This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is shown how the choice of integration technique implicitly regularizes the learned model, and how the solver's corresponding stability region affects training and prediction performance. From this analysis, a stability-informed parameter initialization technique is introduced. The effectiveness of the initialization method is displayed across several learning benchmarks and industrial applications.

翻译：本文研究神经常微分方程（Neural ODEs）的训练问题，重点探讨数值积分方法、稳定区域、步长与初始化技术之间的相互作用。研究表明，积分方法的选择会隐式正则化所学习的模型，而求解器对应的稳定区域会影响训练与预测性能。基于此分析，提出了一种稳定性启发的参数初始化技术。该初始化方法在多项学习基准测试和工业应用中的有效性得到了验证。