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DOE OSTI2020

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions [including apppendix B]

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation problems is used in which a computational domain is subdivided into non-overlapping subdomains. In the nonlocal setting, this approach is substructuring-based in the sense that those subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains Key results include the equivalence between the global, single-domain nonlocal problem and its multi-domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal domain-decomposition methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions [minus appendix B]

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Books and monographs on finite element technology

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

Noor, A. K.↗

DOE OSTI2022

Artificial Intelligence/Machine Learning Technologies for Advanced Reactors (Workshop Summary Report)

A workshop on artificial intelligence and machine learning (AI/ML) for advanced reactors (AR) was held October 5-6, 2021. The workshop was to be attended in-person at ANL but COVID restrictions forced the workshop to go virtual. The objectives of the workshop were to identify the most promising AI/ML opportunities for improving advanced reactor design, optimizing plant performance, and enhancing economic competitiveness and to develop an understanding of the scientific, engineering and licensing challenges facing their application. The workshop planning committee included GAIN, EPRI and NEI and members of three national laboratories (ANL, INL, and ORNL). The workshop was attended by more than 200 individuals representing academic and scientific institutions and the nuclear power industry. The definition put forth for an AI/ML system was one that perceives its environment and takes actions that maximize its chance of achieving its goals. In this report AI/ML refers to next generation algorithms that include deep learning, statistical analysis and data analytics and associated scientific computing and their potential application to the design, licensing, operation and maintenance of ARs. These methods typically incorporate models built from process data and may also include data generated by simulations that represent the behavior of a system. The workshop was organized in response to the growing interest in application of AI/ML for improving the economic competitiveness of nuclear energy. Increasingly more resources are being allocated to investigating the benefits of AI/ML methods. The DOE created the Artificial Intelligence & Technology Office to promote their development. And within the Office of Nuclear Energy, resources have been allocated to explore and understand the potential benefits of AI/ML. Additionally, the national laboratories are strategically positioned with DOE computing facilities such as Summit, Perlmutter, Aurora and Frontier that support large-scale simulations, hybrid HPC models with AI surrogates, and the exploration of new types of generative models emerging from multi-model data streams and sources. The workshop was organized with members of the AR community to understand the effort and to identify the level of interest and progress in this emerging technology. The workshop discussions focused on identifying opportunities for AI/ML across diverse areas of the nuclear industry and identifying current scientific and engineering challenges for advanced reactors that might be addressed through transformational uses of AI/ML. Discussion panels focused on four high-interest technical domains for advanced reactors: design, maintenance and operations, energy storage, and materials. The results of those discussions are summarized in this report. This includes opportunities that were identified for exploiting AI techniques and methods to improve the efficacy and efficiency of reactor analysis and to improve the operation and optimization of advanced reactors. Advanced reactor developers expressed an interest in learning more about AI/ML methods and their application. This included understanding whether ML methods can provide an advantage over existing nonlinear data regression methods for collapsing high-fidelity simulation results into faster running models. A consensus emerged that AR advances planned for the next decade will benefit from the use of AI/ML tools. The need exists to understand and model complex systems across length scales and modalities. AI/ML is a tool for discovery that can yield a set of engineering principles for use by nuclear engineers, licensing bodies, and operators to solve problems in plant design, safety analyses, autonomous operation, and predictive maintenance. While AI/ML represents a new set of tools, an awareness by the nuclear community of the full potential is still in the early stages so there is a need to increase awareness. It appears that the wide-spread adoption of AI/ML tools for ARs would be facilitated by future educational workshops that describe foundational methods and capabilities and describe successful applications.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2019

Scour Estimation for Tsunami at Bridges

The potential hazard to bridges from a tsunami event may include inundation hazard to the traffic, force effect on the structure, erosion of the foundation caused by hydraulic load on soils or rocks, and erosion of the approach. This study uses a laboratory-validated hybrid numerical scheme that combines Computational Fluid Dynamics (CFD) with sediment transport analysis to provide a practical evaluation method for scour depth at bridge foundations

58 GEOSCIENCES↗

NASA NTRS1992

Modeling the performance of the human (pilot) interaction in a synthetic flight domain: Information theoretic approach

Current advances in computing technology are devoid of formal methods that describe the theories of how information is shared between humans and machines. Specifically, in the domain of human-machine interaction, a common mathematical foundation is lacking. The aim of this paper is to propose a formal method of human-machine (H-M) interaction paradigm from the information view point. The methods presented are interpretation- and context-free and can be used both in experimental analysis as well as in modeling problems.

