用数学算子让轨迹预测更准更快，还能看懂为什么这样预测。
KoopCast: Trajectory Forecasting via Koopman Operators
- 先猜目标位置，再用算子理论线性化非线性运动，分步优化。
- 在三个真实数据集上准确率领先，且推理延迟低。
- 适合需要高精度、可解释性与实时性的自动驾驶场景。
我们提出KoopCast，一种轻量高效的一般动态环境轨迹预测模型。该方法基于柯普曼算子理论，通过将轨迹提升至高维空间实现非线性动力学的线性表征。框架采用两阶段设计：首先，概率神经目标估计器预测长期可行目标，确定“去哪”；其次，基于柯普曼算子的精修模块融合意图与历史信息，在非线性特征空间中实现线性预测，决定“怎么去”。该双重结构不仅保证强预测准确性，还保留了线性算子的优良性质，同时忠实捕捉非线性动态。实验验证表明，该模型在ETH/UCY、Waymo Open Motion Dataset和nuScenes数据集上均表现出色，涵盖复杂多智能体交互与地图约束的非线性运动。跨基准测试中，KoopCast持续保持高预测精度，兼具模式级可解释性与实际效率。
原文摘要 · Abstract (English)
We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting trajectories into a higher-dimensional space. The framework follows a two-stage design: first, a probabilistic neural goal estimator predicts plausible long-term targets, specifying where to go; second, a Koopman operator-based refinement module incorporates intention and history into a nonlinear feature space, enabling linear prediction that dictates how to go. This dual structure not only ensures strong predictive accuracy but also inherits the favorable properties of linear operators while faithfully capturing nonlinear dynamics. As a result, our model offers three key advantages: (i) competitive accuracy, (ii) interpretability grounded in Koopman spectral theory, and (iii) low-latency deployment. We validate these benefits on ETH/UCY, the Waymo Open Motion Dataset, and nuScenes, which feature rich multi-agent interactions and map-constrained nonlinear motion. Across benchmarks, KoopCast consistently delivers high predictive accuracy together with mode-level interpretability and practical efficiency.
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