Physics-Informed Neural Networks for Solving Coupled Stokes-Darcy Equation.

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Machine learning

Background:

• Coupled Stokes-Darcy equations model fluid flow in porous media.
• Traditional numerical methods face challenges with grid generation and computational cost.
• Existing physics-informed neural network (PINN) methods struggle with interface discontinuities and small parameters in these equations.

Purpose of the Study:

• To develop a grid-free deep learning method for solving coupled Stokes-Darcy equations with Bever-Joseph-Saffman interface conditions.
• To enhance the approximation accuracy of PINNs for challenging fluid dynamics problems.
• To introduce strategies that improve the robustness and efficiency of PINNs.

Main Methods:

• A grid-free deep learning approach utilizing physics-informed neural networks (PINNs).
• Implementation of a loss-function-weighted strategy to manage equation complexities.
• Adoption of a parallel network structure and local adaptive activation functions to boost approximation capabilities.

Main Results:

• The proposed method effectively solves coupled Stokes-Darcy equations with Bever-Joseph-Saffman interface conditions.
• Numerical experiments validate the enhanced accuracy and computational efficiency compared to direct PINN application.
• The strategies significantly improve the handling of rigid terms and interface discontinuities.

Conclusions:

• The developed grid-free deep learning method offers a robust and efficient solution for coupled Stokes-Darcy equations.
• The proposed enhancements to PINNs provide a promising direction for tackling complex multi-physical field coupling problems.
• This approach demonstrates significant potential for advancing numerical simulations in fluid dynamics and related scientific fields.