Data-Driven Approach for the Rosenbluth Fokker-Planck Equation

In this study, we demonstrate a data-driven technique to efficiently obtain an accurate approximation of the transport coefficients in the Rosenbluth-Fokker-Planck equation. Our approach is based on an end-to-end mapping between the statistical moments of plasma particles and the corresponding transport coefficients. The mapping is accomplished by training the finely tuned multilayer perceptron (MLP) architecture. The training data is created by introducing the accurately approximated probability density function (PDF) using the entropic closure, and the PDF bridges the moments and the coefficients by solving the Poisson equation of the Rosenbluth potential. This approach ensures accurate consideration of all nonlinearities in the system, hence the quality of the training data is guaranteed. We integrated the proposed model in a stochastic particle Fokker-Planck method. By adopting the particle method,  we exploit benefits in the computational costs and are able to fix the imbalance of the collision symmetries induced by the discretization in the computational domain. The proposed scheme is validated for a highly nonlinear system and compared to the Direct Simulation Monte Carlo (DSMC) method. The results show that our approach successfully reproduces the correct anisotropic relaxation behavior and improves the computational cost compared to not only the direct evaluation of the transport coefficients but also the DSMC method.