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DOE OSTI2019

Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

Nonlinear effects of the various electric field and magnetic field components of storage rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent tune shifts within the beam. Furthermore, tune shifts are often sensitive to variations of system parameters, e.g. total particle momentum offsets $δp$. Such amplitude- and parameter-dependent tune shifts influence the dynamics and stability of a beam in particle storage rings. Thus, it is critical for high precision measurements to analyze and understand these influences. On this basis, we present in this paper normal form methods for the calculation of high order amplitude and system parameter dependencies of the horizontal and vertical tunes in storage rings using the differential algebra (DA) framework within COSY INFINITY. A storage ring is simulated using COSY INFINITY to generate a DA Poincaré return map describing the transverse phase space behavior after each revolution in the storage ring. The map is expanded around the parameter-dependent closed orbit of the system before transforming the resulting map into normal form coordinates to extract the high order tune dependencies on the phase space amplitude and variation in the system parameters. As a specific example, a storage ring similar to the Storage Ring of the Muon g-2 Experiment at Fermilab (E989) is investigated.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Data and scripts associated with “Non-random processes impacting organic matter chemistry are maximized in mid-order streams”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the publication “Non-random processes impacting organic matter chemistry are maximized in mid-order streams” submitted to Limnology and Oceanography (L&O) by Danczak et al. (in review). This package contains data and scripts used to investigate dissolved organic matter (DOM) molecular chemistry and diversification processes across 47 surface-water sampling sites in the Yakima River Basin, Washington, USA, during an August 2021 sampling campaign. The package contains analyses of ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), geochemical measurements, geospatial attributes, molecular diversity, and meta-metabolome ecological null models needed to reproduce the main manuscript results. The underlying field data were pulled from exising data packages at https://doi.org/10.15485/1892052 (Fulton et al., 2022) and https://doi.org/10.15485/1898914 (Grieger et al., 2022). For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. We thank the following organizations for providing access to field locations for sample collection: the United States Forest Service, Washington Department of Fish and Wildlife, Washington Department of Natural Resources, the Confederated Tribes and Bands of the Yakama Nation, and the Cowiche Canyon Conservatory. Research was conducted under Washington State Parks and Recreation Commission Scientific Research Permit #210901. We are grateful to the Yakama Nation Tribal Council and Yakama Nation Fisheries for their collaboration in facilitating sample collection and ensuring data usage aligns with their values and worldview. This data package contains an R-Markdown file for analyses and five folders: (1) Data, (2) Geospatial Data, (3) Supplemental_Files, (5) Figures_pdf, (4) and src. The Data folder contains tabular inputs and derived files used in the manuscript analysis. The Geospatial Data folder contains climate and water-balance, hydrologic, land-cover, population/regional water-use, stream, topographic, and stream-order attribute CSV files. The src folder contains scripts used to process data, run analyses, and generate figures. The Figures_pdf folder contains manuscript figure outputs. The Supplemental_Files folder contains supplemental analysis products. All files are .csv, .pdf, .html, .png, .R, .Rmd, .svg, or .tre. This data package is associated with the rcfsa-RC2-SPS_Null_Modeling repository found at https://github.com/river-corridors-sfa/rcfsa-RC2-SPS_Null_Modeling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Non-Diffusive Volume Advection with A High Order Interface Reconstruction Method

We show that non-diffusive volume advection in two-dimensions is achieved with several benchmark problems using a newly developed high-order volume of fluids (VOF) interface reconstruction method. (1) A new VOF interface reconstruction method using circular/corner facets (linear facets are a degenerate case of arcs). We create a circular interface facet in each mixed zone by matching neighbor volume with a hybrid Newton’s-bisection method and the local solution is final. In the general case, the new VOF interface reconstruction has 3rd order accuracy and can be easily made seamless. The new method addresses intrinsic issues with Young’s method such as gaps between interface facets in the case of a curved interface, and inability to define curvature nor identify corners. (2) A non-diffusive volume advection scheme. In an ALE advection step, a well-defined interface can be carried over through a Lagrange step and used to compute volume distribution into a relaxed mesh. Then, an interface reconstruction step is performed to redefine the interface in the relaxed mesh. We must point out that the interface carried over is also a solution of interface reconstruction because all the volume fractions in the relaxed mesh are naturally matched. We provide an interface tracking method compatible with our reconstruction scheme, where it is granted to use the prior info as an initial guess to capture sub-mesh resolution features. As a result, we are able to treat multiple facets inside a single mixed cell and obtain highly accurate, non-diffusive solution for advection problems with rather coarse meshes. We show our solutions for two-dimensional incompressible flows with two materials with a) the X + O diagonal translation; b) the Zalesak rotational test; and c) the single vortex spiral test.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Prompt Phrase Ordering Using Large Language Models in HPC: Evaluating Prompt Sensitivity

