标题： 基于神经网络平滑的电子能量概率函数鲁棒提取 显示英文标题

标题： Robust Extraction of Electron Energy Probability Function via Neural Network-Based Smoothing

摘要： 电子能量概率函数（EEPF）的精确确定对于理解等离子体中的电子动力学和能量分布至关重要。 然而，解释朗缪尔探针电流-电压（I-V）特性通常受到非线性鞘层动力学、等离子体不稳定性以及诊断噪声的阻碍。 这些因素引入了波动和失真，使得二阶导数计算高度敏感且容易出错。 传统的平滑方法，如萨维茨基-戈拉耶（SG）滤波器和交流调制技术，依赖于局部数据相关性，并难以区分噪声和有意义的等离子体行为。 在本研究中，我们提出了一种基于神经网络的机器学习方法，用于稳健的EEPF提取，专门设计用于解决非麦克斯韦电子能量分布带来的挑战。 一个多层感知机结合集成平均捕捉了I-V特性的全局结构，实现了自适应且一致的平滑处理，而不会损害物理保真度。 与传统的SG滤波相比，所提出的方法在二阶导数的平滑方面表现出色，从而在整个电子能量范围内实现了更稳定和准确的EEPF重建。 这种能力在束驱动、低压或其他非平衡等离子体条件下具有显著的诊断优势，其中准确表征非麦克斯韦EEPF至关重要。 显示英文摘要

摘要： Accurate determination of the electron energy probability function (EEPF) is vital for understanding electron kinetics and energy distributions in plasmas. However, interpreting Langmuir probe current-voltage (I-V) characteristics is often hindered by nonlinear sheath dynamics, plasma instabilities, and diagnostic noise. These factors introduce fluctuations and distortions, making second derivative calculations highly sensitive and error-prone. Traditional smoothing methods, such as the Savitzky-Golay (SG) filter and AC modulation techniques, rely on local data correlations and struggle to differentiate between noise and meaningful plasma behavior. In this study, we present a neural network-based machine learning approach for robust EEPF extraction, specifically designed to address the challenges posed by non-Maxwellian electron energy distributions. A multi-layer perceptron combined with ensemble averaging captures the global structure of the I-V characteristics, enabling adaptive and consistent smoothing without compromising physical fidelity. Compared to conventional SG filtering, the proposed method achieves superior smoothing of the second derivative, resulting in more stable and accurate EEPF reconstruction across the entire electron energy range. This capability confers a strong diagnostic advantage in beam-driven, low-pressure, or other non-equilibrium plasma conditions, where accurate characterization of non-Maxwellian EEPFs is essential.