We reinterpret 4D Gaussian Splatting as a continuous-time dynamical system, where scene motion arises from integrating a learned neural dynamical field rather than applying per-frame deformations. This formulation, which we call EvoGS, treats the Gaussian representation as an evolving physical system whose state evolves continuously under a learned motion law. This unlocks capabilities absent in deformation-based approaches:(1) sample-efficient learning from sparse temporal supervision by modeling the underlying motion law; (2) temporal extrapolation enabling forward and backward prediction beyond observed time ranges; and (3) compositional dynamics that allow localized dynamics injection for controllable scene synthesis. Experiments on dynamic scene benchmarks show that EvoGS achieves better motion coherence and temporal consistency compared to deformation-field baselines while maintaining real-time rendering

翻译：我们将4D高斯溅射重新阐释为一个连续时间动力系统，其中场景运动源于对学习到的神经动力场的积分，而非施加逐帧形变。这一被我们称为EvoGS的表述，将高斯表示视为一个演化的物理系统，其状态在学习到的运动定律下连续演化。这释放了基于形变的方法所不具备的能力：(1) 通过对底层运动定律建模，实现从稀疏时间监督中进行样本高效学习；(2) 时间外推，能够在观测时间范围之外进行前向和后向预测；(3) 组合动力学，允许注入局部化动力学以实现可控场景合成。在动态场景基准上的实验表明，与基于形变场的基线方法相比，EvoGS在保持实时渲染的同时，实现了更好的运动连贯性和时间一致性。