Hierarchical Bayesian Modeling for Time-Dependent Inverse Uncertainty Quantification

TL;DR

This paper presents a hierarchical Bayesian framework combining Gaussian Processes, PCA, and Neural Networks to improve inverse uncertainty quantification in time-dependent nuclear thermal hydraulics systems, demonstrating enhanced accuracy and reduced over-fitting.

Contribution

The paper introduces a novel hierarchical Bayesian model integrating GP, PCA, and NN for efficient IUQ in complex time-dependent systems, advancing beyond traditional single-level approaches.

Findings

Improved posterior estimates of physical model parameters.

Reduced over-fitting compared to conventional models.

Effective handling of high-dimensional, correlated time-dependent data.

Abstract

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.