This work suggests several methods of uncertainty treatment in multiscale modelling and describes their application to a system of coupled turbulent transport simulations of a tokamak plasma. We propose a method to quantify the usually aleatoric uncertainty of a system in a quasi-stationary state, estimating the mean values and their errors for quantities of interest, which is average heat fluxes in the case of turbulence simulations. The method defines the stationarity of the system and suggests a way to balance the computational cost of simulation and the accuracy of estimation. This allows, contrary to many approaches, to incorporate aleatoric uncertainties in the analysis of the model and to have a quantifiable decision for simulation runtime. Furthermore, the paper describes methods for quantifying the epistemic uncertainty of a model and the results of such a procedure for turbulence simulations, identifying the model's sensitivity to particular input parameters and sensitivity to uncertainties in total. Finally, we introduce a surrogate model approach based on Gaussian Process Regression and present a preliminary result of training and analysing the performance of such a model based on turbulence simulation data. Such an approach shows a potential to significantly decrease the computational cost of the uncertainty propagation for the given model, making it feasible on current HPC systems.

翻译：本工作提出了几种不确定性处理方法在多尺度建模中的应用，并描述了将其应用于托卡马克等离子体耦合湍流输运模拟系统的过程。我们提出了一种量化准稳态系统中通常为偶然性不确定性的方法，该方法可估计感兴趣量（在湍流模拟中为平均热通量）的均值及其误差。该方法定义了系统的平稳性，并提出了一种平衡模拟计算成本与估计精度的途径。与许多其他方法不同，该方法允许将偶然性不确定性纳入模型分析，并为模拟运行时间提供可量化的决策依据。此外，本文描述了模型认知不确定性量化的方法及其在湍流模拟中的实施结果，识别了模型对特定输入参数的敏感性以及总体不确定性敏感性。最后，我们引入了基于高斯过程回归的代理模型方法，并展示了基于湍流模拟数据训练和评估该类模型性能的初步结果。该方法展现出显著降低给定模型不确定性传播计算成本的潜力，使其可部署于当前的高性能计算系统。