论文标题
学习时间延迟系统具有神经常规微分方程
Learning Time Delay Systems with Neural Ordinary Differential Equations
论文作者
论文摘要
提出了一种使用神经网络来学习从顺序数据的时间延迟系统动态的新型方法。具有训练延迟的神经网络用于近似延迟微分方程的右侧。我们通过离散时间历史记录并训练相应的神经普通微分方程（节点）来学习动力学，将延迟微分方程与普通微分方程联系起来。使用来自混沌行为的数据来学习Mackey-Glass方程的动力学的一个示例。在学习了非线性和时间延迟之后，我们证明了神经网络的分叉图与原始系统的分叉图相匹配。
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate the delay differential equation to an ordinary differential equation by discretizing the time history and train the corresponding neural ordinary differential equation (NODE) to learn the dynamics. An example on learning the dynamics of the Mackey-Glass equation using data from chaotic behavior is given. After learning both the nonlinearity and the time delay, we demonstrate that the bifurcation diagram of the neural network matches that of the original system.
