论文标题
时间离散化对与ANN的抛物线PDE溶液的影响
The effect of time discretization on the solution of parabolic PDEs with ANNs
论文作者
论文摘要
我们通过极端学习机（ELMS）神经网络研究了抛物线PDE的分辨率，该网络具有单个隐藏层，并且与深度学习神经网络相比，可以以适中的计算成本进行训练。我们的方法通过应用经典的ODE技术来解决时间的演变，并使用基于ELM的搭配来解决所得的固定椭圆问题。在此框架中，对一些线性抛物线PDE进行了研究$θ$ -METHOD和向后差公式（BDF）技术，这些PDE是解决方法的稳定性和准确性属性的问题。数值实验的结果证实，基于ELM的溶液技术与BDF方法相结合可以提供抛物线PDE的高精度解决方案。
We investigate the resolution of parabolic PDEs via Extreme Learning Machine (ELMs) Neural Networks, which have a single hidden layer and can be trained at a modest computational cost as compared with Deep Learning Neural Networks. Our approach addresses the time evolution by applying classical ODEs techniques and uses ELM-based collocation for solving the resulting stationary elliptic problems. In this framework, the $θ$-method and Backward Difference Formulae (BDF) techniques are investigated on some linear parabolic PDEs that are challeging problems for the stability and accuracy properties of the methods. The results of numerical experiments confirm that ELM-based solution techniques combined with BDF methods can provide high-accuracy solutions of parabolic PDEs.
