AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression
2026-06-03 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors developed AdaKoop, a method to quickly understand and predict complex patterns that change over time in data streams. They use Koopman operator theory to turn complicated nonlinear changes into simpler linear ones, making calculations faster and more stable. AdaKoop also adapts when sudden changes happen in the data by detecting shifts and updating its model on the fly. Tests on many datasets showed it predicts better and runs more efficiently than current methods.
Koopman operator theorynonlinear dynamicsnonstationary datastreaming algorithmreproducing kernel Hilbert space (RKHS)statistical hypothesis testingreal-time forecastinglatent vectorsincremental learning
Authors
Naoki Chihara, Ren Fujiwara, Yasuko Matsubara, Yasushi Sakurai
Abstract
Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency. However, nonlinear dynamics are so complex that capturing dynamically changing nonlinear patterns and utilizing them for downstream tasks under strict time constraints is nontrivial. To bridge the gap between nonlinear complexity and computational tractability, this study applies Koopman operator theory, which states that nonlinear dynamics can be represented as linear transitions in an infinite-dimensional space. Building upon finite-dimensional approximations of this operator, we present AdaKoop, an efficient streaming algorithm for modeling nonlinear dynamics over nonstationary data streams. Our approach utilizes a probabilistic framework grounded in Koopman operator theory, treating both raw observations and reproducing kernel Hilbert space (RKHS) features as emissions from latent vectors. This dual-view formulation allows nonlinear dynamics to be expressed as a tractable linear system. Therefore, AdaKoop enables the efficient and stable modeling of nonlinear dynamics in a streaming fashion, avoiding the prohibitive computational costs of iterative nonlinear optimization. Furthermore, to address nonstationarity in data streams, AdaKoop adaptively detects the switching of patterns via statistical hypothesis testing for abrupt pattern shifts and incrementally updates model parameters to handle continuous changes. Extensive experiments on a total of 71 practical benchmark datasets across various domains demonstrate that AdaKoop outperforms state-of-the-art methods in terms of real-time forecasting accuracy and computational efficiency.