KALIKO: Kalman-Implicit Koopman Operator Learning For Prediction of Nonlinear Dynamical Systems

TL;DR

KALIKO introduces a novel Kalman filter-based method to implicitly learn Koopman embeddings for nonlinear dynamical systems, enabling accurate long-term predictions and control without explicit basis selection.

Contribution

The paper proposes KALIKO, a Kalman filter-based approach that implicitly learns Koopman embeddings, improving prediction accuracy and interpretability in complex nonlinear systems.

Findings

Outperforms baselines in wave data prediction

Achieves high-quality reconstructions of latent dynamics

Successfully stabilizes an underactuated manipulator in simulations

Abstract

Long-horizon dynamical prediction is fundamental in robotics and control, underpinning canonical methods like model predictive control. Yet, many systems and disturbance phenomena are difficult to model due to effects like nonlinearity, chaos, and high-dimensionality. Koopman theory addresses this by modeling the linear evolution of embeddings of the state under an infinite-dimensional linear operator that can be approximated with a suitable finite basis of embedding functions, effectively trading model nonlinearity for representational complexity. However, explicitly computing a good choice of basis is nontrivial, and poor choices may cause inaccurate forecasts or overfitting. To address this, we present Kalman-Implicit Koopman Operator (KALIKO) Learning, a method that leverages the Kalman filter to implicitly learn embeddings corresponding to latent dynamics without requiring an explicit encoder. KALIKO produces interpretable representations consistent with both theory and prior works, yielding high-quality reconstructions and inducing a globally linear latent dynamics. Evaluated on wave data generated by a high-dimensional PDE, KALIKO surpasses several baselines in open-loop prediction and in a demanding closed-loop simulated control task: stabilizing an underactuated manipulator's payload by predicting and compensating for strong wave disturbances.