Benchmarking deep learning models for accurate and efficient 2D simulations of microwave-plasma interaction

Efficient numerical simulation of microwave-plasma interactions is challenging due to the interplay of electromagnetic (EM) wave transmission, reflection, and absorption in inhomogeneous plasma, leading to complex field distributions and high computational demands for accurate results. In this study, we investigate four deep learning (DL) models, U-Net, variational autoencoder, Pixel-to-Pixel, and a custom hybrid UNet-vision transformer (ViT), as alternative methods to traditional simulation techniques. These models are trained on a comprehensive and diverse dataset that encompasses a wide spectrum of plasma densities and topologies exposed to plane EM waves with fixed frequency (110 GHz) and amplitude (1 V/m). The 2D plasma density profiles are obtained from fluid simulations of high power microwave breakdown. A training dataset, consisting of plasma density profiles and their corresponding root mean square (RMS) total electric field distributions, is generated using 2D finite-difference time-domain (FDTD) simulations, where the total field comprises incident and scattered components. We have performed entropy and similarity analysis on the dataset to characterize the complexity of the EM-plasma interaction problem. Once trained, these DL models are used to predict the 2D RMS total electric field for an incident microwave interacting with previously unseen plasma density profiles. We benchmark the performance of these DL models by comparing their results with those obtained from established 2D FDTD-based methods using multiple performance metrics. Our results indicate that DL approaches, in general, provide a speedup of around 1000× compared to FDTD simulations, with the hybrid UNet-ViT model demonstrating the highest accuracy. Additionally, we have also conducted latent space analysis to introduce explainability in the DL models.