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

TL;DR

This paper introduces PIDG, a physics-informed extension of 3D Gaussian Splatting, which models dynamic scenes with physically consistent material points, improving reconstruction quality and physical accuracy.

Contribution

We propose PIDG, integrating physics constraints into 3D Gaussian Splatting to model time-evolving material properties and motion in dynamic scenes.

Findings

Enhanced physical consistency in dynamic scene reconstruction.

Improved monocular dynamic reconstruction quality.

Faster convergence and better generalization due to physics supervision.

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.