MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts

Mahmoud Selim, Sriharsha Bhat, Karl Henrik Johansson

Keywords: Meta Learning, Koopman Theory, Motion Planning

TL;DR: MetaKoopman is a Bayesian meta-learning method for the Koopman operator that enables fast, uncertainty-aware prediction and planning for nonlinear dynamics under distribution shifts.

Abstract: Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose **MetaKoopman**, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (*MNIW*) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios—including snow, ice, and mixed-friction conditions—as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: [https://mahmoud-selim.github.io/MetaKoopman/](https://mahmoud-selim.github.io/MetaKoopman/)

Primary Area: Reinforcement learning (e.g., decision and control, planning, hierarchical RL, robotics)

Submission Number: 28132