Learning to Forecast Dynamical Systems from Streaming Data

TL;DR

This paper introduces a streaming algorithm for Kernel Analog Forecasting that reduces computational costs significantly while maintaining high forecasting accuracy for various dynamical systems.

Contribution

It presents a novel streaming KAF algorithm that requires only a single pass over data, making it more efficient without losing forecast quality.

Findings

Successfully forecasts periodic, quasi-periodic, and chaotic systems

Operates effectively in both data-scarce and data-rich regimes

Reduces training and prediction costs substantially

Abstract

Kernel analog forecasting (KAF) is a powerful methodology for data-driven, non-parametric forecasting of dynamically generated time series data. This approach has a rigorous foundation in Koopman operator theory and it produces good forecasts in practice, but it suffers from the heavy computational costs common to kernel methods. This paper proposes a streaming algorithm for KAF that only requires a single pass over the training data. This algorithm dramatically reduces the costs of training and prediction without sacrificing forecasting skill. Computational experiments demonstrate that the streaming KAF method can successfully forecast several classes of dynamical systems (periodic, quasi-periodic, and chaotic) in both data-scarce and data-rich regimes. The overall methodology may have wider interest as a new template for streaming kernel regression.