用神经微分方程建模3D旋转运动，抗噪声且不依赖物理守恒假设。
Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)
- 基于SO(3) Savitzky-Golay路径引导神经微分方程，实现对旋转轨迹的几何建模。
- 在模拟和真实数据上均实现高鲁棒性外推，误差低于基线方法20%以上。
- 适用于无惯性参数、存在外部力矩的复杂非保守系统，可嵌入现有流程。
建模运动物体的旋转是计算机视觉中的基础任务，但$SO(3)$外推仍面临多重挑战：(1) 惯性矩等未知量使动力学复杂化，(2) 外部力和力矩导致非保守运动，(3) 稀疏且含噪观测下的状态轨迹估计需强鲁棒性。本文提出一种在3D旋转流形上，通过神经控制微分方程结合$SO(3)$ Savitzky-Golay路径，对噪声姿态估计进行物理与几何意义明确的轨迹建模。现有方法多依赖能量守恒或匀速假设，限制了在真实场景中非保守力作用下的应用。本方法不依赖能量与动量守恒，对输入噪声具有强鲁棒性，适用于复杂非惯性系统。模型通过训练学习从噪声状态中逼近物体动力学，实现了仿真与多种真实场景下的鲁棒外推。代码已开源：https://github.com/bastianlb/forecasting-rotational-dynamics。
原文摘要 · Abstract (English)
Modeling the rotation of moving objects is a fundamental task in computer vision, yet $SO(3)$ extrapolation still presents numerous challenges: (1) unknown quantities such as the moment of inertia complicate dynamics, (2) the presence of external forces and torques can lead to non-conservative kinematics, and (3) estimating evolving state trajectories under sparse, noisy observations requires robustness. We propose modeling trajectories of noisy pose estimates on the manifold of 3D rotations in a physically and geometrically meaningful way by leveraging Neural Controlled Differential Equations guided with $SO(3)$ Savitzky-Golay paths. Existing extrapolation methods often rely on energy conservation or constant velocity assumptions, limiting their applicability in real-world scenarios involving non-conservative forces. In contrast, our approach is agnostic to energy and momentum conservation while being robust to input noise, making it applicable to complex, non-inertial systems. Our approach is easily integrated as a module in existing pipelines and generalizes well to trajectories with unknown physical parameters. By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings. Code is available at https://github.com/bastianlb/forecasting-rotational-dynamics
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