@article{akins_furlong_kohler_clifford_brady_alsafadi_wu_2024, title={ARTISANS—Artificial Intelligence for Simulation of Advanced Nuclear Systems for Nuclear Fission Technology}, url={https://doi.org/10.1016/j.nucengdes.2024.113170}, DOI={10.1016/j.nucengdes.2024.113170}, journal={Nuclear Engineering and Design}, author={Akins, Alexandra and Furlong, Aidan and Kohler, Lauren and Clifford, Jason and Brady, Christopher and Alsafadi, Farah and Wu, Xu}, year={2024}, month={Jul} }
 @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{alsafadi_wu_2023, title={Deep generative modeling-based data augmentation with demonstration using the BFBT benchmark void fraction datasets}, volume={415}, ISSN={["1872-759X"]}, url={https://doi.org/10.1016/j.nucengdes.2023.112712}, DOI={10.1016/j.nucengdes.2023.112712}, abstractNote={Deep learning (DL) has achieved remarkable successes in many disciplines such as computer vision and natural language processing due to the availability of “big data”. However, such success cannot be easily replicated in many nuclear engineering problems because of the limited amount of training data, especially when the data comes from high-cost experiments. To overcome such a data scarcity issue, this paper explores the applications of deep generative models (DGMs) that have been widely used for image data generation to scientific data augmentation. DGMs, such as generative adversarial networks (GANs), normalizing flows (NFs), variational autoencoders (VAEs), and conditional VAEs (CVAEs), can be trained to learn the underlying probabilistic distribution of the training dataset. Once trained, they can be used to generate synthetic data that are similar to the training data and significantly expand the dataset size. By employing DGMs to augment TRACE simulated data of the steady-state void fractions based on the NUPEC Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark, this study demonstrates that VAEs, CVAEs, and GANs have comparable generative performance with similar errors in the synthetic data, with CVAEs achieving the smallest errors. The findings shows that DGMs have a great potential to augment scientific data in nuclear engineering, which proves effective for expanding the training dataset and enabling other DL models to be trained more accurately.}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Alsafadi, Farah and Wu, Xu}, year={2023}, month={Dec} }
 @article{yaseen_yushu_german_wu_2023, title={Fast and accurate reduced-order modeling of a MOOSE-based additive manufacturing model with operator learning}, volume={129}, ISSN={["1433-3015"]}, DOI={10.1007/s00170-023-12471-1}, number={7-8}, journal={INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY}, author={Yaseen, Mahmoud and Yushu, Dewen and German, Peter and Wu, Xu}, year={2023}, month={Dec}, pages={3123–3139} }
 @book{wang_wu_kozlowski_2023, title={Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Application in Nuclear System Thermal-Hydraulics Codes}, DOI={10.48550/arXiv.2305.16622}, abstractNote={Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which aims to mitigate two existing challenges in IUQ: the high variability of PMPs under varying experimental conditions, and unknown model discrepancies or outliers causing over-fitting issues. The proposed hierarchical model is compared with the conventional single-level Bayesian model using TRACE code and the measured void fraction data in the BFBT benchmark. A Hamiltonian Monte Carlo Method - No U-Turn Sampler (NUTS) is used for posterior sampling. The results demonstrate the effectiveness of the proposed hierarchical model in providing better estimates of the posterior distributions of PMPs and being less prone to over-fitting. The proposed method also demonstrates a promising approach for generalizing IUQ to larger databases with broad ranges of experimental conditions.}, number={2305.166222305.16622}, author={Wang, C. and Wu, X. and Kozlowski, T.}, year={2023} }
 @article{moloko_bokov_wu_ivanov_2023, title={Prediction and uncertainty quantification of SAFARI-1 axial neutron flux profiles with neural networks}, volume={188}, ISSN={["1873-2100"]}, url={https://doi.org/10.1016/j.anucene.2023.109813}, DOI={10.1016/j.anucene.2023.109813}, abstractNote={Artificial Neural Networks (ANNs) have been successfully used in various nuclear engineering applications, such as predicting reactor physics parameters within reasonable time and with a high level of accuracy. Despite this success, they cannot provide information about the model prediction uncertainties, making it difficult to assess ANN prediction credibility, especially in extrapolated domains. In this study, Deep Neural Networks (DNNs) are used to predict the assembly axial neutron flux profiles in the SAFARI-1 research reactor, with quantified uncertainties in the ANN predictions and extrapolation to cycles not used in the training process. The training dataset consists of copper-wire activation measurements, the axial measurement locations and the measured control bank positions obtained from the reactor's historical cycles. Uncertainty Quantification of the regular DNN models' predictions is performed using Monte Carlo Dropout (MCD) and Bayesian Neural Networks solved by Variational Inference (BNN VI). The regular DNNs, DNNs solved with MCD and BNN VI results agree very well among each other as well as with the new measured dataset not used in the training process, thus indicating good prediction and generalization capability. The uncertainty bands produced by MCD and BNN VI agree very well, and in general, they can fully envelop the noisy measurement data points. The developed ANNs are useful in supporting the experimental measurements campaign and neutronics code Verification and Validation (V&V).