Extracting Electron Scattering Cross Sections from Swarm Data using Deep Neural Networks

TL;DR

This paper explores the use of deep neural networks, especially DenseNet, to accurately infer electron scattering cross sections from swarm data, addressing the inverse problem with improved precision and uncertainty estimation.

Contribution

It introduces CNN and DenseNet architectures for the inverse swarm problem, demonstrating superior accuracy of DenseNet and incorporating Bayesian methods for uncertainty quantification.

Findings

DenseNet outperforms other neural networks in predicting cross sections.

Deep learning models can effectively solve the inverse swarm problem.

Bayesian approximation provides uncertainty estimates for the predictions.

Abstract

Electron-neutral scattering cross sections are fundamental quantities in simulations of low temperature plasmas used for many technological applications today. From these microscopic cross sections, several macro-scale quantities (called "swarm" parameters) can be calculated. However, measurements as well as theoretical calculations of cross sections are challenging. Since the 1960s researchers have attempted to solve the inverse swarm problem of obtaining cross sections from swarm data; but the solutions are not necessarily unique. To address this issues, we examine the use of deep learning models which are trained using the previous determinations of elastic momentum transfer, ionization and excitation cross sections for different gases available on the LXCat website and their corresponding swarm parameters calculated using the BOLSIG+ solver for the numerical solution of the Boltzmann equation for electrons in weakly ionized gases. We implement artificial neural network (ANN), convolutional neural network (CNN) and densely connected convolutional network (DenseNet) for this investigation. To the best of our knowledge, there is no study exploring the use of CNN and DenseNet for the inverse swarm problem. We test the validity of predictions by all these trained networks for a broad range of gas species and we deduce that DenseNet effectively extracts both long and short term features from the swarm data and hence, it predicts cross sections with significantly higher accuracy compared to ANN. Further, we apply Monte Carlo dropout as Bayesian approximation to estimate the probability distribution of the cross sections to determine all plausible solutions of this inverse problem.