate a range of diverse applications. This work establishes another avenue for developing real-time, high-quality fluid simulations, enriching the space of fluid simulation techniques in interactive graphics and animation.

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BibTeX

@article{chen2025dmd,
  title = {Fast Subspace Fluid Simulation with a Temporally-Aware Basis},
  author = {Siyuan Chen and Yixin Chen and Jonathan Panuelos and Otman Benchekroun and Yue Chang and Eitan Grinspun and Zhecheng Wang},
  year = {2025},
  journal = {ACM Transactions on Graphics},
}

Acknowledgements

We are grateful to Jonathan Chalaturnyk for illuminating discussions that shaped the early stages of this research. We thank Xinwen Ding for helpful proofreading feedback. This research was made possible with the administrative support of our lab's system administrator, John Hancock, and financial officer, Xuan Dam. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant RGPIN-2021-03733, whose funding made this work possible.