}, journal={ANNALS OF NUCLEAR ENERGY}, author={Moloko, Lesego E. and Bokov, Pavel M. and Wu, Xu and Ivanov, Kostadin N.}, year={2023}, month={Aug} }
 @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{yaseen_wu_2022, title={Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models}, volume={11}, ISSN={["1943-748X"]}, url={https://doi.org/10.1080/00295639.2022.2123203}, DOI={10.1080/00295639.2022.2123203}, abstractNote={Abstract Recent performance breakthroughs in artificial intelligence (AI) and machine learning (ML), especially advances in deep learning, the availability of powerful and easy-to-use ML libraries (e.g., scikit-learn, TensorFlow, PyTorch), and increasing computational power, have led to unprecedented interest in AI/ML among nuclear engineers. For physics-based computational models, verification, validation, and uncertainty quantification (VVUQ) processes have been very widely investigated, and many methodologies have been developed. However, VVUQ of ML models has been relatively less studied, especially in nuclear engineering. This work focuses on uncertainty quantification (UQ) of ML models as a preliminary step of ML VVUQ, more specifically Deep Neural Networks (DNNs) because they are the most widely used supervised ML algorithm for both regression and classification tasks. This work aims at quantifying the prediction or approximation uncertainties of DNNs when they are used as surrogate models for expensive physical models. Three techniques for UQ of DNNs are compared, namely, Monte Carlo Dropout (MCD), Deep Ensembles (DE), and Bayesian Neural Networks (BNNs). Two nuclear engineering examples are used to benchmark these methods: (1) time-dependent fission gas release data using the Bison code and (2) void fraction simulation based on the Boiling Water Reactor Full-size Fine-Mesh Bundle Tests (BFBT) benchmark using the TRACE code. It is found that the three methods typically require different DNN architectures and hyperparameters to optimize their performance. The UQ results also depend on the amount of training data available and the nature of the data. Overall, all three methods can provide reasonable estimations of the approximation uncertainties. The uncertainties are generally smaller when the mean predictions are close to the test data while the BNN methods usually produce larger uncertainties than MCD and DE.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Yaseen, Mahmoud and Wu, Xu}, year={2022}, month={Nov} }
 @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{che_wu_pastore_li_shirvan_2021, title={Application of Kriging and Variational Bayesian Monte Carlo method for improved prediction of doped UO2 fission gas release}, volume={153}, ISSN={["1873-2100"]}, DOI={10.1016/j.anucene.2020.108046}, abstractNote={One of the advanced nuclear fuel concepts for current commercial water-cooled reactors focuses on microstructural modification of UO2 fuel via dopants. Dopants can effectively promote grain growth and suppress fission gas release (FGR), a key parameter that dictates the overall nuclear fuel performance. This work improves the BISON FGR model for chromia/alumina-doped UO2 fuel through statistical calibration with in-reactor experimental data. The high computing cost and nonintrusive nature of BISON limit the application of conventional techniques under the Bayesian framework. Dimensionality reduction is performed using principal component analysis (PCA) to deal with the FGR time series data. Kriging is used as metamodel of BISON to reduce the computing cost. A novel optimization framework, Variational Bayesian Monte Carlo (VBMC) is demonstrated as a low-cost nonintrusive approach for Bayesian calibration. The performance of VBMC is compared to the conventional statistical Markov Chain Monte Carlo (MCMC) sampling showing similar accuracy but superior efficiency.}, journal={ANNALS OF NUCLEAR ENERGY}, author={Che, Yifeng and Wu, Xu and Pastore, Giovanni and Li, Wei and Shirvan, Koroush}, year={2021}, month={Apr} }
