发表机构
National Taiwan University; National Institute of Information and Communications Technology; Research Center for Information Technology Innovation（台湾大学; 信息通信研究机构; 资讯科技创新研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出名为NDKoop的端到端架构，将可学习信号分解模块与两类Koopman网络结合，在统一框架内实现端到端Koopman建模与信号分解，提升了时间序列预测精度。
AI 中文摘要
Koopman理论通过将观测值提升到由线性时不变Koopman算子控制演化的空间，为非线性序列动力学提供线性算子视角。Koopman算子虽能表示非线性动力学，但通常为无限维且基于时不变假设，要建模具有频率相关行为的非平稳信号，需频率可变扩展。近年来深度学习因强大的函数逼近能力被越来越多地用于学习Koopman算子。本研究提出名为神经分解Koopman（NDKoop）的新方法，它是一种端到端架构，将可学习信号分解模块与基于频率无关及频率相关Koopman的网络相结合，用于序列预测。据所知，这是首个在统一神经框架内联合实现端到端Koopman建模与信号分解的工作。研究表明，将信号分解为受对应Koopman算子控制的频率无关趋势分量和频率相关周期分量，在线性化不完美时可提升预测精度。在多个预测基准上的数值实验显示，所提NDKoop具有优异性能。
英文摘要
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.
