用微分方程建模时间序列，更好处理不规则采样和连续动态。
Comprehensive Review of Neural Differential Equations for Time Series Analysis
- 将神经网络与微分方程结合，实现对连续时间过程的建模。
- 支持不规则采样数据，比RNN、Transformer更适配真实场景。
- 适合研究时序建模的学者和需要高精度预测的工业用户。
时间序列建模在多个领域至关重要。传统方法如RNN和Transformer虽在离散时间与规则采样数据上表现良好，但在捕捉真实世界中固有的连续动态和不规则采样模式方面面临挑战。神经微分方程（NDE）通过融合神经网络的灵活性与微分方程的数学严谨性，带来范式转变。本文系统综述了基于NDE的时间序列分析方法，包括神经常微分方程（Neural ODEs）、神经控制微分方程（Neural CDEs）和神经随机微分方程（Neural SDEs），详述其数学形式、数值方法与应用，突出其建模连续时间动态的能力。同时探讨关键挑战与未来方向。本综述为研究人员与实践者利用NDE进行先进时序分析提供基础。
原文摘要 · Abstract (English)
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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