 @article{lu_wu_wu_2021, title={Enhancing the One-Dimensional SFR Thermal Stratification Model via Advanced Inverse Uncertainty Quantification Methods}, volume={10}, url={https://doi.org/10.1080/00295450.2020.1805259}, DOI={10.1080/00295450.2020.1805259}, abstractNote={Abstract Thermal stratification (TS) is a thermal-fluid phenomenon that can introduce large uncertainties to nuclear reactor safety. The stratified layers caused by TS can lead to temperature oscillations in the reactor core. They can also result in damages to both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracks. More importantly, TS can impede the establishment of natural circulation, which is widely used for passive cooling and ensures the inherent safety of numerous reactor designs. A fast-running one-dimensional (1-D) model was recently developed in our research group to predict the TS phenomenon in pool-type sodium-cooled fast reactors. The efficient 1-D model provided reasonable temperature predictions for the test conditions investigated, but nonnegligible discrepancies between the 1-D predictions and the experimental temperature measurements were observed. These discrepancies are attributed to the model uncertainties (also known as model bias or errors) in the 1-D model and the parameter uncertainties in the input parameters. In this study, we first recognized through a forward uncertainty analysis that the observed discrepancies between the computational predictions and the experimental temperature measurements could not be explained solely by input uncertainty propagation. We then performed an inverse uncertainty quantification (UQ) study to reduce the model uncertainties of the 1-D model using a modular Bayesian approach based on experimental data. Inverse UQ serves as a data assimilation process to simultaneously minimize the mismatches between the predictions and experimental measurements, while quantifying the associated parameter uncertainties. The solutions of the modular Bayesian approach were in the form of posterior probability density functions, which were explored by rigorous Markov Chain Monte Carlo sampling. Results showed that the quantified parameters obtained from the inverse UQ effectively improved the predictive capability of the 1-D TS model.}, journal={Nuclear Technology}, publisher={Informa UK Limited}, author={Lu, Cihang and Wu, Zeyun and Wu, Xu}, year={2021}, month={May}, pages={1–19} }
 @book{yan_sandhu_bodda_gupta_wu_sabharwall_2021, title={Structural Health Monitoring of Microreactor Safety Systems Using Convolutional Neural Networks}, url={http://dx.doi.org/10.2172/1824205}, DOI={10.2172/1824205}, abstractNote={Microreactors, a class of modular reactors with net power output of less than 20 MWth, have innovative applications in nuclear and nonnuclear industries due to their portability, reliability, resilience, and high capacity factors. In order to operate microreactors on a wider scale, it is essential to bring down maintenance life-cycle costs while ensuring the integrity of operating such systems. Autonomous operations in microreactors using augmented digital-twin (DT) technology can serve as a cost-effective solution by increasing awareness about the system’s health. Structural health monitoring (SHM) is a key component of nuclear DT frameworks. Artificial neural networks can be beneficial to detect degradation in the nuclear safety systems, such as piping equipment systems, by monitoring the sensor data obtained from the plant and its corresponding structures, systems and components. In this report, an SHM methodology is presented which uses convolutional neural networks to determine degraded locations and their corresponding degradation-severity levels at various locations of nuclear piping equipment systems. A simple pipe system, subjected to seismic loads, is selected to design the post-hazard SHM framework. The effectiveness of the proposed SHM methodology is demonstrated by obtaining high accuracy in detecting degraded locations as well as the severity levels.}, institution={Office of Scientific and Technical Information (OSTI)}, author={Yan, Erin and Sandhu, Harleen and Bodda, Saran and Gupta, Abhinav and Wu, Xu and Sabharwall, Piyush}, year={2021}, month={Jul} }
 @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} }
 @article{jin_wu_shirvan_2020, title={System code evaluation of near-term accident tolerant claddings during pressurized water reactor station blackout accidents}, volume={368}, ISSN={["1872-759X"]}, DOI={10.1016/j.nucengdes.2020.110814}, abstractNote={Following the Fukushima Daiichi nuclear accident in 2011, researches on Accident-tolerant fuels (ATFs) are currently of high interest in not only the nuclear industry but also governmental and international organizations. In this work, a quantitative evaluation of the performance of monolithic FeCrAl cladding and Cr-coated Zircaloy cladding has been performed for Pressurized Water Reactor (PWR) Station Blackout (SBO) accidents. A generic PWR model has been built in system thermal-hydraulics code TRACE based on the Surry Nuclear Power Station with counter-current natural circulation modelling capability for hotleg and steam generator U-tube components during the accidents. The base model results are then compared to MELCOR and RELAP simulations to verify the system component implementation in TRACE. Two PWR SBO scenarios were investigated, including: short-term SBO and