mlsanityData to 14 Oct 2026

Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts

arXiv 2210.03675 ↗First posted 7 Oct 2022cs.LG stat.MLcited by 37

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Abstract (arXiv)

Temporal distributional shifts, with underlying dynamics changing over time, frequently occur in real-world time series and pose a fundamental challenge for deep neural networks (DNNs). In this paper, we propose a novel deep sequence model based on the Koopman theory for time series forecasting: Koopman Neural Forecaster (KNF) which leverages DNNs to learn the linear Koopman space and the coefficients of chosen measurement functions. KNF imposes appropriate inductive biases for improved robustness against distributional shifts, employing both a global operator to learn shared characteristics and a local operator to capture changing dynamics, as well as a specially-designed feedback loop to continuously update the learned operators over time for rapidly varying behaviors. We demonstrate that ours achieves superior performance compared to the alternatives, on multiple time series datasets that are shown to suffer from distribution shifts.

Key facts. Cited by 37 papers in the map (data through 14 Oct 2026). Builds on 33 of its 60 references that are in the map. First posted on arXiv 7 Oct 2022.

Builds on

33 of 60 references.

References · 33

  1. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  2. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,676
  3. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,424
  4. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,210
  5. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 753
  6. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  7. 2020Learning under Concept Drift: A Reviewcited by 477
  8. 2022Message Passing Neural PDE Solverscited by 386
  9. 2021Modern Koopman Theory for Dynamical Systemscited by 276
  10. 2021Monash Time Series Forecasting Archivecited by 267
  11. 2019Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecastingcited by 161
  12. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 158
21 more
  1. 2022CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecastingcited by 144
  2. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 134
  3. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 127
  4. 2020Forecasting Sequential Data using Consistent Koopman Autoencoderscited by 115
  5. 2018An introduction to domain adaptation and transfer learningcited by 112
  6. 2021Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Taskscited by 101
  7. 2019Deep Factors for Forecastingcited by 86
  8. 2020Meta-learning framework with applications to zero-shot time-series forecastingcited by 70
  9. 2021Domain Adaptation for Time Series Forecasting via Attention Sharingcited by 68
  10. 2019Learning Compositional Koopman Operators for Model-Based Controlcited by 67
  11. 2014Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decompositioncited by 49
  12. 2020Machine Learning Advances for Time Series Forecastingcited by 49
  13. 2021Long Expressive Memory for Sequence Modelingcited by 41
  14. 2020Deep Learning of Koopman Representation for Controlcited by 26
  15. 2020Bridging Physics-based and Data-driven modeling for Learning Dynamical Systemscited by 25
  16. 2019Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Controlcited by 18
  17. 2020Detecting and Adapting to Irregular Distribution Shifts in Bayesian Online Learningcited by 18
  18. 2021Learning Stable Koopman Embeddingscited by 18
  19. 2022Decoupling Local and Global Representations of Time Seriescited by 17
  20. 2022Self-Adaptive Forecasting for Improved Deep Learning on Non-Stationary Time-Seriescited by 14
  21. 2022Time Series Prediction under Distribution Shift using Differentiable Forgettingcited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 6; 2025: 12; 2026: 13.

37 papers.

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  1. 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 113
  2. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 49
  3. 2024Frequency Adaptive Normalization For Non-stationary Time Series Forecastingcited by 47
  4. 2024Wavelet Diffusion Neural Operatorcited by 29
  5. 2023Model scale versus domain knowledge in statistical forecasting of chaotic systemscited by 27
  6. 2024Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamicscited by 27
  7. 2025Non-stationary Diffusion For Probabilistic Time Series Forecastingcited by 27
  8. 2025True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statisticscited by 20
  9. 2024Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstructioncited by 19
  10. 2024Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspectivecited by 17
  11. 2025Learning Robust Spectral Dynamics for Temporal Domain Generalizationcited by 14
  12. 2023LANISTR: Multimodal Learning from Structured and Unstructured Datacited by 11
25 more
  1. 2025Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systemscited by 5
  2. 2024KODA: A Data-Driven Recursive Model for Time Series Forecasting and Data Assimilation using Koopman Operatorscited by 4
  3. 2026Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modelingcited by 4
  4. 2025Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecastingcited by 3
  5. 2025Deep Koopman operator framework for causal discovery in nonlinear dynamical systemscited by 2
  6. 2025SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecastingcited by 2
  7. 2025EventTSF: Event-Aware Non-Stationary Time Series Forecastingcited by 2
  8. 2023Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equationscited by 1
  9. 2023Hierarchical Ensemble-Based Feature Selection for Time Series Forecastingcited by 0
  10. 2025KoopAGRU: A Koopman-based Anomaly Detection in Time-Series using Gated Recurrent Unitscited by 0
  11. 2025Wavelet-based Disentangled Adaptive Normalization for Non-stationary Times Series Forecastingcited by 0
  12. 2025DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecastingcited by 0
  13. 2025Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentationcited by 0
  14. 2026Koopman Regularized Deep Speech Disentanglement for Speaker Verificationcited by 0
  15. 2026Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstructioncited by 0
  16. 2026Topological Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 0
  17. 2026Learning the Koopman Operator using Attention Free Transformerscited by 0
  18. 2026A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systemscited by 0
  19. 2026MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shiftscited by 0
  20. 2026Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecastingcited by 0
  21. 2026Stable Multi-Step Rollouts via Uncertainty-Guided Hybrid Dynamicscited by 0
  22. 2026FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalizationcited by 0
  23. 2026Principled Koopman Representations with Kalman Inference for Efficient Time-Series Predictioncited by 0
  24. 2026TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectracited by 0
  25. 2026Beyond Static Positional Encoding: Bayesian Time-aware Attention for Non-Stationary Long-term Time Series Forecastingcited by 0