Solving forward and inverse problems for atmospheric radio frequency discharge by Physics-Informed Neural Networks

With the requirement of intelligent control of atmospheric plasmas system, more Artificial Intelligence (AI) algorithms should be introduced into the field of plasma simulation. In this study, an innovative Physics-Informed Neural Networks (PINNs) framework for solving both forward and inverse problems in atmospheric radio frequency (RF) plasma is explored. For forward problems, the PINNs architecture with multi-scale feature is established by coupling Poisson’s equation, continuity equations, and drift-diffusion approximation equations into the loss function, to successfully capture the key plasma characteristics, showing good agreement with results from fluid simulation by discretization methods. For inverse problems that usually cannot be solved by discretization methods, by incorporating additional simulated (or measured) data of electric field as constraints in loss function, PINNs can accurately infer the applied voltage with relative errors smaller than 1%. The influence of various sampling positions, number of sampling points, and noise on the inversion of discharge parameter by PINNs is also investigated. In this study, according to the computational data, this mesh-less approach of PINNs successfully solves the fluid equations without relying on discretization methods and also shows the ability to inverse the discharge parameters such as applied voltage, driving frequency, or electrode spacing, given the data of electric field or plasma density, offering novel methodologies and insights for the intelligent control of atmospheric plasma systems.