# Online Kernel Dynamic Mode Decomposition for Streaming Time Series Forecasting with Adaptive Windowing

arXiv: https://arxiv.org/abs/2510.15404 · HTML: https://mlsanity.com/paper/2510.15404/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Online dynamic mode decomposition for time-varying systems](https://mlsanity.com/paper/1707.02876/) (2017)
- [Learning to Forecast Dynamical Systems from Streaming Data](https://mlsanity.com/paper/2109.09703/) (2021)
- [A Distance Correlation-Based Approach to Characterize the Effectiveness of Recurrent Neural Networks for Time Series Forecasting](https://mlsanity.com/paper/2307.15830/) (2023)

## Abstract (arXiv)

Real-time forecasting from streaming data poses critical challenges: handling non-stationary dynamics, operating under strict computational limits, and adapting rapidly without catastrophic forgetting. However, many existing approaches face trade-offs between accuracy, adaptability, and efficiency, particularly when deployed in constrained computing environments. We introduce WORK-DMD (Windowed Online Random Kernel Dynamic Mode Decomposition), a method that combines Random Fourier Features with online Dynamic Mode Decomposition to capture nonlinear dynamics through explicit feature mapping, while preserving fixed computational cost and competitive predictive accuracy across evolving data. WORK-DMD employs Sherman-Morrison updates within rolling windows, enabling continuous adaptation to evolving dynamics from only current data, eliminating the need for lengthy training or large storage requirements for historical data. Experiments on benchmark datasets across several domains show that WORK-DMD achieves higher accuracy than several state-of-the-art online forecasting methods, while requiring only a single pass through the data and demonstrating particularly strong performance in short-term forecasting. Our results show that combining kernel evaluations with adaptive matrix updates achieves strong predictive performance with minimal data requirements. This sample efficiency offers a practical alternative to deep learning for streaming forecasting applications.