Quantifying the effects of input variations on computed outputs is critical in scientific computing; it is generally referred to as sensitivity analysis (SA). SA plays a key role in the verification, the understanding and, central to this proposal, the simplification of models. Indeed, models are often "simplified" by constructing mathematical surrogates whose properties approximate some������������������but not all������������������of the properties of the original model with the goal of enabling computational study. We propose to develop computational methods to (i) identify of the ���������������"important parts" of a model and (ii) quantify the effects of ignoring the "less important parts." In other words, our work will contribute to dimension reduction and sensitivity analysis. The research is organized around three complementary thrusts in numerical linear algebra, nonlinear solvers and global sensitivity analysis. The RTG participants will not just "be trained," they will play an essential role in our research activities. Group dynamic and esprit de corps will be generated through working groups. Every year, we will organize three working groups consisting of undergraduates, graduate trainees, postdocs and faculty. Each group will be active for one semester and be led by a member of the senior personnel, possibly jointly with one of the postdoctoral fellows. The working groups will concentrate on specific aspects of randomized numerical analysis through hands-on exploratory activities of either computational or analytical nature. Advanced graduate students will be in charge of introducing the undergraduates to basic concepts through short presentations. The project will support 5 undergraduates per year as well as, over the duration of the award, 9 graduate students and 2 postdocs. The project will have a lasting impact on curriculum and departmental activities. It also has significant outreach components to (i) industry and national labs, (ii) to high school (North Carolina School of Science and Mathematics) and (iii) to the public as well as through the development on graduate distance education courses. Our public outreach efforts will take place in collaboration with the NC State Office of Public Science.

The focus of this project is based on three major objectives. First, we will develop mathematical and statistical methodology necessary to quantify the uncertainty of coupled models arising in our two example systems. Second, we will construct emulators with space-time output fields as required by the underlying models in our two example systems. Third, we will integrate these new methodologies into the two applications which are porous media flow including fracture modeling in the geosciences, and the biomechanics and mechanobiology of native and tissue-engineered articular cartilage. Because of the different settings of the two applications, the nature of the coupling of the flow and deformation equations is often different. Hence, the research questions to be addressed will differ in important details for the two applications and lead to novel outcomes and impacts in each setting.

We propose research with two distinct but related thrusts: (1) development of non-destructive model evaluation techniques for CMC undergoing material altering stresses; and (2) model comparison and model differences evaluation techniques for stochastic systems.

This partnering program will strongly support AEROFUSION-MLUQ through its focus on quantifying uncertainties inherent to large-scale aerodynamic models employed for entry, descent and landing (EDL) trajectory estimation to improve predictive capabilities for future Mars missions. To achieve these goals, the program will have four primary thrusts. (i) The first focuses on the development of sensitivity analysis and active subspace techniques to compute subsets or subspaces of influential parameters in state-of-the-art aerodynamic models, which will be informed by wind tunnel test (WTT) or high-fidelity computational fluid dynamic (CFD) data. (ii) Secondly, we will develop model- and data-driven surrogate models having embedded uncertainties. This will include response surface models, such as Gaussian Process (GP) emulators and Neural Network (NN) representations in addition to Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) reduced-order models. This thrust will be coordinated with the team investigating Machine Learning (ML). (iii)~We will subsequently implement highly robust Bayesian Markov chain Monte Carlo (MCMC) techniques, based on the surrogate models, to employ WTT and CFD data to infer distributions for model parameters and experimental observation errors. As part of this thrust, we will employ mutual information-based experimental design to determine specific data which optimally informs parameters. This comprises an important data fusion step in the analysis. (iv) In the final thrust, we will employ Monte Carlo and Latin Hypercube sampling to propagate parameter and experimental data uncertainties through the surrogate models to provide distributions or prediction intervals for statistical Quantities of Interest (QoI) associated with the high-fidelity aerodynamic models.

The primary goal of the proposed project is to demonstrate the utilization of high-fidelity Nuclear Energy Advanced Modeling and Simulation (NEAMS) tools (PROTEUS, Nek5000, and BISON)) to inform the improved use of conventional tools (DIF-3D, CTF, and CTFFuel) within the NEAMS Workbench on the NEA/OECD C5G7-TD benchmark. The project will highlight/illustrate some of the main objectives of the NEAMS workbench: to enable end users to use high-fidelity NEAMS tools to inform the improved use of lower-order conventional tools within the Workbench as well as to demonstrate the values of NEAMS tools as applied to collaborative benchmarks from a common input/template. Once demonstrated the proposed approach could also be extended and applied to different geometries and reactor types for structured and unstructured grids. The proposed project is envisioned as a partnership with the developers of the high-fidelity NEAMS tools and the NEAMS workbench and an industrial user of the tools. In order to make the project results relevant to industrial applications the focus will be on obtaining an optimal combination of accuracy and efficiency, which satisfies the current industry needs and performance requirements