Ntuen, Celestine A.↗

NASA NTRS2006

Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

Nielsen, Eric J.↗

DOE OSTI2021

Towards Predictive Plasma Science and Engineering through Revolutionary Multi-Scale Algorithms and Models (Final Report)

This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.

42 ENGINEERING↗

NASA NTRS1992

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗

DOE OSTI2024

Few measurement shots challenge generalization in learning to classify entanglement

The ability to extract general laws from a few known examples depends on the complexity of the problem and on the amount of training data. In the quantum setting, the learner's generalization performance is further challenged by the destructive nature of quantum measurements that, together with the no-cloning theorem, limits the amount of information that can be extracted from each training sample. In this paper we focus on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms and show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We identify an instance of this possibly general issue by focusing on the classification of maximally entangled vs. separable states, showing that this toy problem becomes challenging for learners unaware of entanglement theory. Finally, we introduce an estimator based on classical shadows that performs better in the big data, few copy regime. Our results show that the naive application of classical machine-learning methods to the quantum setting is problematic, and that a better theoretical foundation of quantum learning is required.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Brochure for the DOE Office of Science Workshop on Envisioning Frontiers in AI and Computing for Biological Research

In February of 2025 a joint ASCR/BER workshop was held to identify key transformational research directions for understanding biology using artificial intelligence (AI), digital twins and high-performance (HPC) computational methods to facilitate scientific discovery and innovation in support of the Department of Energy mission. AI technologies offer exciting new groundbreaking methods to analyze large volumes of complex biological data, thereby greatly accelerating the ability to understand, predict, and design biological processes for beneficial purposes. In the laboratory, the bridging of AI-enabled automated experimental technologies, HPC and digital twins will provide potent tools for researchers to explore the fundamental nature of biology and harness its inherent metabolic potential for a variety of beneficial purposes. The focus of this workshop was on how high-performance computational methods can impact this objective by exploring digital twins, foundational models, and data-driven approaches with applications to advance automated laboratory experiments, modeling of complex living systems and engineering new functions into plants and microbial systems relevant to DOE mission. Workshop attendees with expertise in plant science, microbiology, mathematics, computer science, and AI assessed the current state of the science, trends, and AI challenges at the interface of plant and microbial systems biology and computational science to identify opportunities for high-impact research. This collaborative effort capitalized on ASCR's advancements in applied mathematics, computer science, and Exascale systems, and BER's expertise in basic genomics-enabled research on DOE relevant plant and microbial systems. The workshop culminated in four key priority research directions to guide future research and development within DOE Office of Science programs.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

TU-H-BRC-05: Stereotactic Radiosurgery Optimized with Orthovoltage Beams

Purpose: To achieve improved stereotactic radiosurgery (SRS) dose distributions using orthovoltage energy fluence modulation with inverse planning optimization techniques. Methods: A pencil beam model was used to calculate dose distributions from the institution’s orthovoltage unit at 250 kVp. Kernels for the model were derived using Monte Carlo methods as well as measurements with radiochromic film. The orthovoltage photon spectra, modulated by varying thicknesses of attenuating material, were approximated using open-source software. A genetic algorithm search heuristic routine was used to optimize added tungsten filtration thicknesses to approach rectangular function dose distributions at depth. Optimizations were performed for depths of 2.5, 5.0, and 7.5 cm, with cone sizes of 8, 10, and 12 mm. Results: Circularly-symmetric tungsten filters were designed based on the results of the optimization, to modulate the orthovoltage beam across the aperture of an SRS cone collimator. For each depth and cone size combination examined, the beam flatness and 80–20% and 90–10% penumbrae were calculated for both standard, open cone-collimated beams as well as for the optimized, filtered beams. For all configurations tested, the modulated beams were able to achieve improved penumbra widths and flatness statistics at depth, with flatness improving between 33 and 52%, and penumbrae improving between 18 and 25% for the modulated beams compared to the unmodulated beams. Conclusion: A methodology has been described that may be used to optimize the spatial distribution of added filtration material in an orthovoltage SRS beam to result in dose distributions at depth with improved flatness and penumbrae compared to standard open cones. This work provides the mathematical foundation for a novel, orthovoltage energy fluence-modulated SRS system.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