Large language models (LLMs) have demonstrated effective performance in domain-specific tasks, often requiring a well-designed prompt to guide their responses. However, optimizing the right prompt is challenging due to prompt sensitivity—the phenomenon where small changes in the prompt can lead to significant variations in performance. In this study, we evaluate prompt performance by examining all permutations of independent phrases to investigate prompt sensitivity and robustness. We used two datasets: the GSM8k dataset, which assesses mathematical reasoning, and a custom template prompt for summarizing database metadata. Our goal was to evaluate the performance across all permutations of a sequence of prompt phrases. The study was conducted using the llama3-instruct- 7B model hosted on Ollama, with computations parallelized in a high-performance computing environment. By comparing the average index of phrases in the best and worst-performing prompts, we found that the order of independent phrases within a prompt significantly impacts LLM performance. Additionally, we used Hamming distance to assess changes between phrase orderings, concluding that prompt modifications can dramatically affect scores, often by almost random chance. These findings support existing research on prompt sensitivity. We discuss the challenges of prompt optimization, noting that altering phrases in a successful prompt does not always result in another successful prompt.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Medium-Range Order Resists Deformation in Metallic Liquids and Glasses

In crystals, lattice defects, such as dislocations, control mechanical deformation. Similarly, it is widely believed that even in glasses and liquids some kinds of defects, strongly disordered regions, play a major role in deformation. To identify defects researchers focused on the nature of the short-range order (SRO) in the nearest neighbor cage of atoms. However, recent results by experiment, simulation and theory raise serious questions about this assumption. They suggest that the atomic medium-range order (MRO) provides resistance against flow at the atomic level. Because the MRO is a bulk property, it implies that defects play only a limited role. This new insight is supported by the density wave theory which shows that the MRO is driven by a top-down global force, rather than being a consequence of the SRO in the bottom-up manner, and the MRO provides stiffness to resist deformation. We briefly summarize the density wave theory, show that the MRO is related to ductility of metallic glasses, and discuss the implications on the role of the MRO in the atomic-level mechanism of deformation.

36 MATERIALS SCIENCE↗

NASA NTRS2013

Development and Evaluation of an Order-N Formulation for Multi-Flexible Body Space Systems

This paper presents development of a generic recursive Order-N algorithm for systems with rigid and flexible bodies, in tree or closed-loop topology, with N being the number of bodies of the system. Simulation results are presented for several test cases to verify and evaluate the performance of the code compared to an existing efficient dense mass matrix-based code. The comparison brought out situations where Order-N or mass matrix-based algorithms could be useful.

Multibody dynamics↗

NASA NTRS2015

A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

High-Order↗

NASA NTRSDate not supplied

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗

NASA NTRSDate not supplied

Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling

Uncertainty quantification of computational fluid dynamics (CFD) simulations is a complicated procedure which still relies in many cases on engineering judgment and factors of safety. This is in part because the computational cost of measuring the simulation's sensitivity to all meaningful parameters (e.g., body surface roughness) and hyperparameters (e.g., subiteration convergence criterion) is intractable for even a single simulation. Reduced-order modeling dramatically lowers this computational cost of simulating fluid flows, but usually only where similar data is already available. In this work, fluid reduced-order models are utilized to quantify a flow's sensitivity to certain physical parameters for the purposes of improved uncertainty quantification. Characteristic observability and sensitivity are both explored. The resulting sensitivity quantifications enable more informed CFD frameworks and more rigorous uncertainty bounds on the resulting data.

uncertainty quantification↗

NASA NTRSDate not supplied

Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling

uncertainty quantification↗

NASA NTRSDate not supplied

Impact of Traffic-Following on Order of Autonomous Airspace Operations

In this paper, we investigate the dynamic emergence of traffic order in a distributed multi-agent system, aiming to minimize inefficiencies that stem from unnecessary structural impositions. We introduce a methodology for developing a dynamically updating traffic pattern map of the airspace by leveraging information about the consistency and frequency of flow directions used by current as well as preceding traffic. Informed by this map, an agent can discern the degree to which it is advantageous to follow traffic by trading off utilities such as time and order. We show that for the traffic levels studied, for low degrees of traffic-following behavior, there is minimal penalty in terms of aircraft travel times while improving the overall orderliness of the airspace. On the other hand, heightened traffic-following behavior may result in increased aircraft travel times, while marginally reducing the overall entropy of the airspace. Ultimately, the methods and metrics presented in this paper can be used to optimally and dynamically adjust an agent’s traffic-following behavior based on these trade-offs.

