End-to-End Neural Decomposition with Koopman Operators for Time-Series Forecasting

• URL: http://arxiv.org/abs/2608.08788v1
• Date: Sun, 09 Aug 2026 16:08:54 GMT
• Title: End-to-End Neural Decomposition with Koopman Operators for Time-Series Forecasting
• Abstract summary: We propose a novel approach called neural decomposition Koopman (NDKoop)<n>NDKoop integrates a learnable signal decomposition module with both frequency-independent and frequency-dependent networks for sequence forecasting.<n>We demonstrate that decomposing a signal into a frequency-independent trend component and a frequency-dependent periodic component, each governed by a corresponding Koopman operator, improves prediction accuracy when perfect linearization is unattainable.
• Score: 25.01602116375264
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Koopman theory offers a linear-operator view of nonlinear sequence dynamics by lifting observations into a space where evolution is governed by a linear time-invariant Koopman operator. While the Koopman operator provides a linear representation of nonlinear dynamics, it is generally infinite dimensional and defined under time-invariant assumptions. To model non-stationary signals with frequency-dependent behavior, a frequency-varying extension is required. In recent years, deep learning has been increasingly employed to exploit its powerful function-approximation ability for learning the Koopman operator. In this study, we propose a novel approach called neural decomposition Koopman (NDKoop), an end-to-end architecture that integrates a learnable signal decomposition module with both frequency-independent and frequency-dependent Koopman based networks for sequence forecasting. To the best of our knowledge, this is the first work to jointly realize end-to end Koopman modeling and signal decomposition within a unified neural framework. We demonstrate that decomposing a signal into a frequency-independent trend component and a frequency-dependent periodic component, each governed by a corresponding Koopman operator, improves prediction accuracy when perfect linearization is unattainable. Numerical experiments across several forecasting benchmarks indicate that the proposed NDKoop provides strong performance.

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