long-term SBO with early reactor coolant pump (RCP) seal failure. These scenarios are defined to be very similar to the accidents studied in the State-of-the-Art Reactor Consequence Analysis (SOARCA) project. TRACE code is modified to reflect the oxidation kinetics of FeCrAl and Cr-coating. Larson-Miller creep rupture model is also implemented in TARCE using its built-in control systems to simulate the creep rupture of hotlegs. The comparison between the TRACE models with and without the counter-current flow modeling resulted in significant difference when comparing ATF cladding to Zircaloy for short term SBO, while it marginal impacted the performance during long term SBO with RCP seal failure. For short term SBO, both ATF cladding underwent hot leg creep rupture ~20 min after Zircaloy cladding. While Zircaloy and Cr-coated cladding had generated significant amount of hydrogen gas (>10 kg) before the creep rupture event, FeCrAl cladding had only generated <0.5 kg of hydrogen gas. For long term SBO with RCP seal failure, significant hydrogen generation and fuel melting was predicted before hot leg creep rupture for the ATF cladding while providing only 10–20 min additional coping time compared to Zircaloy.}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Jin, Yue and Wu, Xu and Shirvan, Koroush}, year={2020}, month={Nov} }
 @article{wu_shirvan_kozlowski_2019, title={Demonstration of the relationship between sensitivity and identifiability for inverse uncertainty quantification}, volume={396}, url={http://dx.doi.org/10.1016/j.jcp.2019.06.032}, DOI={10.1016/j.jcp.2019.06.032}, abstractNote={Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the process to quantify the uncertainties of random input parameters based on experimental data. The introduction of model discrepancy term is significant because “over-fitting” can theoretically be avoided. But it also poses challenges in the practical applications. One of the mostly concerned and unresolved problem is the “lack of identifiability” issue. With the presence of model discrepancy, inverse UQ becomes “non-identifiable” in the sense that it is difficult to precisely distinguish between the parameter uncertainties and model discrepancy when estimating the calibration parameters. Previous research to alleviate the non-identifiability issue focused on using informative priors for the calibration parameters and the model discrepancy, which is usually not a viable solution because one rarely has such accurate and informative prior knowledge. In this work, we show that identifiability is largely related to the sensitivity of the calibration parameters with regards to the chosen responses. We adopted an improved modular Bayesian approach for inverse UQ that does not require priors for the model discrepancy term. The relationship between sensitivity and identifiability was demonstrated with a practical example in nuclear engineering. It was shown that, in order for a certain calibration parameter to be statistically identifiable, it should be significant to at least one of the responses whose data are used for inverse UQ. Good identifiability cannot be achieved for a certain calibration parameter if it is not significant to any of the responses. It is also demonstrated that “fake identifiability” is possible if model responses are not appropriately chosen, or if inaccurate but informative prior distributions are specified.}, journal={Journal of Computational Physics}, publisher={Elsevier BV}, author={Wu, Xu and Shirvan, Koroush and Kozlowski, Tomasz}, year={2019}, month={Nov}, pages={12–30} }
 @article{wang_wu_kozlowski_2019, title={Gaussian Process–Based Inverse Uncertainty Quantification for TRACE Physical Model Parameters Using Steady-State PSBT Benchmark}, volume={193}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85051918828&partnerID=MN8TOARS}, DOI={10.1080/00295639.2018.1499279}, abstractNote={Abstract In the framework of Best Estimate Plus Uncertainty methodology, the uncertainties involved in model predictions must be quantified to prove that the investigated design is reasonable and acceptable. The uncertainties in predictions are usually calculated by propagating input uncertainties through the simulation model, which requires knowledge of the model or code input uncertainties, for example, the means, variances, distribution types, etc. However, in best-estimate system thermal-hydraulic codes such as TRACE, some parameters in empirical correlations may have large uncertainties that are unknown to code users, and their uncertainties are therefore simply ignored or described by expert opinion. In this paper, the issue of missing uncertainty information for physical model parameters in the thermal-hydraulic code TRACE is addressed with inverse uncertainty quantification (IUQ), using the steady-state void fraction experimental data in the Organisation for Economic Co-operation and Development/Nuclear Energy Agency PSBT (Pressurized water reactor Sub-channel and Bundle Tests benchmark. The IUQ process is formulated through a Bayesian perspective, which can yield the posterior distributions of the uncertain inputs. A Gaussian process emulator is employed to significantly reduce the computational burden involved in sampling the posteriors using the Markov Chain Monte Carlo method. The posterior distributions are further used in forward uncertainty quantification and sensitivity analysis to quantify the influences of those parameters on the quantities of interest. The results demonstrate the effectiveness of the IUQ framework with a practical nuclear engineering example and show the necessity of quantifying and reducing uncertainty of physical model parameters in future work.