Transfer Learning using Neural Ordinary Differential Equations

New Designed Loss Functions to Solve Ordinary Differential Equations with Artificial Neural Network

This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE. In section 2, the loss function is generalized to $n^\text{th}$ order ordinary differential equation(ODE). Other methods of construction are examined in Section 3 and applied to three different models to assess their effectiveness.

使用神经常微分方程建模化学反应网络

Modelling Chemical Reaction Networks using Neural Ordinary Differential Equations

本文提出使用神经常微分方程结合深度学习建模化学反应网络，以揭示经验模型未捕捉的隐藏动态，并辅助未来反应网络设计。

多重打靶神经常微分方程的一种凝缩方法

A condensing approach to multiple shooting neural ordinary differential equation

针对神经常微分方程中多重打靶因等式约束难以引入而应用受限的问题，提出一种基于凝缩的方法，使Adam等一阶优化方法能成功训练多重打靶神经常微分方程（MS-NODE）。

Learning Time Delay Systems with Neural Ordinary Differential Equations

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 del…