Airspace Operations↗

NASA NTRSDate not supplied

Impact of Traffic-Following on Order of Autonomous Airspace Operations

We investigate the dynamic emergence of traffic order in a distributed multi-agent system, aiming to minimize inefficiencies that stem from unnecessary structural impositions. We introduce a methodology for developing a dynamically updating traffic pattern map of the airspace by leveraging information about the consistency and frequency of flow directions used by current as well as preceding traffic. Informed by this map, an agent can discern the degree to which it is advantageous to follow traffic by trading off utilities such as time and order. We show that for the traffic levels studied, for low degrees of traffic-following behavior, there is minimal penalty in terms of aircraft travel times while improving the overall orderliness of the airspace. On the other hand, heightened traffic-following behavior may result in increased aircraft travel times, while marginally reducing the overall entropy of the airspace. Ultimately, the methods and metrics presented in this paper can be used to optimally and dynamically adjust an agent’s traffic-following behavior based on these trade-offs.

Airspace Operations↗

NASA NTRSDate not supplied

Comparison of Two Approaches to Constructing Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Methods for Mixed-Element Grids

In this paper, we introduce a third-order nodal-gradient cell-centered ﬁnite volume scheme applicable to mixed-element grids based on a single numerical ﬂux per face. Previously, we considered a split-quadrilateral-face approach, where we split each quadrilateral face of a non-tetrahedral cell into two triangles and then apply second- and third-order schemes designed for tetrahedral grids. This approach is relatively simple to implement but expensive because it requires two numerical ﬂux evaluations per quadrilateral face. In this study, we consider another approach, where the surface ﬂux quadrature is performed with a single numerical ﬂux per face with ﬂux corrections. It requires a 3×3 correction matrix to be stored at each face but is more economical than the split-quadrilateral-face approach. The two approaches are compared for three-dimensional ﬂows on irregular hexahedral grids, and their relative merits are discussed.

Third-order scheme↗

DOE OSTI2022

Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Generating An Advanced Cross-section Library For HTGR Pebble Bed Depletion Calculations Using Reduced-Order Model Generation Techniques

For code development, Advanced Reactor Technologies - Gas Cooled Reactors Program (ART-GCR) rely on a collaboration with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, but the cross sections generation and the methodology definition is part of this program area goals. Based on previous studies in FY23, the size of microscopic cross section libraries increases rapidly with the number of tabulations, requiring significant amount of memory and drastically slowing down the Griffin calculations when evaluating cross sections via the multivariate linear interpolation approach. Rising to these challenges, this work investigates constructing Reduced-order Models (ROMs) for the multi-group microscopic cross sections to accelerate the cross section evaluation in Griffin. A database of multigroup cross sections is first collected considering all possible parameters that a designer could change for optimization. Down-selection of the ROM techniques afterward shows Deep Neural Network (DNN) as the best candidate when jointly consider memory efficiency, predictive accuracy, computational cost, scalability, flexibility and ease of implementation of the algorithms in comparison to the multidimensional interpolation. This work develops a specific interface that enables the cross section predictions using pre-trained DNN models into Griffin leveraging the existing ROM capabilities. DNNs have been trained for all isotopes for use in Griffin. Preliminary Griffin testing shows that DNNs exhibit exceptional predictive accuracy and the use of DNNs provides orders of magnitude improvement in memory efficiency compared to conventional interpolation techniques. With such ROM techniques, it holds great promise to further increase the fidelity of the Pebble Bed Reactor (PBR) simulation by increasing the number of tabulations/state variables during cross section evaluation, while maintaining the computational cost affordable in Griffin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗

DOE OSTI2023

Sensitivity Analysis, Reduced-order Modeling, and Optimization of a Gas-Cooled Pebble Bed Reactor using Equilibrium-Core and DLOFC Performance

This work presents and applies a workflow for performing design optimization on gas-cooled pebble-bed reactors. Based on previous research, a representative equilibrium core of a pebble-bed reactor and a depressurized loss-of-forced-cooling model are created. These applications are built using the Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically utilizing Griffin, Pronghorn, and Bison. After defining design-related parameters and quantities of interest regarding reactor safety and efficiency, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of reduced-order models. Subsequently, the dataset and reduced-order models are employed in an optimization study aimed at maximizing fuel utilization while adhering to safety and operational constraints. The optimization process leads to an improvement of fuel utilization by approximately 10\%, compared to engineering-judgment-based nominal conditions.

97 - MATHEMATICS AND COMPUTING↗