AI4Plasma I: Data-Efficient Surrogate Modeling of Capacitively Coupled Plasma Fields

Reference capacitively coupled plasma (CCP) simulations provide spatially resolved plasma fields but are costly to generate across operating conditions. We compare the data efficiency of five surrogate architectures--Coordinate MLP, PCA-Net, U-Net, Fourier neural operator (FNO), and Transolver--for predicting RF-cycle-averaged electron density, ion density, electric potential, and electron temperature in 1D planar and 2D axisymmetric GEC CCP benchmarks. We assess the number of reference simulations needed to achieve 1% and 2% mean relative L2 error for parameter-interior and parameter-boundary test cases, and examine architecture-specific mechanisms. FNO achieves the lowest or joint-lowest reference-case requirement in seven of eight comparisons. In 1D, FNO reaches 1% interior error with 50 training cases, compared with 100 for Transolver and 200 for U-Net. In 2D, FNO and U-Net each reach 1% interior error with 100 cases; FNO and Transolver each reach 2% parameter-boundary error with 200 cases, compared with 400 for U-Net. At the stricter 1% 2D parameter-boundary target, Transolver requires 400 cases versus 800 for FNO. Additional analyses investigate FNO spectral modes and padding, U-Net skip connections, Transolver adaptive slicing, and PCA-Net projection versus prediction error. The results support FNO as a data-efficient baseline for the tested CCP settings, while showing that the preferred architecture depends on the accuracy target and operating-parameter region.