Efficient coupled deep neural networks for the time-dependent coupled Stokes-Darcy problems
作者：
Highlights：
• Our method compiles the interface conditions of the coupled PDEs into the networks properly.
• This method can be served as an efficient alternative to the complex coupled problems.
• We sampled randomly and only input spatial coordinates without being restricted by the nature of samples.
• Our method is meshfree and parallel which can solve multiple variables independently at the same time.
• We give the theory to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution.
• We present the numerical examples in both 2D and 3D cases.
摘要
•Our method compiles the interface conditions of the coupled PDEs into the networks properly.•This method can be served as an efficient alternative to the complex coupled problems.•We sampled randomly and only input spatial coordinates without being restricted by the nature of samples.•Our method is meshfree and parallel which can solve multiple variables independently at the same time.•We give the theory to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution.•We present the numerical examples in both 2D and 3D cases.
论文关键词：Scientific computing,Deep neural networks,Stokes problem,Darcy equation,Beavers-Joseph-Saffman-Jones interface condition
论文评审过程：Received 28 March 2022, Revised 23 August 2022, Accepted 27 August 2022, Available online 16 September 2022, Version of Record 16 September 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127514
