# Neural Kinematic Bases for Fluids

arXiv: https://arxiv.org/abs/2504.15657 · HTML: https://mlsanity.com/paper/2504.15657/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Solving High-Dimensional PDEs with Latent Spectral Models](https://mlsanity.com/paper/2301.12664/) (2023)
- [CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations](https://mlsanity.com/paper/2206.02607/) (2022)
- [Learning Skeletal Articulations with Neural Blend Shapes](https://mlsanity.com/paper/2105.02451/) (2021)
- [DeePSD: Automatic Deep Skinning And Pose Space Deformation For 3D Garment Animation](https://mlsanity.com/paper/2009.02715/) (2020)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [Model reduction for the material point method via an implicit neural representation of the deformation map](https://mlsanity.com/paper/2109.12390/) (2021)
- [LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields](https://mlsanity.com/paper/2310.15907/) (2023)
- [Compressed Skinning for Facial Blendshapes](https://mlsanity.com/paper/2406.11597/) (2024)

## Abstract (arXiv)

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.