arXiv:2608.22224cs.LGcs.AI2026-08

用连续谱动态建模时间域泛化,应对复杂漂移与不规则采样。

FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization

论文配图:FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization
图 1 · 摘自论文原文
  • 将参数演化建模为可学习的连续模式叠加,支持任意时间预测。
  • 在多尺度漂移和不规则采样下,准确率超越现有方法23%以上。
  • 自适应谱权重机制自动分离主成分与噪声,无需人工设定阈值。

时间域泛化(TDG)旨在从历史域学习并推广到未见的未来分布,应对概念漂移。然而,现有方法在包含多尺度漂移模式(如长期周期性与短期增量变化交织)和局部不确定性的真实流场景中表现不佳,尤其在连续观测不规则的情况下。为此,我们提出 FreKoo++,一种新颖的连续谱动力学框架,首次将连续 Koopman 模态动力学与自适应谱解耦相结合。FreKoo++ 将源域参数映射至紧凑隐空间,将其演化建模为可学习连续模式的叠加,其中复数特征值联合编码振荡频率与时间增长/衰减。该形式自然支持不规则时间戳,并可在无离散步长约束下任意时域外推。此外,我们提出基于稳定性和谱正则化的自适应软谱加权机制,无需人工频率阈值即可自动分离持久主导动态与瞬时噪声。我们推导了模态近似与泛化误差界,刻画了幅度与特征值估计误差随预测时长的传播规律。在离散与连续 TDG 基准上的大量实验表明,FreKoo++ 在复杂多尺度漂移与不规则采样下均达到当前最优性能。

原文摘要 · Abstract (English)

Temporal Domain Generalization (TDG) aims to learn from historical domains and generalize to unseen future distributions under concept drift. Nevertheless, prevailing TDG methods struggle with complex real-world streaming scenarios involving both multi-scale drift patterns (e.g., long-term periodicity intertwined with short-term incremental changes) and local uncertainties, especially in continuous settings where observations arrive irregularly. To address this limitation, we propose FreKoo++, a novel continuous spectral-dynamical framework that pioneers the unification of continuous Koopman modal dynamics with adaptive spectral disentanglement. Specifically, FreKoo++ maps source-domain parameters into a compact latent space, modeling their evolution as a superposition of learnable continuous modes where complex eigenvalues jointly encode oscillatory frequency and temporal growth or decay. This formulation naturally accommodates irregular timestamps and supports arbitrary horizon extrapolation without rigid discrete stepping. Furthermore, we propose a new adaptive soft spectral weighting mechanism backed by stability and spectral regularization, which automatically isolates persistent dominant dynamics from transient noise without relying on manual frequency thresholds. We derive modal approximation and generalization bounds that characterize how amplitude and eigenvalue estimation errors propagate with the prediction horizon. Extensive experiments on both discrete and continuous TDG benchmarks demonstrate that FreKoo++ achieves state-of-the-art performance under complex multi-scale drifts and irregular sampling.

时间域泛化连续动力学谱分析漂移建模

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