论文标题
从数据中学习微分方程
Learning differential equations from data
论文作者
论文摘要
微分方程用于模拟起源于物理，生物学，化学和工程等学科的问题。近来，由于数据的丰富性，可以主动搜索数据驱动的方法，以从数据中学习微分方程模型。但是，许多数值方法通常会缺乏。神经网络和深度学习的进步，促使向数据驱动的深度学习方法转向从数据学习微分方程的方法。在这项工作中，我们建议使用不同数量的隐藏层和不同的神经网络宽度来从数据中学习诸如Fitzhugh-Nagumo方程之类的ODE（例如Fitzhugh-Nagumo方程）来测试其性能。
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.