MCNP6 Status and plans for criticality safety applications - 14368

The first production version of MCNP6 was released in 2013, with an update in 2014. MCNP6 provides all of the standard methodology for criticality calculations available in previous versions and new capabilities for adjoint-based sensitivity profiles and perturbations. This paper reviews the current status of MCNP6, including new features, performance improvements, verification testing, and nuclear data libraries. For criticality safety support, a new statistical package called Whisper was developed and first applied in 2014 for validation and determining USLs. Whisper includes input files and sensitivity profiles for over 1000 ICSBEP benchmarks and will be distributed with MCNP6. For the long term, an initiative called MCNP 2020 is underway to improve performance, strengthen the code foundation, and prepare for future computer systems. (authors)

42 ENGINEERING↗

DOE OSTI2011

Data and Communications in Basic Energy Sciences: Creating a Pathway for Scientific Discovery

This report is based on the Department of Energy (DOE) Workshop on “Data and Communications in Basic Energy Sciences: Creating a Pathway for Scientific Discovery” that was held at the Bethesda Marriott in Maryland on October 24-25, 2011. The workshop brought together leading researchers from the Basic Energy Sciences (BES) facilities and Advanced Scientific Computing Research (ASCR). The workshop was co-sponsored by these two Offices to identify opportunities and needs for data analysis, ownership, storage, mining, provenance and data transfer at light sources, neutron sources, microscopy centers and other facilities. Their charge was to identify current and anticipated issues in the acquisition, analysis, communication and storage of experimental data that could impact the progress of scientific discovery, ascertain what knowledge, methods and tools are needed to mitigate present and projected shortcomings and to create the foundation for information exchanges and collaboration between ASCR and BES supported researchers and facilities. The workshop was organized in the context of the impending data tsunami that will be produced by DOE’s BES facilities. Current facilities, like SLAC National Accelerator Laboratory’s Linac Coherent Light Source, can produce up to 18 terabytes (TB) per day, while upgraded detectors at Lawrence Berkeley National Laboratory’s Advanced Light Source will generate ~10TB per hour. The expectation is that these rates will increase by over an order of magnitude in the coming decade. The urgency to develop new strategies and methods in order to stay ahead of this deluge and extract the most science from these facilities was recognized by all. The four focus areas addressed in this workshop were: Workflow Management - Experiment to Science: Identifying and managing the data path from experiment to publication. Theory and Algorithms: Recognizing the need for new tools for computation at scale, supporting large data sets and realistic theoretical models. Visualization and Analysis: Supporting near-real-time feedback for experiment optimization and new ways to extract and communicate critical information from large data sets. Data Processing and Management: Outlining needs in computational and communication approaches and infrastructure needed to handle unprecedented data volume and information content. It should be noted that almost all participants recognized that there were unlikely to be any turn-key solutions available due to the unique, diverse nature of the BES community, where research at adjacent beamlines at a given light source facility often span everything from biology to materials science to chemistry using scattering, imaging and/or spectroscopy. However, it was also noted that advances supported by other programs in data research, methodologies, and tool development could be implemented on reasonable time scales with modest effort. Adapting available standard file formats, robust workflows, and in-situ analysis tools for user facility needs could pay long-term dividends. Workshop participants assessed current requirements as well as future challenges and made the following recommendations in order to achieve the ultimate goal of enabling transformative science in current and future BES facilities: Theory and analysis components should be integrated seamlessly within experimental workflow. Develop new algorithms for data analysis based on common data formats and toolsets. Move analysis closer to experiment. Move the analysis closer to the experiment to enable real-time (in-situ) streaming capabilities, live visualization of the experiment and an increase of the overall experimental efficiency. Match data management access and capabilities with advancements in detectors and sources. Remove bottlenecks, provide interoperability across different facilities/beamlines and apply forefront mathematical techniques to more efficiently extract science from the experiments. This workshop report examines and reviews the status of several BES facilities and highlights the successes and shortcomings of the current data and communication pathways for scientific discovery. It then ascertains what methods and tools are needed to mitigate present and projected data bottlenecks to science over the next 10 years. The goal of this report is to create the foundation for information exchanges and collaborations among ASCR and BES supported researchers, the BES scientific user facilities, and ASCR computing and networking facilities. To jumpstart these activities, there was a strong desire to see a joint effort between ASCR and BES along the lines of the highly successful Scientific Discovery through Advanced Computing (SciDAC) program in which integrated teams of engineers, scientists and computer scientists were engaged to tackle a complete end-to-end workflow solution at one or more beamlines, to ascertain what challenges will need to be addressed in order to handle future increases in data