Data-Enabled, Interdisciplinary Research Traineeships in the Science and Engineering of Atomic Structure (SEAS) are proposed at the intersection of materials research, statistics, mathematics, and education. The vision of the SEAS traineeship program is to train a new generation of interdisciplinary, data-driven physical scientists who can develop and apply advanced statistical methods to the data being generated from cutting-edge scattering and imaging experiments; SEAS specifically addresses the NRT priority area of Data-Enabled Science and Engineering (DESE). SEAS graduates will be prepared to develop new ways to analyze data (including ����������������Big Data���������������) coming from a new and evolving generation of atomically sensitive instruments, including modern synchrotron and free electron laser X-ray sources, reactor and spallation neutron sources, and state-of-the-art electron microscopes. SEAS trainees and the tools they create (e.g., algorithms, software) are urgently needed in the field of materials science and physics, where instrumentation for materials research has evolved significantly faster than the ability to properly analyze the data. The effort integrates advanced instrumentation, data analysis, and computational tools, consistent with the NSF Strategic Plan and contributes directly and indirectly to the national Materials Genome Initiative (MGI), a multi-agency initiative spearheaded by the White House that advances the U.S. economy by enabling faster deployment of new materials. The proposed SEAS traineeships are the result of a two-year planning effort at NC State to bring together the materials science and statistics communities, including hosting of two interdisciplinary workshops and seeding interdisciplinary collaborative research projects (sponsored by the Kenan Institute for Engineering, Technology and Science and the Eastman Chemical Company - University Engagement Fund). Under SEAS, NC State will collaborate with staff scientists from national user facilities to pilot a new graduate training model for interdisciplinary traineeships in this national priority area. The effort will leverage several programs and initiatives at NC State, including the Analytical Instrumentation Facility (AIF, Director: J. Jones), Laboratory for Analytic Sciences (LAS, PI: Wilson), Statistical and Applied Mathematical Sciences Initiative (SAMSI, former A/Director: Smith), Data Sciences Initiative (DSI, Founding Director: Vouk), Research Triangle Nanotechnology Network (RTNN, Director: J. Jones), Center for Dielectrics and Piezoelectrics (CDP, Director: Dickey), and the Data-Driven Science cluster (Coordinator: Wilson).

The project is aimed at estimating material properties of layered media with the help of PI's recently developed techniques of guided wave simulations and inversion, combined with the extensive expertise of the co-PI in uncertainty quantification and Bayesian inversion. At the end, the project is expected to result in methodologies applicable for characterizing layered media ranging from geotechnical sites, composite laminates, thin films on substrates, immersed and buried pipelines as well as human arteries.

The Consortium for Advanced Simulation of Light Water Reactors, CASL, supports the broad national missions of enabling energy independence; supporting economic growth through the offering of superior technology ; and being good stewards of the environment, buy enabling predictive simulation of nuclear power plants. Such capability will make possible power uprates, lifetime extension and higher fuel burnups for currently operating and new Generation III+ nuclear power plants.

NC State University, in partnership with University of Michigan, Purdue University, University of Illinois at Urbana Champaign, Kansas State University, Georgia Institute of Technology, NC A&T State University, Los Alamos National Lab, Oak Ridge National Lab, and Pacific Northwest National lab, proposes to establish a Consortium for Nonproliferation Enabling Capabilities (CNEC). The vision of CNEC is to be a pre-eminent research and education hub dedicated to the development of enabling technologies and technical talent for meeting the grand challenges of nuclear nonproliferation in the next decade. CNEC research activities are divided into four thrust areas: 1) Signatures and Observables (S&O); 2) Simulation, Analysis, and Modeling (SAM); 3) Multi-source Data Fusion and Analytic Techniques (DFAT); and 4) Replacements for Potentially Dangerous Industrial and Medical Radiological Sources (RDRS). The goals are: 1) Identify and directly exploit signatures and observables (S&O) associated with special nuclear material (SNM) production, storage, and movement; 2) Develop simulation, analysis, and modeling (SAM) methods to identify and characterize SNM and facilities processing SNM; 3) Apply multi-source data fusion and analytic techniques to detect nuclear proliferation activities; and 4) Develop viable replacements for potentially dangerous existing industrial and medical radiological sources. In addition to research and development activities, CNEC will implement educational activities with the goal to develop a pool of future nuclear non-proliferation and other nuclear security professionals and researchers.

The Consortium for Advanced Simulation of Light Water Reactors, CASL, supports the broad national missions of enabling energy independence; supporting economic growth through the offering of superior technology ; and being good stewards of the environment, buy enabling predictive simulation of nuclear power plants. Such capability will make possible power uprates, lifetime extension and higher fuel burnups for currently operating and new Generation III+ nuclear power plants. This proposal is for work that ORNL will pay TN state takes on.