利用深度神经网络从Swarm数据中提取电子散射截面
Extracting Electron Scattering Cross Sections from Swarm Data using Deep Neural Networks
摘要：
电子中性散射截面是低温等离子体模拟的基本量，在许多技术应用中得到了广泛的应用。从这些微观截面，可以计算出几个宏观尺度的量（称为“群”参数）。然而，截面的测量以及理论计算是具有挑战性的。自20世纪60年代以来，研究人员试图解决从群数据中获得截面的逆群问题，但解决方案不一定是唯一的。为了解决这个问题，我们研究了深度学习模型的使用，这些模型是使用LXCat网站上提供的不同气体的弹性动量转移，电离和激发截面的先前确定以及使用BOLSIG+求解器计算的相应群参数进行训练的，用于弱电离气体中电子的玻尔兹曼方程的数值解。我们实现了人工神经网络（ANN），卷积神经网络（CNN）和密集连接的卷积网络（DenseNet）的调查。据我们所知，目前还没有研究探索使用CNN和DenseNet来解决逆群问题。我们测试了所有这些经过训练的网络对广泛气体种类的预测的有效性，并且我们推断DenseNet有效地从群数据中提取长期和短期特征，因此，与ANN相比，它以显著更高的准确度预测截面。我们应用蒙特卡罗丢弃作为贝叶斯近似来估计截面的概率分布，以确定所有可能的解这个逆问题的答案。
英文摘要：
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.
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