Differential equations are used to model problems that originate in disciplines such as physics, biology, chemistry, and engineering. In recent times, due to the abundance of data, there is an active search for data-driven methods to learn Differential equation models from data. However, many numerical methods often fall short. Advancements in neural networks and deep learning, have motivated a shift towards data-driven deep learning methods of learning differential equations from data. In this work, we propose a forward-Euler based neural network model and test its performance by learning ODEs such as the FitzHugh-Nagumo equations from data using different number of hidden layers and different neural network width.

翻译：不同方程式被用于模拟源自物理、生物学、化学和工程等学科的问题。最近,由于数据丰富,正在积极寻找数据驱动的方法,以便从数据中学习差异方程模型。然而,许多数字方法往往不尽如人意。神经网络和深层学习的进步促使人们转向数据驱动的深层学习方法,从数据中学习差异方程。在这项工作中,我们建议采用基于前向的神经网络模型,并通过学习代码来测试其性能,例如FitzHugh-Nagumo等方程式,这些数据来自不同层次和不同神经网络宽度的数据。