KALIKO: Kalman-Implicit Koopman Operator Learning for Prediction of Nonlinear Dynamical Systems
Albert H. Li, Ivan Dario Jimenez Rodriguez Rodriguez, Joel Burdick, Yisong Yue, Aaron Ames
AI summary
Problem
Explicitly parameterizing Koopman embedding functions is difficult and prone to overfitting or poor forecasts, while existing data-driven methods often require complex multi-objective losses and careful tuning.
Approach
KALIKO reframes embedding learning as a Bayesian state estimation problem, using a Kalman filter and smoother to implicitly recover latent states governed by globally linear dynamics, trained end-to-end with a reconstruction loss.
Key results
- Accurately reconstructs nonlinear dynamics across canonical systems without explicit encoders
- Implicitly recovers interpretable Koopman eigenfunctions consistent with theory
- Outperforms baselines in open-loop prediction on high-dimensional PDE wave data
- Successfully stabilizes an underactuated manipulator in a demanding closed-loop control task
Why it matters
Provides a robust, parameter-tuning-free framework for learning linear latent dynamics, advancing data-driven control and prediction for complex robotics and engineering systems.
Abstract
Long-horizon dynamical prediction is fundamen- tal 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 representa- tional 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 con- sistent 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: stabi- lizing an underactuated manipulator’s payload by predicting and compensating for strong wave disturbances.