Exploring Physics Informed Neural Networks for Solving an Anisotropic Diffusion Equation Arising in Plasma Kinetics

The recent success of deep neural networks in artificial intelligence encourages their applications to solve high-dimensional Partial Differential Equations (PDEs) describing the particle kinetics in low-temperature plasma (LTP). Physics-informed neural networks (PINNs) have already been implemented in the NVIDIA’s SimNet and Modulus software and demonstrated for different physical systems. Although traditional numerical methods are still generally favored for forward problems, PINNs have been applied to inverse problems that cannot be solved with traditional techniques. In this work, we report on investigations to apply statistical factor analysis techniques to tune hyperparameters of PINNs for solving PDFs arising in plasma physics. The case is the anisotropic diffusion equation, which describes, for example, a surface diffusion over a sphere. This equation appears in modeling electron kinetics in phase space in collisional LTP. We test the effects of hyperparameters and platforms on the performance and accuracy of PINN solvers on modern GPU/CUDA platforms. Our experiments indicate an overall 8x speedup effect from the mean due to GPU and CUDA libraries versus CPU-based processing and indicate a correlation of the number of hidden layers with the number of epochs of training, showing that with an increase in hidden layers, the number of epochs of training can be lowered without impacting the accuracy of results.