We propose mesh-free fluid simulations that exploit a kinematic neural basis for velocity fields represented by an MLP. We design a set of losses that ensures that these neural bases approximate fundamental physical properties such as orthogonality, divergence-free, boundary alignment, and smoothness. Our neural bases can then be used to fit an input sketch of a flow, which will inherit the same fundamental properties from the bases. We then can animate such flow in real-time using standard time integrators. Our neural bases can accommodate different domains, moving boundaries, and naturally extend to three dimensions.
@article{arxiv.2504.15657,
title = {Neural Kinematic Bases for Fluids},
author = {Yibo Liu and Zhixin Fang and Sune Darkner and Noam Aigerman and Kenny Erleben and Paul Kry and Teseo Schneider},
journal= {arXiv preprint arXiv:2504.15657},
year = {2025}
}