}, number={1-2}, journal={Nuclear Science and Engineering}, author={Wang, C. and Wu, X. and Kozlowski, T.}, year={2019}, pages={100–114} }
 @inproceedings{wang_wu_borowiec_kozlowski_2018, title={Bayesian calibration and uncertainty quantification for trace based on PSBT benchmark}, volume={118}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85062963843&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Wang, C. and Wu, X. and Borowiec, K. and Kozlowski, T.}, year={2018}, pages={419–422} }
 @article{wu_kozlowski_meidani_shirvan_2018, title={Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian Process, Part 2: Application to TRACE}, volume={335}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85048431095&partnerID=MN8TOARS}, DOI={10.1016/j.nucengdes.2018.06.003}, abstractNote={Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an improved modular Bayesian approach based on Gaussian Process (GP) for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy is described with a GP emulator. Numerical tests have demonstrated that such treatment of model discrepancy can avoid over-fitting. Furthermore, we constructed a fast-running and accurate GP emulator to replace TRACE full model during Markov Chain Monte Carlo (MCMC) sampling. The computational cost was demonstrated to be reduced by several orders of magnitude. A sequential approach was also developed for efficient test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first selects experimental tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it selects tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that one can extract the most information for posterior probability distributions of calibration parameters using only a relatively small number of tests. This research addresses the "lack of input uncertainty information" issue for TRACE physical input parameters, which was usually ignored or described using expert opinion or user self-assessment in previous work. The resulting posterior probability distributions of TRACE parameters can be used in future uncertainty, sensitivity and validation studies of TRACE code for nuclear reactor system design and safety analysis.}, journal={Nuclear Engineering and Design}, author={Wu, X. and Kozlowski, T. and Meidani, H. and Shirvan, K.}, year={2018}, pages={417–431} }
 @article{wu_kozlowski_meidani_shirvan_2018, title={Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: Theory}, volume={335}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85048576082&partnerID=MN8TOARS}, DOI={10.1016/j.nucengdes.2018.06.004}, abstractNote={In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. “Expert opinion” and “user self-evaluation” have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-hoc specifications of the input uncertainty information. In this paper, we used Bayesian analysis to establish the inverse UQ formulation, with systematic and rigorously derived metamodels constructed by Gaussian Process (GP). Due to incomplete or inaccurate underlying physics, as well as numerical approximation errors, computer models always have discrepancy/bias in representing the realities, which can cause over-fitting if neglected in the inverse UQ process. The model discrepancy term is accounted for in our formulation through the “model updating equation”. We provided a detailed introduction and comparison of the full and modular Bayesian approaches for inverse UQ, as well as pointed out their limitations when extrapolated to the validation/prediction domain. Finally, we proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain.}, journal={Nuclear Engineering and Design}, author={Wu, X. and Kozlowski, T. and Meidani, H. and Shirvan, K.}, year={2018}, pages={339–355} }
