Comprehensive Review of Neural Differential Equations for Time Series Analysis

Oh, YongKyung; Kam, Seungsu; Lee, Jonghun; Lim, Dong-Young; Kim, Sungil; Bui, Alex A. T.

doi:10.24963/ijcai.2025/1179

Comprehensive Review of Neural Differential Equations for Time Series Analysis

YongKyung Oh, Seungsu Kam, Jonghun Lee, Dong-Young Lim, Sungil Kim, Alex A. T. Bui

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Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence. Survey Track. Pages 10621-10631.

https://doi.org/10.24963/ijcai.2025/1179

Keywords

Machine Learning: ML: Time series and data streams
Data Mining: DM: Mining spatial and/or temporal data
Machine Learning: ML: Learning theory
Machine Learning: ML: Deep learning architectures

Abstract

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.

YongKyung Oh, Seungsu Kam, Jonghun Lee, Dong-Young Lim, Sungil Kim, and Alex A. T. Bui. 2025. Comprehensive Review of Neural Differential Equations for Time Series Analysis. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25. IJCAI, 10621–10631. https://doi.org/10.24963/ijcai.2025/1179

@inproceedings{ijcai2025p1179,
  title     = {Comprehensive Review of Neural Differential Equations for Time Series Analysis},
  author    = {Oh, YongKyung and Kam, Seungsu and Lee, Jonghun and Lim, Dong-Young and Kim, Sungil and Bui, Alex A. T.},
  booktitle = {Proceedings of the Thirty-Fourth International Joint Conference on
               Artificial Intelligence, {IJCAI-25}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {James Kwok},
  pages     = {10621--10631},
  year      = {2025},
  month     = {8},
  note      = {Survey Track},
  doi       = {10.24963/ijcai.2025/1179},
  url       = {https://doi.org/10.24963/ijcai.2025/1179},
}

TY  - CPAPER
TI  - Comprehensive Review of Neural Differential Equations for Time Series Analysis
AU  - Oh, YongKyung
AU  - Kam, Seungsu
AU  - Lee, Jonghun
AU  - Lim, Dong-Young
AU  - Kim, Sungil
AU  - Bui, Alex A. T.
T2  - Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2025
SP  - 10621
EP  - 10631
DO  - 10.24963/ijcai.2025/1179
UR  - https://doi.org/10.24963/ijcai.2025/1179
ER  -