KoopCast: Trajectory Forecasting via Koopman Operators

2025-09-18

AI Summary

To address the challenge of multi-agent trajectory prediction in complex dynamic environments, this paper proposes a lightweight two-stage probabilistic model grounded in the Koopman operator. The first stage employs Koopman linearization to model nonlinear agent dynamics, enabling probabilistic estimation of intent-to-goal mappings. The second stage operates in the high-dimensional linear Koopman space, decoupling goal prediction (spatial destination distribution) from motion trajectory generation, while jointly incorporating historical states and map-based constraints. The method uniquely balances linear tractability—enabling closed-form inference and end-to-end differentiability—with expressive nonlinear representation. It supports real-time deployment due to its computational efficiency. Evaluated on ETH/UCY, Waymo Open Dataset, and nuScenes, it achieves state-of-the-art accuracy while providing modality-level interpretability. This enhances interactive awareness and cross-scenario generalization capability without sacrificing inference speed or model compactness.

Technology Category

• Multiagent Systems: Multiagent Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Forecasting trajectories in dynamic environments using Koopman operators
• Predicting plausible long-term targets and refining motion paths
• Capturing nonlinear dynamics with linear representations for accuracy

Innovation

• Leverages Koopman operator theory
• Two-stage neural network design
• Linear prediction in nonlinear space