 @article{wu_kozlowski_meidani_2018, title={Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data}, volume={169}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85030669828&partnerID=MN8TOARS}, DOI={10.1016/j.ress.2017.09.029}, abstractNote={In nuclear reactor fuel performance simulation, fission gas release (FGR) and swelling involve treatment of several complicated and interrelated physical processes, which inevitably depend on uncertain input parameters. However, the uncertainties associated with these input parameters are only known by “expert judgment”. In this paper, inverse Uncertainty Quantification (UQ) under the Bayesian framework is applied to BISON code FGR model based on Risø-AN3 time series experimental data. Inverse UQ seeks statistical descriptions of the uncertain input parameters that are consistent with the available measurement data. It always captures the uncertainties in its estimates rather than merely determining the best-fit values. Kriging metamodel is applied to greatly reduce the computational cost during Markov Chain Monte Carlo sampling. We performed a dimension reduction for the FGR time series data using Principal Component Analysis. We also projected the original FGR time series measurement data onto the PC subspace as “transformed experiment data”. A forward uncertainty propagation based on the posterior distributions shows that the agreement between BISON simulation and Risø-AN3 time series measurement data is greatly improved. The posterior distributions for the uncertain input factors can be used to replace the expert specifications for future uncertainty/sensitivity analysis.}, journal={Reliability Engineering and System Safety}, author={Wu, X. and Kozlowski, T. and Meidani, H.}, year={2018}, pages={422–436} }
 @inproceedings{wu_shirvan_kozlowski_2018, title={On the connection between sensitivity and identifiability for inverse uncertainty quantification}, volume={118}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85062995468&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Wu, X. and Shirvan, K. and Kozlowski, T.}, year={2018}, pages={411–414} }
 @inproceedings{che_wu_pastore_hales_shirvan_2018, title={Sensitivity and uncertainty analysis for fuel performance evaluation of Cr <inf>2</inf> O <inf>3</inf> -doped UO <inf>2</inf> fuel under LB-LOCA}, volume={119}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85060860913&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Che, Y. and Wu, X. and Pastore, G. and Hales, J. and Shirvan, K.}, year={2018}, pages={440–443} }
 @inproceedings{wu_shirvan_2018, title={System code evaluation of accident tolerant claddings during BWR station blackout accident}, volume={119}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85060862292&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Wu, X. and Shirvan, K.}, year={2018}, pages={444–447} }
 @inproceedings{wu_shirvan_kozlowski_2018, title={Validating trace void fraction predictive capability using the quantitative area validation metric}, volume={118}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85062957450&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Wu, X. and Shirvan, K. and Kozlowski, T.}, year={2018}, pages={423–426} }
 @article{wu_mui_hu_meidani_kozlowski_2017, title={Inverse uncertainty quantification of TRACE physical model parameters using sparse gird stochastic collocation surrogate model}, volume={319}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85019363804&partnerID=MN8TOARS}, DOI={10.1016/j.nucengdes.2017.05.011}, abstractNote={Within the BEPU (Best Estimate plus Uncertainty) methodology uncertainties must be quantified in order to prove that the investigated design remains within acceptance criteria. For best-estimate system thermal-hydraulics codes like TRACE and RELAP5, significant uncertainties come from the closure laws which are used to describe transfer terms in the balance equations. The accuracy and uncertainty information of these correlations are usually unknown to the code users, which results in the user simply ignoring or describing them using expert opinion or personal judgment during uncertainty and sensitivity analysis. The purpose of this paper is to replace such ad-hoc expert judgment of the uncertainty information of TRACE physical model parameters with inverse Uncertainty Quantification (UQ) based on OECD/NRC BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. Inverse UQ seeks statistical descriptions of the physical model random input parameters that are consistent with the experimental data. Inverse UQ always captures the uncertainty of its estimates rather than merely determining point estimates of the best-fit input parameters. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Sparse Gird Stochastic Collocation (SGSC). Global sensitivity analysis including Sobol' indices and correlation coefficients are used to identify the important TRACE input parameters. Several adaptive Markov Chain Monte Carlo (MCMC) sampling techniques are investigated and implemented to explore the posterior probability density functions. This research solves the problem of lack of uncertainty information for TRACE physical model parameters for the closure relations. The quantified uncertainties are necessary for future uncertainty and sensitivity study of TRACE code in nuclear reactor system design and safety analysis.}, journal={Nuclear Engineering and Design}, author={Wu, X. and Mui, T. and Hu, G. and Meidani, H. and Kozlowski, T.}, year={2017}, pages={185–200} }
