CPINNs: A coupled physics-informed neural networks for the closed-loop geothermal system

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a kind of coupled physics-informed neural networks (CPINNs) for the closed -loop geothermal system, which is a new coupled multi-physics PDEs and mainly consists of a framework of underground heat exchange pipelines to extract the geothermal heat from the geothermal reservoir. The approach embeds the PDEs formula into the loss function of the neural networks and the resulting networks is trained to meet the equations along with the boundary conditions, initial conditions and interface conditions. The advantage of this method is that it avoids grid generation compared with the grid based methods and it is parallel for the equations and variables. In order to improve the approximation ability of the CPINNs, we add the loss weights before some terms of the loss function. Moreover, the approximate ability of the CPINNs is demonstrated by the theoretical analysis of convergence. Finally, some numerical examples are carried out to demonstrate the effectiveness of the CPINNs intuitively.