We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods, which rely on time-conditioned deformation networks and are limited to interpolation within a fixed time window, ODE-GS eliminates timestamp dependency by modeling Gaussian parameter trajectories as continuous-time latent dynamics. Our approach first learns an interpolation model to generate accurate Gaussian trajectories within the observed window, then trains a Transformer encoder to aggregate past trajectories into a latent state evolved via a neural ODE. Finally, numerical integration produces smooth, physically plausible future Gaussian trajectories, enabling rendering at arbitrary future timestamps. On the D-NeRF, NVFi, and HyperNeRF benchmarks, ODE-GS achieves state-of-the-art extrapolation performance, improving metrics by 19.8% compared to leading baselines, demonstrating its ability to accurately represent and predict 3D scene dynamics.

翻译：我们提出ODE-GS，一种创新方法，将三维高斯泼溅法与潜在神经常微分方程相结合，以实现动态三维场景的未来外推。现有动态场景重建方法依赖时间条件形变网络，且仅限于固定时间窗口内的插值，而ODE-GS通过将高斯参数轨迹建模为连续时间潜在动力学，消除了对时间戳的依赖。该方法首先学习插值模型，在观测窗口内生成精确的高斯轨迹，随后训练Transformer编码器将历史轨迹聚合为潜在状态，并通过神经ODE进行演化。最终，数值积分生成平滑且物理合理的未来高斯轨迹，支持任意未来时间戳的渲染。在D-NeRF、NVFi和HyperNeRF基准测试中，ODE-GS在外推性能上达到当前最优，相较于主流基线方法指标提升19.8%，充分证明其精准表示与预测三维场景动力学的能力。