@article{xie_yaseen_wu_2024, title={Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data}, volume={420}, ISSN={["1879-2138"]}, url={https://doi.org/10.1016/j.cma.2023.116721}, DOI={10.1016/j.cma.2023.116721}, abstractNote={This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.}, journal={COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, author={Xie, Ziyu and Yaseen, Mahmoud and Wu, Xu}, year={2024}, month={Feb} }
 @article{liu_mui_xie_hu_2023, title={Benchmarking FFTF LOFWOS Test# 13 using SAM code: Baseline model development and uncertainty quantification}, volume={192}, ISSN={["1873-2100"]}, DOI={10.1016/j.anucene.2023.110010}, abstractNote={The development and deployment of advanced reactors, such as the sodium-cooled fast reactor (SFR), relies on sophisticated modeling tools to ensure the safety of the design under various transients. The predictive capability of these advanced modeling tools requires validation to garner trust in supporting the licensing of the advanced reactors. For this reason, the International Atomic Energy Agency (IAEA) initiated a coordinated research project (CRP) in 2018 for the analysis of the Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) Test #13. In this study, we present and discuss the benchmarking efforts of the modern system code SAM on the FFTF LOFWOS Test #13. The SAM baseline model was developed according to the benchmark specification, which included a detailed core model with reactivity feedback. Generally, good agreement was observed between the baseline results and benchmark measurements; however, discrepancies persisted, particularly in predicted fuel assembly coolant outlet temperatures. Utilizing the baseline model, uncertainty quantification (UQ) and sensitivity analysis (SA) were conducted with the assistance of various statistical learning and machine learning methods, including kernel density estimation, Gaussian processes, and Sobol indices. Following the baseline model prediction and UQ and SA results, we discuss the reasons for the simulation discrepancies and propose further improvements to the model. This benchmarking effort adheres to the best-estimate plus uncertainty approach and can serve as a valuable example for supporting risk-informed licensing of advanced reactors.}, journal={ANNALS OF NUCLEAR ENERGY}, author={Liu, Yang and Mui, Travis and Xie, Ziyu and Hu, Rui}, year={2023}, month={Nov} }
 @article{wang_wu_xie_kozlowski_2023, title={Scalable Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Variational Inference}, volume={16}, ISSN={["1996-1073"]}, DOI={10.3390/en16227664}, abstractNote={Inverse Uncertainty Quantification (IUQ) has gained increasing attention in the field of nuclear engineering, especially nuclear thermal-hydraulics (TH), where it serves as an important tool for quantifying the uncertainties in the physical model parameters (PMPs) while making the model predictions consistent with the experimental data. In this paper, we present an extension to an existing Bayesian inference-based IUQ methodology by employing a hierarchical Bayesian model and variational inference (VI), and apply this novel framework to a real-world nuclear TH scenario. The proposed approach leverages a hierarchical model to encapsulate group-level behaviors inherent to the PMPs, thereby mitigating existing challenges posed by the high variability of PMPs under diverse experimental conditions and the potential overfitting issues due to unknown model discrepancies or outliers. To accommodate computational scalability and efficiency, we utilize VI to enable the framework to be used in applications with a large number of variables or datasets. The efficacy of the proposed method is evaluated against a previous study where a No-U-Turn-Sampler was used in a Bayesian hierarchical model. We illustrate the performance comparisons of the proposed framework through a synthetic data example and an applied case in nuclear TH. Our findings reveal that the presented approach not only delivers accurate and efficient IUQ without the need for manual tuning, but also offers a promising way for scaling to larger, more complex nuclear TH experimental datasets.}, number={22}, journal={ENERGIES}, author={Wang, Chen and Wu, Xu and Xie, Ziyu and Kozlowski, Tomasz}, year={2023}, month={Nov} }
