Yang Liu’s research while affiliated with Texas A&M University and other places

Accurate predictions and uncertainty quantification (UQ) are essential for decision-making in risk-sensitive fields such as system safety modeling. Deep ensembles (DEs) are efficient and scalable methods for UQ in Deep Neural Networks (DNNs); however, their performance is limited when constructed by simply retraining the same DNN multiple times with randomly sampled initializations. To overcome this limitation, we propose a novel method that combines Bayesian optimization (BO) with DE, referred to as BODE, to enhance both predictive accuracy and UQ. We apply BODE to a case study involving a Densely connected Convolutional Neural Network (DCNN) trained on computational fluid dynamics (CFD) data to predict eddy viscosity in sodium fast reactor thermal stratification modeling. Compared to a manually tuned baseline ensemble, BODE estimates total uncertainty approximately four times lower in a noise-free environment, primarily due to the baseline's overestimation of aleatoric uncertainty. Specifically, BODE estimates aleatoric uncertainty close to zero, while aleatoric uncertainty dominates the total uncertainty in the baseline ensemble. We also observe a reduction of more than 30% in epistemic uncertainty. When Gaussian noise with standard deviations of 5% and 10% is introduced into the data, BODE accurately fits the data and estimates uncertainty that aligns with the data noise. These results demonstrate that BODE effectively reduces uncertainty and enhances predictions in data-driven models, making it a flexible approach for various applications requiring accurate predictions and robust UQ.

Advanced reactors often involve complicated thermal-fluid (T-F) phenomena. Modeling such phenomena with the traditional one-dimensional (1-D) system code is a challenging task. The System Analysis Module (SAM), a modern nuclear system code, has developed a coarse mesh multi-dimensional (multi-D) flow model to capture the spatial effect of T-F phenomena in advanced reactors. As a coarse mesh solver, constitutive relations are required for SAM’s multi-D model for unresolved fine-scale physics, such as turbulence. This work presents a novel approach that integrates neural networks as data-driven closure for SAM’s multi-D flow model. The data-driven closure is trained with fine-resolution data to ensure its accuracy while maintaining a coarse mesh setup to ensure its efficiency and consistency with SAM. We demonstrate the applicability of this SAM-ML capability in an open volume thermal stratification problem, where a neural network model serves as the eddy viscosity closure. A customized interface between the neural network and SAM is developed to ensure flexible and efficient data exchange. The SAM-ML results demonstrate superior performance compared to SAM’s built-in zero-equation eddy viscosity closure. The case study shows that although the generalization capability of the data-driven closure still needs to be improved for different transient case or different geometric setup, SAM-ML demonstrates good potential for challenging simulation problems with improved accuracy and computational efficiency.