Physics-Informed Neural Networks for Solving Parameterized Dual-Domain Darcy–Brinkman Flows in Gradient Porous Mediums

Abstract

The ability to solve parameterized partial differential equations is pivotal to improving engineering design efficiency, and with the advancement of machine learning technologies, physics-informed neural networks (PINNs) provide a promising avenue. In this work, a coupled dual-domain Darcy–Brinkman flow model for gradient porous media is established. Building upon this, the trunk-branch (TB)-net PINN framework, which is capable of dealing with multi-physical field issues, is utilized to conduct predictions for a specific porosity configuration scenario, and the performance of different data collocation strategies is examined. Following this, explorations for parameterized flows are implemented, demonstrating remarkable accuracy in two randomly chosen conditions. This is the first known application of PINNs-like methods to handle such complex parameterized dual-domain Darcy–Brinkman flows, yielding invaluable experience pertinent to engineering design and efficiency optimization.