This paper introduces a novel hierarchical Bayesian model specifically designed to address challenges in Inverse Uncertainty Quantification (IUQ) for time-dependent problems in nuclear Thermal Hydraulics (TH) systems. The unique characteristics of time-dependent data, such as high dimensionality and correlation in model outputs requires special attention in the IUQ process. By integrating Gaussian Processes (GP) with Principal Component Analysis (PCA), we efficiently construct surrogate models that effectively handle the complexity of dynamic TH systems. Additionally, we incorporate Neural Network (NN) models for time series regression, enhancing the computational accuracy and facilitating derivative calculations for efficient posterior sampling using the Hamiltonian Monte Carlo Method - No U-Turn Sampler (NUTS). We demonstrate the effectiveness of this hierarchical Bayesian approach using the transient experiments in the PSBT benchmark. Our results show improved estimates of Physical Model Parameters' posterior distributions and a reduced tendency for over-fitting, compared to conventional single-level Bayesian models. This approach offers a promising framework for extending IUQ to more complex, time-dependent problems.

翻译：本文提出了一种新型分层贝叶斯模型，专门用于解决核热工水力系统中时间相关问题的逆不确定性量化挑战。时间依赖数据的独有特征（如模型输出的高维度和相关性）需要在逆不确定性量化过程中予以特别关注。通过将高斯过程与主成分分析相结合，我们高效构建了能够处理动态热工水力系统复杂性的替代模型。此外，我们引入神经网络模型进行时间序列回归，在提升计算精度的同时便于导数计算，从而利用哈密顿蒙特卡洛方法-无U型转弯采样器实现高效后验采样。我们使用PSBT基准测试中的瞬态实验证明了该分层贝叶斯方法的有效性。结果表明，与传统单层贝叶斯模型相比，物理模型参数后验分布的估计更优，且过拟合倾向显著降低。该方法为将逆不确定性量化扩展至更复杂的时间相关问题提供了有前景的研究框架。