Plasma two-fluid simulation using physics-informed neural networks

We develop a physics-informed neural network (PINN)-based framework for simulating electron–ion two-fluid plasmas with large scale separation. As a benchmark, we examine the one-dimensional diffusion of a magnetized low-temperature plasma and compute the spatiotemporal evolution of the two-fluid variables. The governing equations, initial conditions, and boundary conditions are embedded into the composite loss function, and the forward problem is solved by minimizing this loss function. Accuracy is evaluated by comparison with conventional numerical simulations. To handle the intrinsic electron–ion multiscale nature, we adopt a species-dependent normalization that scales each variable by appropriate thermal and characteristic quantities, yielding improved stability and a mean relative error of 3.08 × 10−3. Although training instability occurs for certain hyperparameter choices, such as different learning rates or random initializations, well-converged cases can be clearly identified from the loss evolution. Therefore, this instability does not constitute a serious practical limitation. The results further indicate that learning stability depends on how strongly the solution is anchored by boundary constraints. Neumann-type boundary conditions exhibit sensitivity to learning rate and initialization, whereas Dirichlet conditions improve reproducibility and robustness. Overall, this study clarifies how normalization and boundary-condition design jointly govern training stability in PINN-based two-fluid plasma simulations.