A physics-constrained deep residual network for solving the sine-Gordon equation

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2021,（1）
• 所属期刊栏目: MATHEMATICAL PHYSICS
• 页码范围: 1-5
• 页数: 5页
• 语种: 英文

摘要

Despite some empirical successes for solving nonlinear evolution equations using deep learning,there are several unresolved issues.First,it could not uncover the dynamical behaviors of some equations where highly nonlinear source terms are included very well.Second,the gradient exploding and vanishing problems often occur for the traditional feedforward neural networks.In this paper,we propose a new architecture that combines the deep residual neural network with some underlying physical laws.Using the sine-Gordon equation as an example,we show that the numerical result is in good agreement with the exact soliton solution.In addition,a lot of numerical experiments show that the model is robust under small perturbations to a certain extent.