# KoopCast: Trajectory Forecasting via Koopman Operators

arXiv: https://arxiv.org/abs/2509.15513 · HTML: https://mlsanity.com/paper/2509.15513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 74 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 30 of 52)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2005.08514/) (2020)
- [Transformer Networks for Trajectory Forecasting](https://mlsanity.com/paper/2003.08111/) (2020)
- [MotionLM: Multi-Agent Motion Forecasting as Language Modeling](https://mlsanity.com/paper/2309.16534/) (2023)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Latent Variable Sequential Set Transformers For Joint Multi-Agent Motion Prediction](https://mlsanity.com/paper/2104.00563/) (2021)
- [Back to MLP: A Simple Baseline for Human Motion Prediction](https://mlsanity.com/paper/2207.01567/) (2022)
- [Uncertainty-aware Short-term Motion Prediction of Traffic Actors for Autonomous Driving](https://mlsanity.com/paper/1808.05819/) (2018)
- [Remember Intentions: Retrospective-Memory-based Trajectory Prediction](https://mlsanity.com/paper/2203.11474/) (2022)
- [An LSTM Network for Highway Trajectory Prediction](https://mlsanity.com/paper/1801.07962/) (2018)
- [M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction](https://mlsanity.com/paper/2202.11884/) (2022)
- [Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANs](https://mlsanity.com/paper/1904.09507/) (2019)
- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Trajectory Forecasts in Unknown Environments Conditioned on Grid-Based Plans](https://mlsanity.com/paper/2001.00735/) (2020)
- [MANTRA: Memory Augmented Networks for Multiple Trajectory Prediction](https://mlsanity.com/paper/2006.03340/) (2020)

## Abstract (arXiv)

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.