Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for monocular dynamic-scene novel-view synthesis. However, purely data-driven approaches struggle to capture the diverse physics-driven motion patterns in real scenes. To bridge this gap, we propose a differentiable physics-informed deformable Gaussian splatting framework that unifies constitutive laws under continuum mechanics. Methodologically, we model each Gaussian particle as a Lagrangian material point with time-varying constitutive parameters, using 2D projections of 3D observations as proxy supervision. Specifically, we adopt static-dynamic decoupled 4D decomposed hash encoding to reconstruct geometry and motion efficiently. Subsequently, we enforce the Cauchy momentum residual as a physics constraint, enabling independent prediction of each particle’s velocity and constitutive stress via a physics-informed 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 existing synthetic and real-world benchmarks demonstrate gains in physical consistency and generalization for monocular dynamic scene reconstruction.