# Comprehensive Review of Neural Differential Equations for Time Series Analysis

arXiv: https://arxiv.org/abs/2502.09885 · HTML: https://mlsanity.com/paper/2502.09885/

## 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 (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Doctor AI: Predicting Clinical Events via Recurrent Neural Networks](https://mlsanity.com/paper/1511.05942/) (2015)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)

## Built on by (most cited first, 20 of 20)

- [Tracing Agentic Failure from the Flow of Success](https://mlsanity.com/paper/2607.12747/) (2026)
- [Equilibrium Propagation for Learning in Lagrangian Dynamical Systems](https://mlsanity.com/paper/2505.07363/) (2025)
- [Bridging Neural ODE and ResNet: A Formal Error Bound for Safety Verification](https://mlsanity.com/paper/2506.03227/) (2025)
- [A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series](https://mlsanity.com/paper/2511.06609/) (2025)
- [Efficient Neural Controlled Differential Equations via Attentive Kernel Smoothing](https://mlsanity.com/paper/2602.02157/) (2026)
- [Oscillators Are All You Need: Irregular Time Series Modelling via Damped Harmonic Oscillators with Closed-Form Solutions](https://mlsanity.com/paper/2602.12139/) (2026)
- [EIDOS: Latent-Space Predictive Learning for Time Series Foundation Models](https://mlsanity.com/paper/2602.14024/) (2026)
- [Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations](https://mlsanity.com/paper/2603.18331/) (2026)
- [One-Step Graph-Structured Neural Flows for Irregular Multivariate Time Series Classification](https://mlsanity.com/paper/2605.10179/) (2026)
- [Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEs](https://mlsanity.com/paper/2606.18898/) (2026)
- [Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression](https://mlsanity.com/paper/2607.00257/) (2026)
- [Convergence, design and training of continuous-time dropout as a random batch method](https://mlsanity.com/paper/2510.13134/) (2025)
- [ARTEMIS: A Neuro Symbolic Framework for Economically Constrained Market Dynamics](https://mlsanity.com/paper/2603.18107/) (2026)
- [Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Method](https://mlsanity.com/paper/2603.25024/) (2026)
- [Neural Ordinary Differential Equations for Modeling Socio-Economic Dynamics](https://mlsanity.com/paper/2604.00632/) (2026)
- [Embedded Variational Neural Stochastic Differential Equations for Learning Heterogeneous Dynamics](https://mlsanity.com/paper/2604.00669/) (2026)
- [Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming](https://mlsanity.com/paper/2606.06094/) (2026)
- [From Coarse to Fine: Managing Temporal Granularity in Spatio-Temporal Data for Fine-Grained Traffic Prediction](https://mlsanity.com/paper/2606.09392/) (2026)
- [INDEQS: Informed Neural controlled Differential EQuationS](https://mlsanity.com/paper/2606.19138/) (2026)
- [Continuous-Time Machine Learning: A Unified Mathematical Perspective](https://mlsanity.com/paper/2609.16710/) (2026)

## 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.