MC-CDNNs: The Monte Carlo-coupled deep neural networks approach for stochastic dual-porosity-Stokes flow coupled model

Abstract

In this paper, we propose a coupled neural network learning method to solve the stochastic dual-porosity-Stokes flow problem. We combine Monte Carlo and coupled deep neural networks methods (MC-CDNNs) to transform the uncertain stochastic coupled problems into a deterministic coupled problem, and compile the complex interface conditions associated with the coupled problem into the neural network to guarantee the physical constraints of the approximate solution. In addition, the convergence analysis illustrates the capability of the method in solving the stochastic coupling problem. Particularly, we conducted 2D/3D numerical experiments to demonstrate the algorithm's effectiveness and efficiency, and to show its advantages in practical applications.