mlsanityData to 7 Oct 2026

Forecasting Sequential Data using Consistent Koopman Autoencoders

arXiv 2003.02236 ↗First posted 4 Mar 2020physics.comp-ph cs.LG math.DScited by 114

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Abstract (arXiv)

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.

Key facts. Cited by 114 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Mar 2020.

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Citing papers per year: 2021: 13; 2022: 16; 2023: 18; 2024: 20; 2025: 23; 2026: 24.

114 papers.

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  1. 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 110
  2. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  3. 2021Cross-Node Federated Graph Neural Network for Spatio-Temporal Data Modelingcited by 69
  4. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  5. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 48
  6. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  7. 2021Noisy Recurrent Neural Networkscited by 42
  8. 2024Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Seriescited by 42
  9. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  10. 2022Koopman Neural Forecaster for Time Series with Temporal Distribution Shiftscited by 35
  11. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 34
  12. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
38 more
  1. 2023Koopman neural operator as a mesh-free solver of non-linear partial differential equationscited by 29
  2. 2022Learning continuous models for continuous physicscited by 28
  3. 2022Deep Koopman Operator with Control for Nonlinear Systemscited by 25
  4. 2023Multifactor Sequential Disentanglement via Structured Koopman Autoencoderscited by 23
  5. 2023Koopman Kernel Regressioncited by 22
  6. 2025True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statisticscited by 20
  7. 2021Deep Learning Enhanced Dynamic Mode Decompositioncited by 19
  8. 2024Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstructioncited by 18
  9. 2023Learning invariant representations of time-homogeneous stochastic dynamical systemscited by 17
  10. 2024Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systemscited by 15
  11. 2024Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Datacited by 14
  12. 2021An Operator Theoretic Approach for Analyzing Sequence Neural Networkscited by 12
  13. 2023Koopman operator learning using invertible neural networkscited by 12
  14. 2024Elucidating the Design Choice of Probability Paths in Flow Matching for Forecastingcited by 12
  15. 2023Consistent Long-Term Forecasting of Ergodic Dynamical Systemscited by 10
  16. 2023KoopmanLab: machine learning for solving complex physics equationscited by 9
  17. 2023Neural Koopman prior for data assimilationcited by 9
  18. 2024Words in Motion: Extracting Interpretable Control Vectors for Motion Transformerscited by 9
  19. 2025One-Step Offline Distillation of Diffusion-based Models via Koopman Modelingcited by 9
  20. 2021Innovations Autoencoder and its Application in One-class Anomalous Sequence Detectioncited by 7
  21. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  22. 2022QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learningcited by 7
  23. 2024Nonparametric Control Koopman Operatorscited by 7
  24. 2025Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systemscited by 7
  25. 2023A polar prediction model for learning to represent visual transformationscited by 6
  26. 2024First-Order Manifold Data Augmentation for Regression Learningcited by 6
  27. 2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
  28. 2022Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learningcited by 5
  29. 2022Gated Recurrent Neural Networks with Weighted Time-Delay Feedbackcited by 5
  30. 2023Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Datacited by 5
  31. 2023Koopman Invertible Autoencoder: Leveraging Forward and Backward Dynamics for Temporal Modelingcited by 5
  32. 2024Deep Bayesian Filter for Bayes-faithful Data Assimilationcited by 5
  33. 2025Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systemscited by 5
  34. 2022DLKoopman: A deep learning software package for Koopman theorycited by 4
  35. 2024SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systemscited by 4
  36. 2021A Differential Geometry Perspective on Orthogonal Recurrent Modelscited by 3
  37. 2022Lyapunov-Guided Representation of Recurrent Neural Network Performancecited by 3
  38. 2023Why should autoencoders work?cited by 3

50 most cited of 114 All 114 (JSON)