通过简单线性模型揭示神经ODE训练困难原因并提出稳定方法
Learning the Simplest Neural ODE
- 用一维线性模型分析神经ODE训练困难的根源
- 提出新稳定方法并完成收敛性理论证明
- 适合初学神经ODE的研究者快速上手
自「神经常微分方程（Neural ODE）」论文问世以来，利用深度学习学习微分方程已在系统辨识、时间序列预测等领域得到应用。借助微分同胚性质，神经ODE也适用于生成建模。尽管能融合多种物理信息，实际训练神经ODE仍具挑战性。本研究通过最简单的单变量线性模型，揭示了神经ODE训练困难的原因，并提出一种新的稳定化方法，同时提供解析收敛性分析。所呈现的洞察与技术可作为神经ODE初学者的简明教程。
原文摘要 · Abstract (English)
Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic nature of ODE solution maps, neural ODEs has also enabled their use in generative modeling. Despite the rich potential to incorporate various kinds of physical information, training Neural ODEs remains challenging in practice. This study demonstrates, through the simplest one-dimensional linear model, why training Neural ODEs is difficult. We then propose a new stabilization method and provide an analytical convergence analysis. The insights and techniques presented here serve as a concise tutorial for researchers beginning work on Neural ODEs.
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