Title: AdaKoop: Streamlining Nonlinear Dynamics Modeling in Nonstationary Data via Koopman Operator Regression

Abstract:

The demand for real-time data analysis necessitates methods that can accurately and adaptively handle nonlinear dynamics within nonstationary data streams without sacrificing computational efficiency. Yet, the inherent complexity of nonlinear dynamics makes it challenging to capture evolving patterns and leverage them for subsequent tasks within tight time limits. To reconcile nonlinear complexity with computational feasibility, this research leverages Koopman operator theory, which posits that nonlinear systems can be modeled as linear transitions within an infinite-dimensional space. By extending finite-dimensional approximations of this operator, we introduce AdaKoop, a streamlined streaming algorithm designed to model nonlinear dynamics in nonstationary environments.

Our method employs a probabilistic framework rooted in Koopman theory, conceptualizing both raw observations and features from the reproducing kernel Hilbert space (RKHS) as emissions derived from latent vectors. This dual-perspective approach transforms nonlinear dynamics into a manageable linear system. Consequently, AdaKoop facilitates the efficient and stable modeling of nonlinear dynamics in a streaming manner, thereby circumventing the excessive computational burdens associated with iterative nonlinear optimization.

To manage the nonstationarity inherent in data streams, AdaKoop incorporates adaptive mechanisms that identify pattern shifts through statistical hypothesis testing for abrupt changes, while simultaneously performing incremental updates to model parameters to accommodate continuous variations. Comprehensive evaluations across 71 practical benchmark datasets spanning diverse domains reveal that AdaKoop surpasses current state-of-the-art techniques in both real-time forecasting precision and computational efficiency.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC