Comprehensive Review of Neural Differential Equations for Time Series Analysis

TL;DR

This paper reviews neural differential equations (NDEs) for time series analysis, emphasizing their ability to model continuous dynamics and handle irregular sampling, offering a comprehensive overview of formulations, applications, and future challenges.

Contribution

It provides the first comprehensive survey of NDE-based methods for time series analysis, detailing mathematical formulations, applications, and future research directions.

Findings

NDEs effectively model continuous-time dynamics in time series.

NDE variants include neural ODEs, CDEs, and SDEs.

The survey highlights challenges and future research avenues.

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.