Determining cross sections from transport coefficients using deep neural networks

TL;DR

This paper introduces a neural network method to derive electron cross sections from swarm transport data, improving accuracy and physical plausibility by training on data from the LXCat project and applying it to helium and argon.

Contribution

The paper presents a novel neural network approach for inverse swarm problems, effectively estimating cross sections from transport data with improved physical consistency.

Findings

Achieved 4% accuracy in cross section determination for helium.

Successfully estimated multiple cross sections of helium with 10-25% accuracy.

Less successful extension to argon, with reasons well-understood.

Abstract

We present a neural network for the solution of the inverse swarm problem of deriving cross sections from swarm transport data. To account for the uncertainty inherent to this somewhat ill-posed inverse problem, we train the neural network using cross sections from the LXCat project, paired with associated transport coefficients found by the numerical solution of Boltzmann's equation. The use of experimentally measured and theoretically calculated cross sections for training encourages the network to avoid unphysical solutions, such as those containing spurious energy-dependent oscillations. We successfully apply this machine learning approach to simulated swarm data for electron transport in helium, separately determining its elastic momentum transfer and ionisation cross sections to within an accuracy of $4\%$ over the range of energies considered. Our attempt to extend our method to argon was less successful, although the reason for that observation is well-understood. Finally, we explore the feasibility of simultaneously determining cross sections of helium using this approach. We have some success here, determining elastic, total $n=2$ excitation and ionisation cross sections to $10\%$, $20\%$ and $25\%$ accuracy, respectively. We are unsuccessful in properly unfolding the separate $n=2$ singlet and triplet excitation cross sections of helium, but this is as expected given their similar threshold energies.