 @article{wu_kozlowski_2017, title={Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion}, volume={313}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85006421201&partnerID=MN8TOARS}, DOI={10.1016/j.nucengdes.2016.11.032}, abstractNote={Modeling and simulations are naturally augmented by extensive Uncertainty Quantification (UQ) and sensitivity analysis requirements in the nuclear reactor system design, in which uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. Historically, expert judgment has been used to specify the nominal values, probability density functions and upper and lower bounds of the simulation code random input parameters for the forward UQ process. The purpose of this paper is to replace such ad-hoc expert judgment of the statistical properties of input model parameters with inverse UQ process. Inverse UQ seeks statistical descriptions of the model random input parameters that are consistent with the experimental data. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Polynomial Chaos Expansion (PCE). The methods developed here are demonstrated with the Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model. Three input parameters, external reactivity, Doppler reactivity coefficient and coolant temperature coefficient are modeled as uncertain input parameters. Their uncertainties are inversely quantified based on synthetic experimental data. Compared with the direct numerical simulation, surrogate model by PC expansion shows high efficiency and accuracy. In addition, inverse UQ with Bayesian analysis can calibrate the random input parameters such that the simulation results are in a better agreement with the experimental data.}, journal={Nuclear Engineering and Design}, author={Wu, X. and Kozlowski, T.}, year={2017}, pages={29–52} }
 @inproceedings{wu_kozlowski_2017, title={Kriging-based inverse uncertainty quantification of BISON fission gas release model}, volume={116}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85033468956&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Wu, X. and Kozlowski, T.}, year={2017}, pages={629–632} }
 @inproceedings{wang_wu_kozlowski_2017, title={Sensitivity and uncertainty analysis of TRACE Physical Model Parameters based on PSBT benchmark using Gaussian process emulator}, volume={2017-September}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85051935457&partnerID=MN8TOARS}, booktitle={17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2017}, author={Wang, C. and Wu, X. and Kozlowski, T.}, year={2017} }
 @inproceedings{wang_wu_kozlowski_2017, title={Surrogate-based inverse uncertainty quantification of TRACE physical model parameters using steady-state PSBT void fraction data}, volume={2017-September}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85051987392&partnerID=MN8TOARS}, booktitle={17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2017}, author={Wang, C. and Wu, X. and Kozlowski, T.}, year={2017} }
 @article{wu_kozlowski_2015, title={Coupling of system thermal-hydraulics and Monte-Carlo code: Convergence criteria and quantification of correlation between statistical uncertainty and coupled error}, volume={75}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84907197788&partnerID=MN8TOARS}, DOI={10.1016/j.anucene.2014.08.016}, abstractNote={Coupled multi-physics approach plays an important role in improving computational accuracy. Compared with deterministic neutronics codes, Monte Carlo codes have the advantage of a higher resolution level. In the present paper, a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code, Serpent, is coupled with a thermal–hydraulics safety analysis code, RELAP5. The coupled Serpent/RELAP5 code capability is demonstrated by the improved axial power distribution of UO2 and MOX single assembly models, based on the OECD-NEA/NRC PWR MOX/UO2 Core Transient Benchmark. Comparisons of calculation results using the coupled code with those from the deterministic methods, specifically heterogeneous multi-group transport code DeCART, show that the coupling produces more precise results. A new convergence criterion for the coupled simulation is developed based on the statistical uncertainty in power distribution in the Monte Carlo code, rather than ad-hoc criteria used in previous research. The new convergence criterion is shown to be more rigorous, equally convenient to use but requiring a few more coupling steps to converge. Finally, the influence of Monte Carlo statistical uncertainty on the coupled error of power and thermal–hydraulics parameters is quantified. The results are presented such that they can be used to find the statistical uncertainty to use in Monte Carlo in order to achieve a desired precision in coupled simulation.}, journal={Annals of Nuclear Energy}, author={Wu, X. and Kozlowski, T.}, year={2015}, pages={377–387} }
 @inproceedings{rose_downar_wu_kozlowski_2015, title={Evaluation of accident tolerant FeCrAl coating for PWR cladding under normal operating conditions with coupled neutron transport and fuel performance}, volume={3}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84949522107&partnerID=MN8TOARS}, booktitle={Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015}, author={Rose, M. and Downar, T.J. and Wu, X. and Kozlowski, T.}, year={2015}, pages={2334–2344} }
