LagrangeGS models dynamic 3DGS as a non-conservative Lagrangian system
zhenjun_zhao · x · 2026-08-26
LagrangeGS formulates dynamic 3D Gaussian Splatting as a non-conservative Lagrangian system, fixing three issues of prior physics-aware extensions that merely fit velocity fields: physically inconsistent trajectories, lack of time-reversibility, and geometric collapse in long-term extrapolation. Key tricks: approximating the velocity-Hessian as an identity matrix to decouple millions of Gaussian particles and avoid costly inversions; restricting non-conservative forces to be time-independent for consistent backward integration; and local rigid alignment to regularize trajectories. Benchmarks show stable long-term extrapolation, consistent time reversal, and counterfactual physics prediction.
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