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Probabilistic parameter estimation using a Gaussian mixture density network: application to X-ray reflectivity data curve fitting
Journal of Applied Crystallography ( IF 5.2 ) Pub Date : 2021-10-20 , DOI: 10.1107/s1600576721009043
Kook Tae Kim , Dong Ryeol Lee

X-ray reflectivity (XRR) is widely used for thin-film structure analysis, and XRR data analysis involves minimizing the difference between experimental data and an XRR curve calculated from model parameters describing the thin-film structure. This analysis takes a certain amount of time because it involves many unavoidable iterations. However, the recently introduced artificial neural network (ANN) method can dramatically reduce the analysis time in the case of repeated analyses of similar samples. Here, the analysis of XRR data using a mixture density network (MDN) is demonstrated, which enables probabilistic prediction while maintaining the advantages of an ANN. First, under the assumption of a unimodal probability distribution of the output parameter, the trained MDN can estimate the best-fit parameter and, at the same time, estimate the confidence interval (CI) corresponding to the error bar of the best-fit parameter. The CI obtained in this manner is similar to that obtained using the Neumann process, a well known statistical method. Next, the MDN method provides several possible solutions for each parameter in the case of a multimodal distribution of the output parameters. An unsupervised machine learning method is used to cluster possible parameter sets in order of probability. Determining the true value by examining the candidates of the parameter sets obtained in this manner can help solve the inherent inverse problem associated with scattering data.

中文翻译:

使用高斯混合密度网络的概率参数估计:应用于 X 射线反射率数据曲线拟合

X 射线反射率 (XRR) 广泛用于薄膜结构分析,XRR 数据分析涉及将实验数据与根据描述薄膜结构的模型参数计算的 XRR 曲线之间的差异最小化。这种分析需要一定的时间,因为它涉及许多不可避免的迭代。然而,最近引入的人工神经网络 (ANN) 方法可以在重复分析相似样本的情况下显着减少分析时间。在这里,演示了使用混合密度网络 (MDN) 对 XRR 数据的分析,它可以在保持 ANN 优势的同时进行概率预测。首先,在输出参数为单峰概率分布的假设下,经过训练的 MDN 可以估计出最佳拟合参数,同时,估计与最佳拟合参数的误差条相对应的置信区间 (CI)。以这种方式获得的 CI 类似于使用 Neumann 过程获得的 CI,这是一种众所周知的统计方法。接下来,MDN 方法在输出参数的多模态分布的情况下为每个参数提供了几种可能的解决方案。使用无监督机器学习方法按概率顺序对可能的参数集进行聚类。通过检查以这种方式获得的参数集的候选来确定真值有助于解决与散射数据相关的固有逆问题。MDN 方法在输出参数的多峰分布情况下为每个参数提供了几种可能的解决方案。使用无监督机器学习方法按概率顺序对可能的参数集进行聚类。通过检查以这种方式获得的参数集的候选来确定真值有助于解决与散射数据相关的固有逆问题。MDN 方法在输出参数的多峰分布情况下为每个参数提供了几种可能的解决方案。使用无监督机器学习方法按概率顺序对可能的参数集进行聚类。通过检查以这种方式获得的参数集的候选来确定真值有助于解决与散射数据相关的固有逆问题。
更新日期:2021-12-06
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