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.
从稀疏的2D视频观测中重建3D流体速度场是一个高度病态的反问题，既要求与观测运动保持传输一致性，又要求符合流体定律的物理有效性。现有方法通常通过软惩罚来施加这些约束，往往导致准确性受损和收敛问题。我们引入了一个在结构上强制执行这两种约束的重建框架。具体而言，我们使用连续的无散度核表示来参数化重建的速度，以驱动拉格朗日3D高斯泼溅表示的对流。这一公式在构造上本质上保证了流动的不可压缩性和长距离传输的一致性。为了实现此类约束系统的高效优化，我们引入了一种新颖的滑动窗口方案，在保持可处理训练成本的同时，在有意义的持续时间范围内传播梯度。在合成和真实数据集上的实验表明，我们的方法在传输一致性和物理准确性方面均优于最先进的基线，从而能够实现高质量重模拟和流场分析等应用。