LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting

A splash lives for a fraction of a second: sheets tear into ligaments and droplets, appearance is view-dependent and nearly textureless, and little persists long enough to track. Reconstruction research has consequently focused on smoke, synthetic liquids, or gently deforming surfaces. To our knowledge, no synchronized multi-view dataset of splashing liquids exists. We therefore introduce a benchmark of 20 real scenes, from coherent streams to violent splashes, captured by seven synchronized, calibrated 4K cameras at 60 fps, with manually refined per-view liquid and container masks and fixed evaluation splits. We further present SplashSplat, built on a single principle: impose physical structure only where the observations can constrain it. Per-frame liquid SDFs fused from the masks provide the geometry, level-set transport between consecutive SDFs yields a coarse velocity field, and Lagrangian carriers advected along this flow, corrected against each new observation and reseeded where coverage is lost, decode local Gaussians for differentiable rendering. SplashSplat outperforms state-of-the-art dynamic Gaussian splatting methods on our real captures and on a synthetic benchmark, with physically more plausible motion and a lower training cost. The same representation supports temporal interpolation and style transfer without re-optimization.

Reconstructing dynamic human--object interaction scenes from monocular video is difficult because the human, manipulated object, and background obey different motion models while sharing the same pixels. Existing dynamic radiance-field and Gaussian-splatting methods often entangle these components, causing object motion to leak into the human or static scene, and monocular human reconstruction remains underconstrained in regions that are rarely observed. We present CoGS, a compositional Gaussian-splatting framework for monocular human--object scene reconstruction. CoGS decomposes the video into three coordinated branches: an articulated human initialized from a complete canonical prior, a rigid object field driven by an estimated object trajectory, and a static scene field regularized by weak scene-only planar primitives when available. A six-stage optimization schedule first stabilizes the human and object independently, then fuses them with the scene under full-image supervision, visibility-aware human anchoring, object silhouette and motion constraints, and delayed scene regularization. This design keeps each component responsible for its own geometry and motion while allowing photometric evidence to correct the final composite. Experiments on HOSNeRF and NeuMan show that CoGS improves both human--object interaction reconstruction and in-the-wild human--scene rendering, achieving stronger fidelity and perceptual quality across full-frame and human-focused evaluations. Code will be released upon publication.

Reconstructing dynamic 3D scenes from multi-view videos is a foundational task for robotics, AR/VR, and digital twins. While 3D Gaussian Splatting (3DGS) provides state-of-the art scene representation, its dynamic adaptations (4DGS) face significant challenges. Early MLP-based deformation models excel at interpolating within training frames but fail at temporal extrapolation --- important feature for forecasting in predictive systems. To address this, physically grounded approaches have been proposed to enable robust future forecasting, while, concurrently, semantic 4DGS methods have been developed for scene analysis and language-driven prompting. However, there is currently no framework that unites both physical consistency and semantic understanding. In this paper, we propose the first, to the best of our knowledge, unified 4DGS approach that is both physically grounded and semantically aware. Furthermore, to optimize computational efficiency, we introduce a novel rigid-body constraint mechanism. Instead of predicting the physical dynamics for every Gaussian particle, our model predicts the motion of a single anchor Gaussian per semantic object, updating the remaining Gaussians via relative transformations. This architectural design significantly accelerates novel view synthesis compared to an unconstrained baseline, while enabling object-accurate extrapolation and intuitive semantic interaction. Our project page: https://be2rlab.github.io/r5dgs/.