A novel solution of fluid equations for radio-frequency plasmas by physics-informed neural networks with transfer learning

Typically, fluid model solved by discretization methods is applied to explore the low-temperature plasmas heavily depending on mesh generation. In this study, a novel approach represented by physics-informed neural networks (PINNs) with transfer learning is introduced to solve the tightly coupled equations in fluid model describing the atmospheric radio frequency discharges, encompassing Poisson equation, continuity equations, and drift-diffusion approximation. By embedding these equations as physical constraints into the loss function and training the model using a combination of boundary and initial condition data, the well-trained PINNs accurately predict the key physical quantities, including electron density, ion density, electron flux, ion flux, and electric field, which exhibit exceptional agreement with traditional fluid simulation outcomes by the finite difference method with L2 errors consistently around 0.001. Moreover, the application of transfer learning to adapt pre-trained PINNs to various voltages underscores the generalization potential of PINNs to explore the discharge evolution. In this study, the simulation results confirm that this mesh-less approach of PINNs effectively solves the fluid equations instead of discretization methods and indicates notable generalization capabilities, paving the way to find the more efficient numerical solutions of fluid model in the era of artificial intelligence.