FluidGS: Physics Informed Gaussian Splatting for Dynamic Fluid Reconstruction from Sparse Views

Dynamic fluid scene reconstruction remains challenging in multimedia applications and digital content creation due to complex motions and changing topology. While Neural Radiance Fields (NeRF) methods are computationally expensive and 3D Gaussian Splatting (3DGS) approaches struggle with fluid phenomena, we propose Fluid-GS, a flexible, efficient end-to-end framework for sparse-view fluid reconstruction that tightly couples density field modeling with velocity estimation via differentiable advection. Our key innovation is a hybrid Lagrangian-Eulerian Gaussian primitive representation that combines the rendering efficiency of 3DGS with physically-accurate fluid motion tracking on Eulerian grid, that enables us to formulate physics-informed constraints derived from Navier-Stokes equations, enforcing temporal coherence and fluid incompressibility. Moreover, to address the inherent challenges of sparse-view reconstruction, we introduce a fluid-specific Gaussian kernel constraint that preserves the spatial characteristics of fluid phenomena, and dynamically adjusts the anisotropic kernel of Gaussian primitives based on local velocity fields, preventing non-physical artifacts. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art methods in both reconstruction quality and computational efficiency.