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

How can autonomous systems maintain accurate and reliable control when operating in non-stationary environments where dynamics—such as terrain friction, payload weight, or mechanical wear—shift unpredictably? The authors seek to bridge the gap between the structured efficiency of Koopman operator theory and the adaptive, data-efficient nature of meta-learning to enable real-time, uncertainty-aware decision-making.

MetaKoopman models nonlinear dynamics by lifting state-action pairs into a latent space where evolution is approximately linear. Instead of learning a static operator, the framework meta-learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator across diverse simulated environments. During deployment, the system uses recent trajectory segments to perform a closed-form Bayesian update, yielding a posterior distribution over the dynamics. This allows the model to quantify both epistemic (model-based) and aleatoric (noise-based) uncertainty. To facilitate real-time planning, the authors introduce a variational action encoder that enables efficient sampling of latent trajectories, bypassing the computational bottlenecks typical of complex model-based planners.

MetaKoopman consistently outperforms non-adaptive baselines in multi-step prediction accuracy and uncertainty calibration across various simulated distribution shifts, including changes in terrain slope and friction. In real-world field experiments involving a 37.5-ton autonomous truck and trailer, the model successfully adapted to harsh winter conditions—such as ice and mixed-friction surfaces—enabling safe evasive maneuvers and braking where static models failed. The inclusion of a meta-learned tempering factor, which modulates the influence of the prior during online adaptation, proved critical for maintaining responsiveness to rapid environmental changes.