用傅里叶分解与柯普曼理论，提升时间序列异常检测精度。
KoopAGRU: A Koopman-based Anomaly Detection in Time-Series using Gated Recurrent Units
- 结合FFT、DeepDMD与柯普曼理论，分离时变与稳态成分。
- 在多个基准数据集上平均F1达90.88%，优于现有方法。
- 适合需要多尺度异常检测的工业实时监控场景。
真实世界的时间序列异常检测因复杂的非线性动态特性而极具挑战。本文提出KoopAGRU，一种融合快速傅里叶变换（FFT）、深度动态模态分解（DeepDMD）与柯普曼理论的新型深度学习模型。FFT将时间序列分解为时变与时不变分量，实现对复杂模式的精确建模。为更好调控这两类成分，KoopAGRU采用门控循环单元（GRU）编码器学习柯普曼可观测量，在多时间尺度上增强检测能力。模型支持单步训练，推理速度快。在多个基准数据集上的实验表明，其在典型时间序列异常检测任务中达到90.88%的平均F1分数，显著优于现有主流方法，验证了其在真实场景中的高效性与可靠性。
原文摘要 · Abstract (English)
Anomaly detection in real-world time-series data is a challenging task due to the complex and nonlinear temporal dynamics involved. This paper introduces KoopAGRU, a new deep learning model designed to tackle this problem by combining Fast Fourier Transform (FFT), Deep Dynamic Mode Decomposition (DeepDMD), and Koopman theory. FFT allows KoopAGRU to decompose temporal data into time-variant and time-invariant components providing precise modeling of complex patterns. To better control these two components, KoopAGRU utilizes Gate Recurrent Unit (GRU) encoders to learn Koopman observables, enhancing the detection capability across multiple temporal scales. KoopAGRU is trained in a single process and offers fast inference times. Extensive tests on various benchmark datasets show that KoopAGRU outperforms other leading methods, achieving a new average F1-score of 90.88\% on the well-known anomalies detection task of times series datasets, and proves to be efficient and reliable in detecting anomalies in real-world scenarios.
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