# AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression

arXiv: https://arxiv.org/abs/2606.04930 · HTML: https://mlsanity.com/paper/2606.04930/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 64 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 28 of 28)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Are Language Models Actually Useful for Time Series Forecasting?](https://mlsanity.com/paper/2406.16964/) (2024)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.14027/) (2022)
- [Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1712.01572/) (2017)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Sharp Spectral Rates for Koopman Operator Learning](https://mlsanity.com/paper/2302.02004/) (2023)
- [Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization](https://mlsanity.com/paper/2206.00176/) (2022)
- [Multifactor Sequential Disentanglement via Structured Koopman Autoencoders](https://mlsanity.com/paper/2303.17264/) (2023)
- [Online dynamic mode decomposition for time-varying systems](https://mlsanity.com/paper/1707.02876/) (2017)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Learning to Forecast Dynamical Systems from Streaming Data](https://mlsanity.com/paper/2109.09703/) (2021)
- [Deep Switching Auto-Regressive Factorization:Application to Time Series Forecasting](https://mlsanity.com/paper/2009.05135/) (2020)
- [Estimating Koopman operators with sketching to provably learn large scale dynamical systems](https://mlsanity.com/paper/2306.04520/) (2023)
- [Modeling Time-evolving Causality over Data Streams](https://mlsanity.com/paper/2502.08963/) (2025)
- [Modeling Latent Non-Linear Dynamical System over Time Series](https://mlsanity.com/paper/2412.08114/) (2024)
- [D-Tracker: Modeling Interest Diffusion in Social Activity Tensor Data Streams](https://mlsanity.com/paper/2505.00242/) (2025)
- [Learning from Snapshots of Discrete and Continuous Data Streams](https://mlsanity.com/paper/2412.06079/) (2024)
- [Fast Mining and Dynamic Time-to-Event Prediction over Multi-sensor Data Streams](https://mlsanity.com/paper/2601.04741/) (2026)
- [Multi-Aspect Mining and Anomaly Detection for Heterogeneous Tensor Streams](https://mlsanity.com/paper/2602.04917/) (2026)

## Abstract (arXiv)

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.