mlsanityData to 7 Oct 2026

Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling

arXiv 2602.16864 ↗First posted 18 Feb 2026cs.LG cs.AI math.DScited by 3

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Abstract (arXiv)

Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective. TS of observations from natural or engineered systems almost always originate from some underlying DS, and arguably access to its governing equations would yield theoretically optimal forecasts. This is the promise of DS reconstruction (DSR), a class of ML/AI approaches that aim to infer surrogate models of the underlying DS from data. But models based on DS principles offer other profound advantages: Beyond short-term forecasts, they enable to predict the long-term statistics of an observed system, which in many practical scenarios may be the more relevant quantities. DS theory furthermore provides domain-independent theoretical insight into mechanisms underlying TS generation, and thereby will inform us, e.g., about upper bounds on performance of any TS model, generalization into unseen regimes as in tipping points, or potential control strategies. After reviewing some of the central concepts, methods, measures, and models in DS theory and DSR, we will discuss how insights from this field can advance TS modeling in crucial ways, enabling better forecasting with much lower computational and memory footprints. We conclude with a number of specific suggestions for translating insights from DSR into TS modeling.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 74 of its 192 references that are in the map. First posted on arXiv 18 Feb 2026.

Builds on

74 of 192 references.

References · 74

  1. 2019Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformercited by 14,491
  2. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  5. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
  6. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
  7. 2024Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Dualitycited by 1,283
  8. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 744
  9. 2024Chronos: Learning the Language of Time Seriescited by 712
  10. 2015Sequence Level Training with Recurrent Neural Networkscited by 568
  11. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  12. 2024xLSTM: Extended Long Short-Term Memorycited by 320
38 more
  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  3. 2021Monash Time Series Forecasting Archivecited by 256
  4. 2016Professor Forcing: A New Algorithm for Training Recurrent Networkscited by 214
  5. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  6. 2020Physics-informed learning of governing equations from scarce datacited by 167
  7. 2024Are Language Models Actually Useful for Time Series Forecasting?cited by 163
  8. 2025Chronos-2: From Univariate to Universal Forecastingcited by 158
  9. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  10. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 142
  11. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 132
  12. 2020Forecasting Sequential Data using Consistent Koopman Autoencoderscited by 114
  13. 2025TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learningcited by 107
  14. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
  15. 2024Context is Key: A Benchmark for Forecasting with Essential Textual Informationcited by 78
  16. 2021On the difficulty of learning chaotic dynamics with RNNscited by 64
  17. 2023Generalized Teacher Forcing for Learning Chaotic Dynamicscited by 55
  18. 2020Machine learning prediction of critical transition and system collapsecited by 54
  19. 2022Forecast Evaluation for Data Scientists: Common Pitfalls and Best Practicescited by 54
  20. 2023Parallelizing non-linear sequential models over the sequence lengthcited by 45
  21. 2023Training neural operators to preserve invariant measures of chaotic attractorscited by 43
  22. 2019Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRIcited by 39
  23. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 36
  24. 2022Koopman Neural Forecaster for Time Series with Temporal Distribution Shiftscited by 35
  25. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  26. 2016Recurrent switching linear dynamical systemscited by 34
  27. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 34
  28. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  29. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  30. 2022A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamicscited by 30
  31. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 29
  32. 2023Model scale versus domain knowledge in statistical forecasting of chaotic systemscited by 27
  33. 2024Zero-shot forecasting of chaotic systemscited by 25
  34. 2025True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statisticscited by 20
  35. 2021Stochastic Physics-Informed Neural Ordinary Differential Equationscited by 19
  36. 2024Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstructioncited by 18
  37. 2020DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Controlcited by 17
  38. 2023Bifurcations and loss jumps in RNN trainingcited by 17

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modelingcited by 1
  2. 2026ChaosNetBench: Benchmarking Spatio-Temporal Graph Neural Networks on Chaotic Lattice Dynamicscited by 0
  3. 2026Continual Learning of Dynamical Systems in Recurrent Neural Networks through Recyclable Unit Gatingcited by 0