mlsanityData to 13 Oct 2026

Neural Controlled Differential Equations for Irregular Time Series

arXiv 2005.08926 ↗First posted 18 May 2020cs.LG stat.MLcited by 503

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Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no mechanism for adjusting the trajectory based on subsequent observations. Here, we demonstrate how this may be resolved through the well-understood mathematics of controlled differential equations. The resulting neural controlled differential equation model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations. We demonstrate that our model achieves state-of-the-art performance against similar (ODE or RNN based) models in empirical studies on a range of datasets. Finally we provide theoretical results demonstrating universal approximation, and that our model subsumes alternative ODE models.

Key facts. Cited by 503 papers in the map (data through 13 Oct 2026). First posted on arXiv 18 May 2020.

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Citing papers per year: 2021: 47; 2022: 64; 2023: 78; 2024: 86; 2025: 109; 2026: 119.

503 papers.

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  1. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,440
  2. 2021Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layerscited by 607
  3. 2022On the Parameterization and Initialization of Diagonal State Space Modelscited by 420
  4. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
  5. 2024Deep Time Series Models: A Comprehensive Survey and Benchmarkcited by 195
  6. 2021Neural SDEs as Infinite-Dimensional GANscited by 161
  7. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  8. 2022Liquid Structural State-Space Modelscited by 134
  9. 2021CKConv: Continuous Kernel Convolution For Sequential Datacited by 117
  10. 2021Graph-Guided Network for Irregularly Sampled Multivariate Time Seriescited by 111
  11. 2021Modeling Irregular Time Series with Continuous Recurrent Unitscited by 102
  12. 2022Monarch: Expressive Structured Matrices for Efficient and Accurate Trainingcited by 101
38 more
  1. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 88
  2. 2022What Makes Convolutional Models Great on Long Sequence Modeling?cited by 86
  3. 2024Theoretical Foundations of Deep Selective State-Space Modelscited by 74
  4. 2022Multivariate Time Series Forecasting with Dynamic Graph Neural ODEscited by 72
  5. 2021Efficient and Accurate Gradients for Neural SDEscited by 69
  6. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  7. 2021FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizescited by 66
  8. 2024ContiFormer: Continuous-Time Transformer for Irregular Time Series Modelingcited by 61
  9. 2021Sig-Wasserstein GANs for Time Series Generationcited by 60
  10. 2022Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equationscited by 59
  11. 2021Neural ODE Processescited by 57
  12. 2025Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baselinecited by 55
  13. 2023Effectively Modeling Time Series with Simple Discrete State Spacescited by 54
  14. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  15. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  16. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 48
  17. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  18. 2021Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamicscited by 46
  19. 2023Parallelizing non-linear sequential models over the sequence lengthcited by 45
  20. 2022GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networkscited by 43
  21. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  22. 2021Noisy Recurrent Neural Networkscited by 42
  23. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  24. 2021Neural Point Process for Learning Spatiotemporal Event Dynamicscited by 42
  25. 2024Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Seriescited by 42
  26. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  27. 2022Deep Latent State Space Models for Time-Series Generationcited by 37
  28. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 37
  29. 2025Streaming Flow Policy: Simplifying diffusion/flow-matching policies by treating action trajectories as flow trajectoriescited by 37
  30. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 36
  31. 2024Oscillatory State-Space Modelscited by 36
  32. 2024Log Neural Controlled Differential Equations: The Lie Brackets Make a Differencecited by 35
  33. 2022Signature Methods in Machine Learningcited by 34
  34. 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Modelcited by 33
  35. 2022Out-of-Distribution Representation Learning for Time Series Classificationcited by 30
  36. 2021Attentive Neural Controlled Differential Equations for Time-series Classification and Forecastingcited by 29
  37. 2023Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Seriescited by 28
  38. 2024Long Range Propagation on Continuous-Time Dynamic Graphscited by 27

50 most cited of 503 All 503 (JSON)