This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and partial differential equations and their analysis who are curious to see their role in machine learning. Using three examples from machine learning and applied mathematics, we will see how neural ODEs can provide new insights into deep learning and a foundation for more efficient algorithms.

翻译：这篇简洁自洽的文章旨在介绍并综述基于神经常微分方程（neural ODEs）的连续时间深度学习方法。本文主要面向熟悉常微分方程和偏微分方程及其分析、并希望了解其在机器学习中作用的读者。通过机器学习与应用数学领域的三个实例，我们将看到神经常微分方程如何为深度学习提供新见解，并为更高效的算法奠定基础。