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

2025-12-02

AI Summary

Addressing the challenge of long-term prediction for nonlinear, chaotic, and high-dimensional dynamical systems, this paper introduces KALIKO: a novel method that couples Kalman filtering with implicit Koopman operator learning—without requiring explicit encoders or hand-crafted basis functions. KALIKO automatically learns globally linear, interpretable dynamics in a latent space. By integrating recursive state estimation, it jointly optimizes implicit embedding and linear latent dynamics, balancing modeling accuracy and generalizability. Evaluated on high-dimensional wave data generated from partial differential equations (PDEs), KALIKO significantly outperforms state-of-the-art baselines. Furthermore, it successfully enables closed-loop stable control of an underactuated robotic manipulator subject to strong wave-induced disturbances, demonstrating its effectiveness and robustness in real-world control tasks.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Predicts nonlinear dynamical systems for long-horizon robotics and control tasks
• Learns implicit embeddings for latent dynamics without requiring an explicit encoder
• Stabilizes underactuated manipulators by predicting and compensating for wave disturbances

Innovation

• Implicitly learns embeddings using Kalman filter
• Avoids explicit encoder for latent dynamics
• Produces globally linear latent dynamics