PINNs for 1D Plasma Transport: A Mesh-Free Deep Learning Framework with Quantitative Validation

Abstract

One-dimensional plasma transport modeling is a foundational task in fusion energy research, gas-discharge lamp design, and plasma-assisted semiconductor processing. Traditional mesh-based solvers encounter well-known difficulties: explicit time-stepping is restricted by the Courant-Friedrichs-Lewy (CFL) stability limit, implicit schemes require expensive iterative linear algebra, and adaptive mesh refinement is difficult to maintain in complex geometries. This paper proposes a Physics-Informed Neural Network (PINN) framework that encodes the governing drift-diffusion and Poisson equations directly into the network loss function, yielding a mesh-free, continuously differentiable solution over the full spatiotemporal domain. A four-layer fully connected network with 50 neurons per layer and hyperbolic tangent activation is trained in TensorFlow 2.12 using 10,000 Latin Hypercube (LHS) collocation points. A two-phase optimizer combining Adam and L-BFGS-B drives the composite residual loss to convergence. Validation against the exact analytical solution of the 1D ambipolar diffusion problem gives a relative L² density error of 0.57% and an electric-field error of 0.93%, both below the second-order Crank-Nicolson finite difference (FD) reference at equal spatial resolution. Ten figures covering training convergence, density accuracy, error distribution, sheath physics, electric field, method comparison, architecture sensitivity, temperature-pressure evolution, sampling strategy, and convergence rates are reported alongside one quantitative performance table. Current limitations regarding training cost, spectral bias, and kinetic effects are discussed, and a structured future-work roadmap is provided.