arXiv:2511.06299v3 Announce Type: replace 
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.

تم اقتراح إطار جديد يسمى Physics-Informed Deformable Gaussian Splatting (PIDG) لتحسين تقنية 3D Gaussian Splatting (3DGS) من خلال دمج أنماط الحركة المدفوعة بالفيزياء. تعالج هذه الطريقة الجسيمات الغاوسية كنقاط مادة لاغرانجية مع معلمات متغيرة زمنياً، مما يحسن دقة تمثيل المشاهد الديناميكية من خلال الإشراف بواسطة تدفق بصري ثنائي الأبعاد وبقايا زخم كوشي.

Se ha propuesto un nuevo marco llamado Physics-Informed Deformable Gaussian Splatting (PIDG) para mejorar el 3D Gaussian Splatting (3DGS) al incorporar patrones de movimiento impulsados por la física. Este método trata las partículas gaussianas como puntos materiales lagrangianos con parámetros que varían en el tiempo, mejorando la precisión de la representación de escenas dinámicas mediante supervisión por flujo óptico 2D y el residuo de momento de Cauchy.

Un nouveau cadre appelé Physics-Informed Deformable Gaussian Splatting (PIDG) a été proposé pour améliorer le 3D Gaussian Splatting (3DGS) en intégrant des motifs de mouvement guidés par la physique. Cette méthode considère les particules gaussiennes comme des points matériels lagrangiens avec des paramètres variant dans le temps, améliorant ainsi la précision de la représentation des scènes dynamiques grâce à une supervision par flux optique 2D et au résidu de moment de Cauchy.

A new framework called Physics-Informed Deformable Gaussian Splatting (PIDG) has been proposed to enhance 3D Gaussian Splatting (3DGS) by incorporating physics-driven motion patterns. This method treats Gaussian particles as Lagrangian material points with time-varying parameters, improving the accuracy of dynamic scene representation through supervision by 2D optical flow and the Cauchy momentum residual.

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

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