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.
Traffic accident reconstruction is a forensic inverse problem that requires recovering physically consistent motion from sparse and heterogeneous evidence. Existing learning-based approaches predominantly optimize for semantic plausibility or visual realism, rather than quantitative agreement with measurable geometry and dynamics. Here, we present TRACER, a training-free framework that formulates reconstruction as a closed-loop structured inference process. Instead of directly generating dense trajectories, our framework constructs and iteratively refines event-anchored motion hypotheses under geometric, kinematic, and interaction constraints, guided by structured case memory and consistency-driven diagnosis. This design enables incremental, interpretable corrections when evidence is insufficient, making the accident reconstruction process more aligned with the workflow of human experts. Experiments on real-world accident data show that TRACER achieves improved geometric fidelity, velocity consistency, and collision accuracy over both data-driven and physics-based baselines.