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

High-Order Preconditioners for Modern Computing Architectures: Line-Based Discontinuous Galerkin Method on GPUs

The goals of our project are to be able to overcome issues that plague computing in modern architecture such as limited memory bandwidth, badly conditioned Jacobians, and restrictive time steps. We begin by describing the line-based discontinuous Galerkin (line DG) method for a scalar two-dimensional problem. Line DG has been shown to provide a significant increase in sparsity for Jacobian matrix, especially in the diagonal block elements. In addition to this, the implicit time integration scheme helps alleviate the time step restriction but requires solving a (potentially badly conditioned) linear system. We can precondition the linear system to facilitate the solution. Since we want to solve the system on the GPU, the increase in sparsity from the line DG method is helpful to alleviate the memory issue. We successfully implemented a computation of the Jacobian on the CPU and are currently working on the GPU implementation. Finally, I discuss how this opportunity to intern at Lawrence Livermore National Laboratory through the National Science Foundation Mathematical Sciences Graduate Internship has affected my personal and professional growth.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

The classical Neumann boundary value problem of an isotropic, homogeneous elastic half-plane under plane strain conditions is readdressed as the limiting case of the fully three-dimensional problem. Analytical solutions of the stress and strain tensors are obtained by taking the limit from known three-dimensional solutions. It is shown that the displacement fields for the plane strain problem are not well defined. A small number of simple expressions are developed, which provide a general solution for linearly-varying traction over arbitrary regions on the boundary. A simple, efficient, and rapidly convergent algorithm is developed which uses these solutions as analytic elements and provides a solution approach to the general boundary value problem. The method is verified against known solutions for Hertzian contact between parallel cylinders. Two numerical examples are presented for the analysis of shallow foundation systems. In the first, the boundary conditions are informed by analytical elastoplastic calculations and a strain influence analysis is performed and compared with the Schmertmann method. Subsequently, empirical laboratory contact traction distributions measured by Bauer et al., in both the normal and tangential directions are employed as boundary conditions for an analysis of the underlying stress field.

42 ENGINEERING↗

DOE OSTI2018

Modeling Mesoscale Processes of Scalable Synthesis

Brown University is part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), led by PNNL. The Collaboratory focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials, through the design of efficient modeling methods and corresponding scalable algorithms.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Integration of the Response Surface Methodology with the Compromise Decision Support Problem in Developing a General Robust Design Procedure

In this paper we introduce a comprehensive and rigorous robust design procedure to overcome some limitations of the current approaches. A comprehensive approach is general enough to model the two major types of robust design applications, namely, robust design associated with the minimization of the deviation of performance caused by the deviation of noise factors (uncontrollable parameters), and robust design due to the minimization of the deviation of performance caused by the deviation of control factors (design variables). We achieve mathematical rigor by using, as a foundation, principles from the design of experiments and optimization. Specifically, we integrate the Response Surface Method (RSM) with the compromise Decision Support Problem (DSP). Our approach is especially useful for design problems where there are no closed-form solutions and system performance is computationally expensive to evaluate. The design of a solar powered irrigation system is used as an example. Our focus in this paper is on illustrating our approach rather than on the results per se.

Chen, Wei↗