用无散度的高斯点云重建流体速度场，更准更稳定。
LagrangianSplats: Divergence-Free Transport of Gaussian Primitives for Fluid Reconstruction
- 用无散度核函数参数化速度场，自然满足流体不可压缩性。
- 在合成与真实数据上优于当前最佳方法，运动一致性提升23%以上。
- 适合需要物理准确性的流体重模拟与分析场景。
从稀疏的2D视频观测中重构3D流体速度场是一个高度病态的逆问题，需同时满足运动传输一致性与流体物理规律。现有方法通常通过软约束施加这些限制，常导致精度下降和收敛困难。本文提出一种结构化强制约束的重建框架：采用连续无散度核表示速度场，驱动拉格朗日3D高斯点云（Gaussian Splatting）的运动。该设计从构造上保证了流体不可压缩性和长程传输一致性。为高效优化此类受限系统，我们引入新颖的滑动窗口机制，在保持可训练成本的前提下，沿有意义的时间跨度传播梯度。在合成与真实世界数据集上的实验表明，本方法在传输一致性和物理准确性上均优于当前最优基线，支持高质量流体重模拟与流动分析应用。
原文摘要 · Abstract (English)
Reconstructing 3D fluid velocity fields from sparse 2D video observations is a highly ill-posed inverse problem, demanding both transport consistency with observed motion and physical validity under fluid laws. Existing methods typically impose these constraints through soft penalties, often leading to compromised accuracy and convergence issues. We introduce a reconstruction framework that structurally enforces both constraints. Specifically, we parameterize the reconstructed velocity using a continuous Divergence-Free Kernel representation, driving the advection of a Lagrangian 3D Gaussian Splatting representation. This formulation intrinsically guarantees both flow incompressibility and long-range transport coherence by construction. To enable the efficient optimization of such a constrained system, we introduce a novel Sliding Window scheme that propagates gradients over meaningful temporal horizons while maintaining tractable training costs. Experiments on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art baselines in both transport consistency and physical accuracy, enabling applications such as high-quality re-simulation and flow analysis.
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