Physics-Informed Deformable Gaussian Splatting: Towards Unified Constitutive Laws for Time-Evolving Material Field
This work addresses the problem of improving physical realism in dynamic novel-view synthesis for computer vision and graphics applications, representing an incremental advancement by integrating physics into an existing representation method.
The paper tackles the challenge of capturing physics-driven motion in dynamic scenes using 3D Gaussian Splatting, proposing PIDG to incorporate physics constraints and optical flow supervision, resulting in significant gains in physical consistency and reconstruction quality on custom and standard datasets.
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.