Physics-Informed Deformable Gaussian Splatting: Towards Unified Constitutive Laws for Time-Evolving Material Field

TL;DR

PIDG addresses the lack of physical consistency in monocular dynamic 3D scene reconstruction by embedding constitutive laws into a deformable Gaussian Splatting framework. It introduces a time-evolving material field and Lagrangian particle flow matching within a 4D decomposed hash space to achieve physically plausible and generalizable dynamics. Experiments on synthetic and real datasets show improved physical consistency and dynamic reconstruction quality, with evidence of better flow alignment and stress/velocity estimation. The approach provides a path toward unified constitutive laws in implicit 3D scene representations and highlights trade-offs in computation and boundary condition assumptions.

Abstract

Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for dynamic novel-view synthesis from monocular video input. However, purely data-driven 3DGS often struggles to capture the diverse physics-driven motion patterns in dynamic scenes. To fill this gap, we propose Physics-Informed Deformable Gaussian Splatting (PIDG), which treats each Gaussian particle as a Lagrangian material point with time-varying constitutive parameters and is supervised by 2D optical flow via motion projection. Specifically, we adopt static-dynamic decoupled 4D decomposed hash encoding to reconstruct geometry and motion efficiently. Subsequently, we impose the Cauchy momentum residual as a physics constraint, enabling independent prediction of each particle's velocity and constitutive stress via a time-evolving material field. Finally, we further supervise data fitting by matching Lagrangian particle flow to camera-compensated optical flow, which accelerates convergence and improves generalization. Experiments on a custom physics-driven dataset as well as on standard synthetic and real-world datasets demonstrate significant gains in physical consistency and monocular dynamic reconstruction quality.

Figures (16)

• Figure 1: Physics-Informed Deformable Gaussian Splatting achieves physically consistent and generalisable monocular dynamic novel-view synthesis effects, performing excellently in physical scenarios such as fluid dynamics and elastic mechanics.
• Figure 2: Overview. It integrates dynamic reconstruction in the canonical hash space (Sec. \ref{['sec:Method']}.1), physics-informed Gaussian representation (Sec. \ref{['sec:Method']}.2), and Lagrangian particle flow matching (Sec. \ref{['sec:Method']}.3) to achieve differentiable and physically consistent monocular dynamic video reconstruction. Training architecture can be found in Supp. Sec. C.
• Figure 3: Forward vs Backward optical flow decomposition.
• Figure 4: The visual results on the PIDG dataset.
• Figure 5: The visual comparison between PIDG (Ours) and MotionGS on the HyperNeRF dataset.