# KoopAGRU: A Koopman-based Anomaly Detection in Time-Series using Gated Recurrent Units

arXiv: https://arxiv.org/abs/2501.17976 · HTML: https://mlsanity.com/paper/2501.17976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 73 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [ETSformer: Exponential Smoothing Transformers for Time-series Forecasting](https://mlsanity.com/paper/2202.01381/) (2022)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Self-Organized Operational Neural Networks with Generative Neurons](https://mlsanity.com/paper/2004.11778/) (2020)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Applied Koopman Operator Theory for Power Systems Technology](https://mlsanity.com/paper/1706.00159/) (2017)
- [A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators](https://mlsanity.com/paper/1712.03132/) (2017)
- [Graph Neural Network and Koopman Models for Learning Networked Dynamics: A Comparative Study on Power Grid Transients Prediction](https://mlsanity.com/paper/2202.08065/) (2022)
- [Model-Agnostic Algorithm for Real-Time Attack Identification in Power Grid using Koopman Modes](https://mlsanity.com/paper/2007.11717/) (2020)
- [Data Driven Online Learning of Power System Dynamics](https://mlsanity.com/paper/2003.05068/) (2020)
- [On analytical construction of observable functions in extended dynamic mode decomposition for nonlinear estimation and prediction](https://mlsanity.com/paper/2008.12874/) (2020)

## Abstract (arXiv)

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.