mlsanityData to 14 Oct 2026

Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors

arXiv 2305.18803 ↗First posted 30 May 2023cs.LGcited by 113

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Abstract (arXiv)

Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution, we tackle non-stationary time series with modern Koopman theory that fundamentally considers the underlying time-variant dynamics. Inspired by Koopman theory of portraying complex dynamical systems, we disentangle time-variant and time-invariant components from intricate non-stationary series by Fourier Filter and design Koopman Predictor to advance respective dynamics forward. Technically, we propose Koopa as a novel Koopman forecaster composed of stackable blocks that learn hierarchical dynamics. Koopa seeks measurement functions for Koopman embedding and utilizes Koopman operators as linear portraits of implicit transition. To cope with time-variant dynamics that exhibits strong locality, Koopa calculates context-aware operators in the temporal neighborhood and is able to utilize incoming ground truth to scale up forecast horizon. Besides, by integrating Koopman Predictors into deep residual structure, we ravel out the binding reconstruction loss in previous Koopman forecasters and achieve end-to-end forecasting objective optimization. Compared with the state-of-the-art model, Koopa achieves competitive performance while saving 77.3% training time and 76.0% memory.

Key facts. Cited by 113 papers in the map (data through 14 Oct 2026). Builds on 35 of its 54 references that are in the map. First posted on arXiv 30 May 2023.

Builds on

35 of 54 references.

References · 35

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23 more
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  2. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,058
  3. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
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  15. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 127
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  18. 2021Domain Adaptation for Time Series Forecasting via Attention Sharingcited by 68
  19. 2020From Fourier to Koopman: Spectral Methods for Long-term Time Series Predictioncited by 50
  20. 2022Learning Fast and Slow for Online Time Series Forecastingcited by 45
  21. 2022Koopman Neural Forecaster for Time Series with Temporal Distribution Shiftscited by 37
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 4; 2024: 39; 2025: 41; 2026: 29.

113 papers.

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  1. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 931
  2. 2024Deep Time Series Models: A Comprehensive Survey and Benchmarkcited by 197
  3. 2025Sundial: A Family of Highly Capable Time Series Foundation Modelscited by 180
  4. 2024TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysiscited by 116
  5. 2024UniTS: A Unified Multi-Task Time Series Modelcited by 94
  6. 2024UniST: A Prompt-Empowered Universal Model for Urban Spatio-Temporal Predictioncited by 87
  7. 2024Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysiscited by 74
  8. 2024AutoTimes: Autoregressive Time Series Forecasters via Large Language Modelscited by 65
  9. 2024Frequency Adaptive Normalization For Non-stationary Time Series Forecastingcited by 47
  10. 2024Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modelingcited by 44
  11. 2024TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecastingcited by 40
  12. 2025TimeXL: Explainable Multi-modal Time Series Prediction with LLM-in-the-Loopcited by 39
38 more
  1. 2024TSI-Bench: Benchmarking Time Series Imputationcited by 33
  2. 2025Non-stationary Diffusion For Probabilistic Time Series Forecastingcited by 27
  3. 2023ST-MLP: A Cascaded Spatio-Temporal Linear Framework with Channel-Independence Strategy for Traffic Forecastingcited by 22
  4. 2024Ada-MSHyper: Adaptive Multi-Scale Hypergraph Transformer for Time Series Forecastingcited by 21
  5. 2024Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspectivecited by 17
  6. 2025Learning Robust Spectral Dynamics for Temporal Domain Generalizationcited by 14
  7. 2024VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecastingcited by 12
  8. 2025TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecastingcited by 12
  9. 2025TimesBERT: A BERT-Style Foundation Model for Time Series Understandingcited by 10
  10. 2025FreCT: Frequency-augmented Convolutional Transformer for Robust Time Series Anomaly Detectioncited by 10
  11. 2024Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecastingcited by 9
  12. 2024Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Modelscited by 8
  13. 2025K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecastingcited by 8
  14. 2024FTS: A Framework to Find a Faithful TimeSievecited by 7
  15. 2024Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecastingcited by 6
  16. 2025LETS Forecast: Learning Embedology for Time Series Forecastingcited by 6
  17. 2024Phase-driven Domain Generalizable Learning for Nonstationary Time Seriescited by 5
  18. 2024AdaWaveNet: Adaptive Wavelet Network for Time Series Analysiscited by 5
  19. 2025Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systemscited by 5
  20. 2024FTMixer: Frequency and Time Domain Representations Fusion for Time Series Modelingcited by 4
  21. 2024KODA: A Data-Driven Recursive Model for Time Series Forecasting and Data Assimilation using Koopman Operatorscited by 4
  22. 2024Online Control-Informed Learningcited by 4
  23. 2024NRFormer: Nationwide Nuclear Radiation Forecasting with Spatio-Temporal Transformercited by 4
  24. 2025Information Shapes Koopman Representationcited by 4
  25. 2023Rethinking Urban Mobility Prediction: A Super-Multivariate Time Series Forecasting Approachcited by 3
  26. 2024Job-SDF: A Multi-Granularity Dataset for Job Skill Demand Forecasting and Benchmarkingcited by 3
  27. 2024FredNormer: Frequency Domain Normalization for Non-stationary Time Series Forecastingcited by 3
  28. 2024When Graph Neural Networks Meet Dynamic Mode Decompositioncited by 3
  29. 2024LiNo: Advancing Recursive Residual Decomposition of Linear and Nonlinear Patterns for Robust Time Series Forecastingcited by 3
  30. 2025Semantic-Enhanced Time-Series Forecasting via Large Language Modelscited by 3
  31. 2024Nonstationary Time Series Forecasting via Unknown Distribution Adaptationcited by 2
  32. 2024TimeSieve: Extracting Temporal Dynamics through Information Bottleneckscited by 2
  33. 2024DRFormer: Multi-Scale Transformer Utilizing Diverse Receptive Fields for Long Time-Series Forecastingcited by 2
  34. 2024RePST: Language Model Empowered Spatio-Temporal Forecasting via Semantic-Oriented Reprogrammingcited by 2
  35. 2025MetaEformer: Unveiling and Leveraging Meta-patterns for Complex and Dynamic Systems Load Forecastingcited by 2
  36. 2025SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecastingcited by 2
  37. 2025EventTSF: Event-Aware Non-Stationary Time Series Forecastingcited by 2
  38. 2025Hierarchical Koopman Diffusion: Fast Generation with Interpretable Diffusion Trajectorycited by 2

50 most cited of 113 All 113 (JSON)