FreKoo++：面向时间域泛化的连续谱动力学学习
FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization
- Australian Artificial Intelligence Institute (AAII)（澳大利亚人工智能研究所（AAII））
- Faculty of Engineering and Information Technology（工程与信息技术学院）
- University of Technology Sydney (UTS)（悉尼科技大学（UTS））
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对时间域泛化中复杂流场景的局限，提出FreKoo++框架，统一连续Koopman模态动力学与自适应谱解耦，在TDG基准上实现最先进性能。
中文摘要 AI 辅助
时间域泛化（Temporal Domain Generalization, TDG）旨在从历史域学习，并在概念漂移下泛化到未见的未来分布。然而，主流TDG方法难以应对涉及多尺度漂移模式（例如长期周期性与短期增量变化交织）和局部不确定性的复杂现实流场景，尤其是在观测不规则到达的连续设置中。为解决这一局限，我们提出FreKoo++，一种新颖的连续谱动力学框架，其首次将连续Koopman模态动力学与自适应谱解耦相统一。具体而言，FreKoo++将源域参数映射到紧凑的潜在空间，将其演化建模为可学习连续模态的叠加，其中复特征值共同编码振荡频率及时间增长或衰减。该公式自然适配不规则时间戳，支持任意时间范围外推，无需严格的离散步进。此外，我们提出一种受稳定性和谱正则化支撑的新型自适应软谱加权机制，其可自动将持久主导动力学与瞬态噪声分离，无需依赖人工频率阈值。我们推导了模态近似和泛化界，以刻画振幅和特征值估计误差如何随预测时间范围传播。在离散和连续TDG基准上的大量实验表明，FreKoo++在复杂多尺度漂移和不规则采样下实现了最先进的性能。
英文摘要
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.
