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

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.

使用深度神经网络从群数据中提取电子散射截面

电子中性散射截面是当今用于许多技术应用的低温等离子体的模拟中的基本量。从这些微观横截面中，可以计算出几个宏观尺度的量（称为“群”参数）。.. 然而，横截面的测量和理论计算是具有挑战性的。自1960年代以来，研究人员一直试图解决从群体数据中获取横截面的反群体问题。但是解决方案并不一定是唯一的。为了解决这个问题，我们研究了深度学习模型的使用，这些模型是根据先前在LXCat网站上获得的各种气体的弹性动量传递，电离和激发截面的确定以及使用BOLSIG +求解器计算的相应群参数来训练的电离气体中电子的玻耳兹曼方程的数值解。我们为此实施了人工神经网络（ANN），卷积神经网络（CNN）和紧密连接的卷积网络（DenseNet）。据我们所知，尚无研究探索将CNN和DenseNet用于反群问题。我们测试了所有这些受过训练的网络对广泛的气体物种进行的预测的有效性，并推断出DenseNet有效地从群数据中提取了长期和短期特征，因此，与ANN相比，其预测截面的准确性明显更高。此外，我们将蒙特卡洛辍学作为贝叶斯近似来估计横截面的概率分布，以确定此反问题的所有合理解。我们测试了所有这些受过训练的网络对广泛的气体物种进行的预测的有效性，并推断出DenseNet有效地从群数据中提取了长期和短期特征，因此，与ANN相比，其预测截面的准确性明显更高。此外，我们将蒙特卡洛辍学作为贝叶斯近似来估计横截面的概率分布，以确定此反问题的所有合理解。我们测试了所有这些受过训练的网络对广泛的气体物种进行的预测的有效性，并推断出DenseNet有效地从群数据中提取了长期和短期特征，因此，与ANN相比，其预测截面的准确性明显更高。此外，我们将蒙特卡洛辍学作为贝叶斯近似来估计横截面的概率分布，以确定此反问题的所有合理解。 （阅读更多）