LagrangeGS: Non-Conservative Lagrangian System on Dynamic 3D Gaussian Splatting
2026-08-24 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors address problems in dynamic 3D Gaussian Splatting (3DGS), a method for creating realistic moving 3D scenes, by applying principles from physics called Lagrangian mechanics. They develop LagrangeGS, which models particle movements in a physically consistent way, fixing issues like unrealistic paths, trouble reversing time, and distortion during long runs. To make this practical, they simplify complex calculations and add methods to keep particle shapes stable. Their experiments show LagrangeGS allows for reliable long-term predictions, time-reversal, and physics-based editing of 3D scenes without needing to retrain the model.
Dynamic 3D Gaussian SplattingLagrangian mechanicsVelocity fieldsTime-reversibilityNon-conservative forcesHessian matrixParticle dynamicsPhysics-based editingLong-term extrapolationRigid alignment
Authors
Shogo Sato, Takuhiro Kaneko, Shoichiro Takeda, Tomoyasu Shimada, Riku Inoue, Kazuhiko Murasaki, Ryuichi Tanida
Abstract
Dynamic 3D Gaussian Splatting (3DGS) achieves photorealistic reconstruction of time-varying scenes, and recent physics-aware extensions improve extrapolation by explicitly predicting velocity fields. However, these extensions merely fit vector fields to visual deformations without satisfying Lagrangian mechanics, leading to three major issues: (i) physically inconsistent trajectories, (ii) lack of time-reversibility, and (iii) geometric collapse during long-term extrapolation. In this paper, we propose LagrangeGS, which formulates dynamic 3DGS as a non-conservative Lagrangian system. While this Lagrangian formulation fundamentally solves (i), a direct application of general LNNs to dynamic 3DGS requires a large velocity-Hessian inversion for millions of Gaussian particles. To overcome this computational bottleneck, we approximate the velocity-Hessian as an identity matrix, decoupling particle dynamics for computational tractability. For (ii), we restrict the non-conservative forces to be explicitly time independent, enabling consistent backward integration. Finally, to address (iii), we introduce local rigid alignment that regularizes particle trajectories. Extensive evaluations on dynamic scene benchmarks demonstrate that LagrangeGS enables stable long-term extrapolation, consistent time reversal, and counterfactual physics-based editing without retraining.