 @article{xie_jiang_wang_wu_2022, title={Bayesian inverse uncertainty quantification of a MOOSE-based melt pool model for additive manufacturing using experimental data}, volume={165}, ISSN={["1873-2100"]}, DOI={10.1016/j.anucene.2021.108782}, abstractNote={Additive manufacturing (AM) technology is being increasingly adopted in a wide variety of application areas due to its ability to rapidly produce, prototype, and customize designs. AM techniques afford significant opportunities in regard to nuclear materials, including an accelerated fabrication process and reduced cost. High-fidelity modeling and simulation (M\&S) of AM processes is being developed in Idaho National Laboratory (INL)'s Multiphysics Object-Oriented Simulation Environment (MOOSE) to support AM process optimization and provide a fundamental understanding of the various physical interactions involved. In this paper, we employ Bayesian inverse uncertainty quantification (UQ) to quantify the input uncertainties in a MOOSE-based melt pool model for AM. Inverse UQ is the process of inversely quantifying the input uncertainties while keeping model predictions consistent with the measurement data. The inverse UQ process takes into account uncertainties from the model, code, and data while simultaneously characterizing the uncertain distributions in the input parameters--rather than merely providing best-fit point estimates. We employ measurement data on melt pool geometry (lengths and depths) to quantify the uncertainties in several melt pool model parameters. Simulation results using the posterior uncertainties have shown improved agreement with experimental data, as compared to those using the prior nominal values. The resulting parameter uncertainties can be used to replace expert opinions in future uncertainty, sensitivity, and validation studies.}, journal={ANNALS OF NUCLEAR ENERGY}, author={Xie, Ziyu and Jiang, Wen and Wang, Congjian and Wu, Xu}, year={2022}, month={Jan} }
 @article{wu_xie_alsafadi_kozlowski_2021, title={A comprehensive survey of inverse uncertainty quantification of physical model parameters in nuclear system thermal-hydraulics codes}, volume={384}, ISSN={["1872-759X"]}, DOI={10.1016/j.nucengdes.2021.111460}, abstractNote={Uncertainty Quantification (UQ) is an essential step in computational model validation because assessment of the model accuracy requires a concrete, quantifiable measure of uncertainty in the model predictions. The concept of UQ in the nuclear community generally means forward UQ, in which the information flow is from the inputs to the outputs. Inverse UQ, in which the information flow is from the model outputs and experimental data to the inputs, is an equally important component of UQ but has been significantly underrated until recently. Forward UQ requires knowledge in the input uncertainties which has been specified by expert opinion or user self-evaluation. Inverse UQ is defined as the process to inversely quantify the input uncertainties based on experimental data. This review paper aims to provide a comprehensive and comparative discussion of the major aspects of the inverse UQ methodologies that have been used on the physical models in system thermal–hydraulics codes. Inverse UQ methods can be categorized by three main groups: frequentist (deterministic), Bayesian (probabilistic), and empirical (design-of-experiments). We used eight metrics to evaluate an inverse UQ method, including solidity, complexity, accessibility, independence, flexibility, comprehensiveness, transparency, and tractability. Twelve inverse UQ methods are reviewed, compared, and evaluated based on these eight metrics. Such comparative evaluation is intended to provide a good guidance for users to select a proper inverse UQ method based on the problem under investigation.}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Wu, Xu and Xie, Ziyu and Alsafadi, Farah and Kozlowski, Tomasz}, year={2021}, month={Dec} }
 @article{xie_alsafadi_wu_2021, title={Towards improving the predictive capability of computer simulations by integrating inverse Uncertainty Quantification and quantitative validation with Bayesian hypothesis testing}, volume={383}, ISSN={["1872-759X"]}, DOI={10.1016/j.nucengdes.2021.111423}, abstractNote={The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A rigorous Uncertainty Quantification (UQ) process should simultaneously consider multiple sources of quantifiable uncertainties: (1) parameter uncertainty due to randomness or lack of knowledge; (2) experimental uncertainty due to measurement noise; (3) model uncertainty caused by missing/incomplete physics and numerical approximation errors, and (4) code uncertainty when surrogate models are used. In this paper, we propose a comprehensive framework to integrate results from inverse UQ and quantitative validation to provide robust predictions so that all these sources of uncertainties can be taken into consideration. Inverse UQ quantifies the parameter uncertainties based on experimental data while taking into account uncertainties from model, code and measurement. In the validation step, we use a quantitative validation metric based on Bayesian hypothesis testing. The resulting metric, called the Bayes factor, is then used to form weighting factors to combine the prior and posterior knowledge of the parameter uncertainties in a Bayesian model averaging process. In this way, model predictions will be able to integrate the results from inverse UQ and validation to account for all available sources of uncertainties. This framework is a step towards addressing the ANS Nuclear Grand Challenge on “Simulation/Experimentation” by bridging the gap between models and data.}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Xie, Ziyu and Alsafadi, Farah and Wu, Xu}, year={2021}, month={Nov} }