Solving second-order nonlinear evolution partial differential equations using deep learning

• 作者: Jun Li Yong Chen
• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2020,（10）
• 所属期刊栏目: MATHEMATICAL PHYSICS
• 页码范围: 42-52
• 页数: 11页
• 语种: 英文

摘要

Solving nonlinear evolution partial differential equations has been a longstanding computational challenge.In this paper,we present a universal paradigm of learning the system and extracting patterns from data generated from experiments.Specifically,this framework approximates the latent solution with a deep neural network,which is trained with the constraint of underlying physical laws usually expressed by some equations.In particular,we test the effectiveness of the approach for the Burgers' equation used as an example of second-order nonlinear evolution equations under different initial and boundary conditions.The results also indicate that for soliton solutions,the model training costs significantly less time than other initial conditions.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	Jun Li		1	0	0.0	0.0
2	Yong Chen		1	0	0.0	0.0