Reproduce “A Variational Optimal Transport Operator on Incompressible Flow” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Jinjin He, Shenyifan Lu, Sinan Wang, Zhiqi Li, Duowen Chen, Bo Zhu
VIOT learns a reusable operator for transporting densities between shapes rather than optimizing each pair separately. Given the current density, target, and time, an FNO predicts a stream function or vector potential whose curl yields a divergence-free velocity, then advances density repeatedly. On MNIST chain, VIOT reaches 0.0007 L2 error versus 0.0079 for EigenFluid; it is dataset-specific.
Key insights
- Hard incompressibility is more reliable than a soft divergence penalty: the spectral curl formulation achieved mean absolute divergence of 4.1×10^-6 versus 0.386 for the soft-penalty model in the reported MNIST comparison.
- The dissipation term is important for preventing high-frequency, unstable motion; removing it raised MPEG-7 relative error to about 0.73 and mean enstrophy to 204.
- Neural-operator resolution transfer is not automatic: grid spacing, spectral cutoffs, velocity units, and advection conventions must remain compatible across resolutions.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.