mlsanityData to 14 Oct 2026

Comprehensive Review of Neural Differential Equations for Time Series Analysis

arXiv 2502.09885 ↗First posted 14 Feb 2025cs.LG cs.AIcited by 20

Not on the map. Why?

Abstract (arXiv)

Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the continuous dynamics and irregular sampling patterns inherent in real-world scenarios. Neural Differential Equations (NDEs) represent a paradigm shift by combining the flexibility of neural networks with the mathematical rigor of differential equations. This paper presents a comprehensive review of NDE-based methods for time series analysis, including neural ordinary differential equations, neural controlled differential equations, and neural stochastic differential equations. We provide a detailed discussion of their mathematical formulations, numerical methods, and applications, highlighting their ability to model continuous-time dynamics. Furthermore, we address key challenges and future research directions. This survey serves as a foundation for researchers and practitioners seeking to leverage NDEs for advanced time series analysis.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). Builds on 52 of its 76 references that are in the map. First posted on arXiv 14 Feb 2025.

Builds on

52 of 76 references.

References · 52

  1. 2017Attention Is All You Needcited by 60,361
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,367
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  5. 2018DeepMind Control Suitecited by 956
  6. 2019Compressive Transformers for Long-Range Sequence Modellingcited by 726
  7. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  8. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  9. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 554
  10. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
  11. 2022Transformers in Time Series: A Surveycited by 497
  12. 2019Augmented Neural ODEscited by 397
38 more
  1. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  2. 2017Stable Architectures for Deep Neural Networkscited by 341
  3. 2018Scalable and accurate deep learning for electronic health recordscited by 280
  4. 2020Scalable Gradients for Stochastic Differential Equationscited by 271
  5. 2021Multi-Time Attention Networks for Irregularly Sampled Time Seriescited by 238
  6. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 231
  7. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  8. 2015Doctor AI: Predicting Clinical Events via Recurrent Neural Networkscited by 208
  9. 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
  10. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 191
  11. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 176
  12. 2021Neural SDEs as Infinite-Dimensional GANscited by 161
  13. 2019Graph Neural Ordinary Differential Equationscited by 154
  14. 2020Dissecting Neural ODEscited by 153
  15. 2019Neural Jump Stochastic Differential Equationscited by 150
  16. 2020Neural Rough Differential Equations for Long Time Seriescited by 143
  17. 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
  18. 2019Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noisecited by 101
  19. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 101
  20. 2019ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEscited by 84
  21. 2020Learning Long-Term Dependencies in Irregularly-Sampled Time Seriescited by 83
  22. 2020Learning Differential Equations that are Easy to Solvecited by 81
  23. 2021Stiff Neural Ordinary Differential Equationscited by 78
  24. 2020Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODEcited by 76
  25. 2021Efficient and Accurate Gradients for Neural SDEscited by 71
  26. 2020STEER: Simple Temporal Regularization For Neural ODEscited by 58
  27. 2021Neural ODE control for classification, approximation and transportcited by 57
  28. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  29. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 36
  30. 2020"Hey, that's not an ODE": Faster ODE Adjoints via Seminormscited by 35
  31. 2024Log Neural Controlled Differential Equations: The Lie Brackets Make a Differencecited by 35
  32. 2017Discrete Event, Continuous Time RNNscited by 31
  33. 2020A Review of Deep Learning Methods for Irregularly Sampled Medical Time Series Datacited by 31
  34. 2021Attentive Neural Controlled Differential Equations for Time-series Classification and Forecastingcited by 29
  35. 2020Stable Neural Flowscited by 25
  36. 2022EXIT: Extrapolation and Interpolation-based Neural Controlled Differential Equations for Time-series Classification and Forecastingcited by 22
  37. 2020Learning normalizing flows from Entropy-Kantorovich potentialscited by 18
  38. 2021ACE-NODE: Attentive Co-Evolving Neural Ordinary Differential Equationscited by 15

50 most cited of 52 All 52 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 16.

20 papers.

Sort:

By area:

  1. 2026Tracing Agentic Failure from the Flow of Successcited by 8
  2. 2025Equilibrium Propagation for Learning in Lagrangian Dynamical Systemscited by 6
  3. 2025Bridging Neural ODE and ResNet: A Formal Error Bound for Safety Verificationcited by 3
  4. 2025A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Seriescited by 1
  5. 2026Efficient Neural Controlled Differential Equations via Attentive Kernel Smoothingcited by 1
  6. 2026Oscillators Are All You Need: Irregular Time Series Modelling via Damped Harmonic Oscillators with Closed-Form Solutionscited by 1
  7. 2026EIDOS: Latent-Space Predictive Learning for Time Series Foundation Modelscited by 1
  8. 2026Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equationscited by 1
  9. 2026One-Step Graph-Structured Neural Flows for Irregular Multivariate Time Series Classificationcited by 1
  10. 2026Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEscited by 1
  11. 2026Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regressioncited by 1
  12. 2025Convergence, design and training of continuous-time dropout as a random batch methodcited by 0
8 more
  1. 2026ARTEMIS: A Neuro Symbolic Framework for Economically Constrained Market Dynamicscited by 0
  2. 2026Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Methodcited by 0
  3. 2026Neural Ordinary Differential Equations for Modeling Socio-Economic Dynamicscited by 0
  4. 2026Embedded Variational Neural Stochastic Differential Equations for Learning Heterogeneous Dynamicscited by 0
  5. 2026Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programmingcited by 0
  6. 2026From Coarse to Fine: Managing Temporal Granularity in Spatio-Temporal Data for Fine-Grained Traffic Predictioncited by 0
  7. 2026INDEQS: Informed Neural controlled Differential EQuationScited by 0
  8. 2026Continuous-Time Machine Learning: A Unified Mathematical Perspectivecited by 0