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

2025-10-17

AI Summary

Addressing three key challenges in real-time forecasting of streaming time series—nonstationary dynamic modeling, constrained computational resources, and catastrophic forgetting—this paper proposes WORK-DMD, a lightweight continual learning framework integrating Random Fourier Features (RFF) with online kernel Dynamic Mode Decomposition (DMD). By leveraging explicit nonlinear feature mapping via RFF, WORK-DMD captures complex temporal dynamics; it further enables efficient model evolution through a single pass over incoming data, using an adaptive sliding window and Sherman–Morrison-based incremental updates—eliminating the need to store historical data. Compared to state-of-the-art online forecasting methods, WORK-DMD achieves significantly improved short-term prediction accuracy across multiple benchmark datasets from diverse domains, while simultaneously reducing memory footprint and computational overhead. Its design balances accuracy, adaptability, and efficiency, making it particularly suitable for edge computing and resource-constrained deployment scenarios.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Data Stream Mining
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Forecasting streaming time series with non-stationary dynamics
• Adapting to evolving data under computational constraints
• Eliminating lengthy training and large storage requirements

Innovation

• Online kernel DMD with adaptive windowing for streaming data
• Sherman-Morrison updates enable continuous adaptation to dynamics
• Random Fourier Features map nonlinear dynamics with fixed cost