KoopCast: Trajectory Forecasting Via Koopman Operators
Jungjin Lee, Jaeuk Shin, Gihwan Kim, Joon Ho Han, Insoon Yang
AI summary
Problem
Forecasting dynamic agent trajectories is hindered by unobservable intentions and complex nonlinear motion, while current deep learning models are computationally heavy and lack the interpretability required for safety-critical deployment.
Approach
The framework first estimates plausible future goals using a probabilistic neural network, then lifts historical states and goals into a higher-dimensional space to predict trajectories via efficient linear Koopman operator propagation.
Key results
- Competitive minADE/minFDE accuracy across ETH/UCY, Waymo, and nuScenes benchmarks
- Spectral analysis confirms bounded spectral radii ensuring forecast stability and mode-level interpretability
- Inference latency reduced by up to 93.5% compared to deep learning baselines
- Generalizes effectively across pedestrians, vehicles, and cyclists in map-constrained environments
Why it matters
It enables reliable, real-time deployment in autonomous navigation by replacing opaque neural networks with a transparent, mathematically grounded linear dynamical model.
Abstract
We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environ- ments. 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.