 @article{wu_kozlowski_hales_2015, title={Neutronics and fuel performance evaluation of accident tolerant FeCrAl cladding under normal operation conditions}, volume={85}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84946728980&partnerID=MN8TOARS}, DOI={10.1016/j.anucene.2015.06.032}, abstractNote={Neutronics and fuel performance analysis is done for enhanced accident tolerance fuel (ATF), with the Monte Carlo reactor physics code Serpent and INL’s fuel performance code BISON. The purpose is to evaluate the most promising ATF candidate material FeCrAl, which has excellent oxidation resistance, as fuel cladding under normal operational conditions. Due to several major disadvantages of FeCrAl coating, such as difficulty in fabrication, diametrical compression from reactor pressurization, coating spallation and inter diffusion with zirconium, a monolithic FeCrAl cladding design is suggested. To overcome the neutron penalty expected when using FeCrAl as cladding for current oxide fuel, an optimized FeCrAl cladding design from a detailed parametric study in literature is adopted, which suggests reducing the cladding thickness and slightly increasing the fuel enrichment. A neutronics analysis is done that implementing this FeCrAl cladding design in a Pressurized Water Reactor (PWR) single assembly. The results show that the PWR cycle length requirements will be matched, with a slight increase in total plutonium production. Fuel performance analysis with BISON code is carried out to investigate the effects with this FeCrAl cladding design. The results demonstrate that the application of FeCrAl cladding could improve performance. For example, the axial temperature profile is flattened. The gap closure is significantly delayed, which means the pellet cladding mechanical interaction is greatly delayed. The disadvantages for monolithic FeCrAl cladding are that: (1) fission gas release is increased; and (2) fuel temperature is increased, but the increase is less than 50 K even at high burnup. The better strength, corrosion, and embrittlement properties of FeCrAl enable the fabrication of FeCrAl cladding with thinner walls. FeCrAl cladding proves to be a good alternate for zircaloy cladding, given the advantages and insignificant disadvantages shown by fuel performance analysis.}, journal={Annals of Nuclear Energy}, author={Wu, X. and Kozlowski, T. and Hales, J.D.}, year={2015}, pages={763–775} }
 @inproceedings{wu_kozlowski_2014, title={Coupling of system thermal-hydraulics and monte-carlo method for a consistent thermal-hydraulics-reactor physics feedback}, volume={2}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84907077778&partnerID=MN8TOARS}, booktitle={International Congress on Advances in Nuclear Power Plants, ICAPP 2014}, author={Wu, X. and Kozlowski, T.}, year={2014}, pages={1164–1174} }
 @inproceedings{wu_kozlowski_heuser_2014, title={Neutronics analysis of improved accident tolerance LWR fuel by modifing Zircaloy cladding of fuel pins}, volume={1}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84907085456&partnerID=MN8TOARS}, booktitle={International Congress on Advances in Nuclear Power Plants, ICAPP 2014}, author={Wu, X. and Kozlowski, T. and Heuser, B.J.}, year={2014}, pages={159–166} }
 @book{wu_sabharwall_hales_2014, title={Neutronics and Fuel Performance Evaluation of Accident Tolerant Fuel under Normal Operation Conditions}, url={http://dx.doi.org/10.2172/1166052}, DOI={10.2172/1166052}, abstractNote={iv ACRONYMS viii 1. INTRODUCTION 1 2. THERMAL-PHYSICAL PROPERTIES OF CANDIDATE MATERIALS 2 2.1 Candidate Materials 2 2.2 Cladding Form 3 2.3 Thermal-physical Properties 3 3. MODEL FOR NEUTRONICS ANALYSIS 5 4. MODEL FOR FUEL PERFORMANCE ANALYSIS 6 4.1 Material Models in BISON 6 4.2 LWR Fuel Pin Model in BISON 7 4.3 Mesh for Coating and Monolithic Cladding Cases 7 5. RESULTS AND DISCUSSION 8 5.1 Neutronics Evaluation 8 5.2 Fuel Performance Evaluation 10 5.2.1 Results for Monolithic Cladding Cases 10 5.2.2 Results for Coating Layer Cases 13 5.3 Comparison of Zircaloy, FeCrAl, and SiC 15 5.4 Comparison of Monolithic Cladding and Coating 15 6. CONCLUSIONS 16 7. APPENDIX 17 7.1 UO2 17 7.2 Zircaloy 18 7.3 FeCrAl 19 7.4 SiC 20 8. REFERENCES 21}, institution={Office of Scientific and Technical Information (OSTI)}, author={Wu, Xu and Sabharwall, Piyush and Hales, Jason}, year={2014}, month={Jul} }
 @inproceedings{wu_kozlowski_2014, title={Uncertainty quantification for coupled Monte Carlo and thermal-hydraulics codes}, volume={110}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84904692027&partnerID=MN8TOARS}, booktitle={Transactions of the American Nuclear Society}, author={Wu, X. and Kozlowski, T.}, year={2014}, pages={189–191} }
 @inproceedings{heuser_kozlowski_xu_2013, title={Engineered Zircaloy cladding modifications for improved accident tolerance of LWR fuel: A summary}, volume={1}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84902344678&partnerID=MN8TOARS}, booktitle={LWR Fuel Performance Meeting, Top Fuel 2013}, author={Heuser, B.J. and Kozlowski, T. and Xu, W.}, year={2013}, pages={56–58} }