KokerNet: Koopman Kernel Network for Time Series Forecasting
Keywords: Spectral kernel, Koopman operator, Time series
Abstract: The Koopman operator has gained increasing attention in time series forecasting due to its ability to simplify the complex evolution of dynamic systems. However, most existing Koopman-based methods suffer from significant computational costs in constructing measurement functions and struggle to address the challenge posed by the variation in data distribution. Additionally, these approaches tend to empirically decompose time series or distributions into combinations of components, lacking interpretability. To tackle these issues, we propose a novel approach, **Ko**opman **ker**nel **net**work (**KokerNet**), for time series forecasting. On one hand, we construct a measurement function space using the spectral kernel method, which enables us to perform Koopman operator learning in a low-dimensional feature space, efficiently reducing computational costs. On the other hand, an index is designed to characterize the stationarity of data in both time and frequency domains. This index can interpretably guide us to decompose the time series into stationary and non-stationary components. The global and local Koopman operators are then learned within the constructed measurement function space to predict the future behavior of the stationary and non-stationary components, respectively. Particularly, to address the challenge posed by the variation in distribution, we incorporate a distribution module for the non-stationary component, ensuring that the model can make aligned distribution predictions. Extensive experiments across multiple benchmarks illustrate the superiority of our proposed KokerNet, consistently outperforming the state-of-the-art models.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 6067
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