Comprehensive Review of Neural Differential Equations for Time Series Analysis

2025/02/14 by Oh, YongKyung, Kam, Seungsu, Lee, Jonghun +3 · 1 citation
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2502.09885

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.

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