Wendelstein 7-X 上多种等离子体诊断的贝叶斯建模
Bayesian modelling of multiple plasma diagnostics at Wendelstein 7-X
AI总结：
本文在 Wendelstein 7-X 上利用贝叶斯方法联合建模多种诊断数据，通过高斯过程和马尔可夫链蒙特卡洛推断电子密度、温度及离子温度剖面，并引入虚拟观测和贝叶斯奥卡姆剃刀实现自洽推断。
摘要：
在 Wendelstein 7-X 装置上，利用多种异质等离子体诊断数据集对电子密度和温度进行了自洽推断。在 Minerva 框架中开发了干涉仪、汤姆森散射和氦束发射光谱系统的预测模型，并将其组合成一个联合模型。电子密度和温度剖面由高斯过程及其超参数建模。模型参数（如汤姆森散射系统的校准因子）和模型预测不确定性被视为额外的未知参数。通过马尔可夫链蒙特卡洛算法探索电子密度和温度剖面、高斯过程超参数及模型参数的后验联合概率分布。从联合后验分布中抽取的后验样本在数值上对超参数和模型参数进行边缘化，以获得电子密度和温度剖面的边缘后验分布。这些剖面的推断使用干涉仪和汤姆森散射数据的不同组合，以及由“虚拟观测”引入的限幅器/偏滤器位置的电子密度和温度经验约束，或来自氦束发射数据的边缘密度和温度。此外，还演示了将 X 射线成像晶体光谱仪加入联合模型以推断离子温度剖面。本工作中呈现的所有剖面均通过探索完整联合后验分布（其内在地体现贝叶斯奥卡姆剃刀原理）以最优超参数和模型参数进行推断。
英文摘要：
Consistent inference of the electron density and temperature has been carried out with multiple heterogeneous plasma diagnostic data sets at Wendelstein 7-X. The predictive models of the interferometer, Thomson scattering and helium beam emission spectroscopy systems have been developed in the Minerva framework and combined to a single joint model. The electron density and temperature profiles are modelled by Gaussian processes with their hyperparameters. The model parameters such as the calibration factor of the Thomson scattering system and the model predictive uncertainties are regarded as additional unknown parameters. The joint posterior probability distribution of the electron density and temperature profiles, hyperparameters of the Gaussian processes and model parameters is explored by Markov chain Monte Carlo algorithms. The posterior samples drawn from the joint posterior distribution are numerically marginalised over the hyperparameters and model parameters to obtain the marginal posterior distributions of the electron density and temperature profiles. The inference of these profiles is performed with different combinations of the interferometer and Thomson scattering data as well as either the empirical electron density and temperature constraints at the limiter/divertor positions introduced by \textit{virtual observations} or the edge density and temperature from the helium beam emission data. Furthermore, the addition of the X-ray imaging crystal spectrometers to the joint model for the ion temperature profiles is demonstrated. All these profiles presented in this work are inferred with the optimal hyperparameters and model parameters by exploring the full joint posterior distribution which intrinsically embodies Bayesian Occam's razor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
