@article{arbanas_williams_leal_dunn_khuwaileh_wang_abdel-khalik_2015, title={Advancing Inverse Sensitivity/Uncertainty Methods for Nuclear Fuel Cycle Applications}, volume={123}, ISSN={["1095-9904"]}, DOI={10.1016/j.nds.2014.12.009}, abstractNote={The inverse sensitivity/uncertainty quantification (IS/UQ) method has recently been implemented in the Inverse Sensitivity/UnceRtainty Estimator (INSURE) module of the AMPX cross section processing system [M.E. Dunn and N.M. Greene, “AMPX-2000: A Cross-Section Processing System for Generating Nuclear Data for Criticality Safety Applications,” Trans. Am. Nucl. Soc. 86, 118–119 (2002)]. The IS/UQ method aims to quantify and prioritize the cross section measurements along with uncertainties needed to yield a given nuclear application(s) target response uncertainty, and doing this at a minimum cost. Since in some cases the extant uncertainties of the differential cross section data are already near the limits of the present-day state-of-the-art measurements, requiring significantly smaller uncertainties may be unrealistic. Therefore, we have incorporated integral benchmark experiments (IBEs) data into the IS/UQ method using the generalized linear least-squares method, and have implemented it in the INSURE module. We show how the IS/UQ method could be applied to systematic and statistical uncertainties in a self-consistent way and how it could be used to optimize uncertainties of IBEs and differential cross section data simultaneously. We itemize contributions to the cost of differential data measurements needed to define a realistic cost function.}, journal={NUCLEAR DATA SHEETS}, author={Arbanas, G. and Williams, M. L. and Leal, L. C. and Dunn, M. E. and Khuwaileh, B. A. and Wang, C. and Abdel-Khalik, H.}, year={2015}, month={Jan}, pages={51–56} }
 @inproceedings{wang_abdel-khalik_2014, title={Stochastic higher-order generalized perturbation theory for neutron diffusion and transport calculations}, DOI={10.1115/icone21-16572}, abstractNote={The role of scientific computing has been heavily promoted in many fields to improve understanding the physics of complex engineering systems in recent years while conduct the experiments can be time-consuming, inflexible, expensive and difficult to repeat, e.g. nuclear reactor systems. The ultimate goal of scientific computing is to provide more reliable predictions for engineering systems within certain acceptable tolerance. To realize the benefits of scientific computing, extensive effort has been devoted to the development of efficient algorithms for Sensitivity Analysis (SA) and Uncertainty Quantification (UQ) whose numerical errors is under control and understood. However, the repeated execution of the simulations with different samples is computationally intractable for large-scale system with large number of Degrees of Freedom (DOF). The object of this manuscript will be focus on presenting our own developments of stochastic higher-order generalized perturbation theory to address the explosion in the computational load burden. Additionally, an overview of the current state-of-the-art of SA/UQ will also be provided.}, booktitle={Proceedings of the 21st International Conference on Nuclear Engineering - 2013, vol 6}, author={Wang, C. J. and Abdel-Khalik, H. S.}, year={2014} }
 @article{wang_abdel-khalik_2013, title={Exact-to-precision generalized perturbation theory for eigenvalue problems}, volume={256}, ISSN={["1872-759X"]}, DOI={10.1016/j.nucengdes.2012.11.006}, abstractNote={This manuscript extends the exact-to-precision generalized perturbation theory (EpGPT), introduced previously, to eigenvalue problems whereby previous developments focused on source driven problems only. The EpGPT collectively denotes new developments in generalized perturbation theory (GPT) that place high premium on computational efficiency in order to render GPT a standard analysis tool in routine design and safety reactor calculations. Unlike GPT, EpGPT defines a small number of what is referred to as the ‘active’ responses which are solely dependent on the physics model rather than on the responses of interest, the number of input parameters, or the number of points in the state phase space. The active responses are captured by determining all possible state variations resulting from all possible parameters perturbations. If r (the number of active responses) is much smaller than n (the size of the state space), one can show that by recasting GPT equations in terms of the active responses, all higher order responses variations can be determined to a user-defined accuracy criterion. In addition to presenting the mathematical theory of EpGPT to eigenvalue problems, illustrative numerical experiments will be conducted serving as proof of principle.}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Wang, Congjian and Abdel-Khalik, Hany S.}, year={2013}, month={Mar}, pages={130–140} }
 @article{abdel-khalik_bang_wang_2013, title={Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis}, volume={52}, ISSN={["1873-2100"]}, DOI={10.1016/j.anucene.2012.07.020}, abstractNote={The role of modeling and simulation has been heavily promoted in recent years to improve understanding of complex engineering systems. To realize the benefits of modeling and simulation, concerted efforts in the areas of uncertainty quantification and sensitivity analysis are required. The manuscript intends to serve as a pedagogical presentation of the material to young researchers and practitioners with little background on the subjects. We believe this is important as the role of these subjects is expected to be integral to the design, safety, and operation of existing as well as next generation reactors. In addition to covering the basics, an overview of the current state-of-the-art will be given with particular emphasis on the challenges pertaining to nuclear reactor modeling. The second objective will focus on presenting our own development of hybrid subspace methods intended to address the explosion in the computational overhead required when handling real-world complex engineering systems.}, journal={ANNALS OF NUCLEAR ENERGY}, author={Abdel-Khalik, Hany S. and Bang, Youngsuk and Wang, Congjian}, year={2013}, month={Feb}, pages={28–46} }
 @article{bang_wang_abdel-khalik_2012, title={State-Based Adjoint Method for Reduced Order Modeling}, volume={41}, ISSN={["1532-2424"]}, DOI={10.1080/00411450.2012.672359}, abstractNote={Introduced here is an adjoint state-based method for model reduction, which provides a single solution to two classes of reduction methods that are currently in the literature. The first class, which represents the main subject of this manuscript, is concerned with linear time invariant problems where one is interested in calculating linear responses variations resulting from initial conditions perturbations. The other class focuses on perturbations introduced in the operator, which result in nonlinear responses variations. Unlike existing adjoint-based methods where an adjoint function is calculated based on a given response, the state-based method employs the state variations to set up a number of adjoint problems, each corresponding to a pseudoresponse. This manuscript extends the applicability of state-based method to generate reduced order models for linear time invariant problems. Previous developments focusing on operator perturbations are reviewed briefly to highlight the common features of the state-based algorithm as applied to these two different classes of problems. Similar to previous developments, the state-based reduction is shown to set an upper-bound on the maximum discrepancy between the reduced and original model predictions. The methodology is applied and compared to other state-of-the-art methods employing several nuclear reactor diffusion and transport models.}, number={1-2}, journal={TRANSPORT THEORY AND STATISTICAL PHYSICS}, author={Bang, Youngsuk and Wang, Congjian and Abdel-Khalik, Hany S.}, year={2012}, pages={101–132} }
 @article{wang_abdel-khalik_2011, title={Exact-to-precision generalized perturbation theory for source-driven systems}, volume={241}, ISSN={["0029-5493"]}, DOI={10.1016/j.nucengdes.2011.09.009}, abstractNote={Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.}, number={12}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Wang, Congjian and Abdel-Khalik, Hany S.}, year={2011}, month={Dec}, pages={5104–5112} }