Physics-Informed neural network for level set method in vapor condensation

Vapor condensation, a common physical phenomenon, is a complex multiphase flow problem involving mass transfer and heat transfer, which presents significant challenges in simulation, particularly regarding accuracy and computational efficiency. Hence, to improve simulation accuracy and achieve rapid prediction of condensation-generated water, this paper introduces an LS-PINN model, combining the precision of the level set method (LS) with the efficiency of the physics-informed neural network (PINN). It comprises two main components: i) a more accurate vapor condensation model is constructed by embedding Lee model as source terms into the two-phase flow model based on the level set method. And then the model is validated through the finite element method (FEM). ii) a dimensionless form suitable for PINN is derived of the governing equations (e.g., continuity equation, Navier-Stokes equations (without considering surface tension), heat equation and level set equation). On this basis, the LS-PINN model is constructed by incorporating the governing equations into the loss function, and trained through adaptive weight algorithm and sequential fixed strategy. Finally, three numerical examples are designed to validate the proposed model. The results show that the LS-PINN model can evaluate the liquid film thickness generated by condensation in one-dimensional and two-dimensional situations effectively. Furthermore, the total training time for the LS-PINN models is no more than 30 h, whereas the finite element calculation time takes approximately 130 h. The prediction time, which is measured in milliseconds, makes the PINN model highly suitable for applications where immediate responses are crucial, such as in digital twin systems.