Finding a natural rhythm
Paul J. Dauenhauer describes the mathematical basis for designing dynamic catalysts that are programmed to change with time.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SEARCH · Engineering Papers
Results for “Mathematical programming”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Cybersecurity Enhancement for Multi-Infeed High-Voltage DC Systems
Composed of multiple two-terminal high-voltage DC (HVDC) transmission systems, a multi-infeed HVDC (MIDC) system exchanges massive power among multiple asynchronous AC systems. However, as an intrinsically cyber-physical system, an MIDC system could suffer from cyber-attacks, leading to massive power mismatches in multiple AC systems, and resulting in catastrophic consequences. Since the sequential responses of an MIDC system and interconnected AC systems are in different timescales, this paper first establishes a two-timescale model to evaluate the sequential impacts caused by cyber-attacks. Then, an event-triggered cyber-defense strategy is proposed to enhance the cybersecurity of an MIDC system by mitigating multiple non-simultaneous cyber-attacks. Whenever new cyber-attack events occur, the proposed cyber-defense strategy, which is mathematically modeled as a mixed-integer quadratic programming problem, is executed on-line and updated in an event-triggered manner. Here, simulation results on an MIDC system demonstrate that the low-cost and almost blind cyber-attacks can cause severe frequency deviations, and the proposed strategy can mitigate multi-cyber-attacks effectively.
24 POWER TRANSMISSION AND DISTRIBUTION↗
su3_bench: Lattice QCD SU(3) matrix-matrix multiply microbenchmark (su3_bench) v1.0
The purpose of this microbenchmark is to provide a means to explore different programming methodologies using a simple, but not trivial, mathematical kernel. The kernel is based on the mult_su3_nn() SU(3) matrix-matrix multiply routine in the MILC Lattice Quantum Chromodynamics(LQCD) code.
Doerfler, Douglas↗
CSBCOO SPMM: Compressed Sparse Block Coordinate format sparse matrix dense vector multiply benchmark (CSBCOO SPMM) v1.0
The purpose of this microbenchmark is to provide a means to explore different programming methodologies using a simple, but not trivial, mathematical kernel. The kernel is based on the matrix vector product in the MFDn nuclear configuration interaction code's LOBPCG eigensolver. This particular mathematical operation is a key element in the solution of systems of equations and block eigensolvers.
Cook, Brandon↗
Summer Internship Project: Set Topology [Slides]
Why a Set Topology? 1. Expand the array of tools given to physicists, educators, and students. 2. Through usages of PIC, MPM, and Monte Carlo. 3. My work at LANL was specified to handle requirements for the usage of MPM with FleCSI. 4. What we want it to do - phase change, simulating plasma, and other Multiphysics applications. 5. In FleCSI we already have mesh structures, we needed a way to represent those particles and certain behavior's of these particles that clients desire.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Preliminary API design to access SG-50 database [Slides]
This presentation details the design and use of a rudimentary example API. The example API reads JSON; eventually it needs to operate with the database. It demonstrates ease in applying powerful, publicly available tools.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines
Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.
Branlard, Emmanuel (ORCID:0000000277506128)↗
There from the Beginning: The Women of Los Alamos National Laboratory Supporting National and International Nuclear Security
From the beginning of the Manhattan Project in the early 1940s, the women of what would become Los Alamos National Laboratory (LANL) worked in technical positions alongside their male counterparts, played a key role as computers, and worked in administrative jobs as secretaries, phone operators, bookkeepers, and on behalf of the U.S. Army in the Women’s Army Corps. Throughout the history of the Laboratory, women experts at LANL helped establish and lead important national and international security programs, with careers in science, technology, engineering, and mathematics. Over time, the women of Los Alamos have come together under various Employee Resource Groups, such as the Atomic Women, to help the next generation succeed in their technical fields. The Laboratory’s commitment to diversity and inclusion continues to this day, with current Laboratory Director Thom Mason leading LANL as the first national laboratory to join the Gender Champions in Nuclear Policy.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
ReEDS Performance Improvement
The Regional Energy Deployment System (ReEDS) is an open-source, spatially explicit, long-term capacity expansion model for the bulk electric power system of the contiguous United States, encompassing multiple scenarios with technological and political assumptions (see https://github.com/NREL/ReEDS-2.0). With the increased needs for capabilities, higher temporal and spatial resolutions to model the evolution of the power system with modern technologies and low-carbon pathways, ReEDS' model solution times have increased significantly from 4-6 hours in 2018 to 18-48+ hours in 2023 . Also, the model size for commonly-run ReEDS scenarios reached 22 and 28 million equations and variables, respectively. These runtimes can be especially challenging under certain scenario settings (e.g., very high temporal or spatial resolution) or with limited computational power. In this presentation, we will discuss several methods we used to improve model runtime, including data preparation, model modification, and solver tuning. The implementation of these methods shrank the model size to 7.2 and 7.3 million equations and variables, respectively. Furthermore, this led to a 77% reduction in the model's run time for commonly-run ReEDS scenarios. We will discuss the process of identifying areas for solve time improvements and how the specific enhancements for the ReEDS model might be applied to other similar large-scale models.
ENERGY PLANNING, POLICY, AND ECONOMY,MATHEMATICS A↗
Automating NISQ Application Design with Meta Quantum Circuits with Constraints (MQCC)
Near-term intermediate scale quantum (NISQ) computers are likely to have very restricted hardware resources, where precisely controllable qubits are expensive, error-prone, and scarce. Programmers of such computers must therefore balance trade-offs among a large number of (potentially heterogeneous) factors specific to the targeted application and quantum hardware. To assist them, we propose Meta Quantum Circuits with Constraints (MQCC), a meta-programming framework for quantum programs. Programmers express their application as a succinct collection of normal quantum circuits stitched together by a set of (manually or automatically) added meta-level choice variables, whose values are constrained according to a programmable set of quantitative optimization criteria. MQCC’s compiler generates the appropriate constraints and solves them via an SMT solver, producing an optimized, runnable program. We showcase a few MQCC’s applications for its generality including an automatic generation of efficient error syndrome extraction schemes for fault-tolerant quantum error correction with heterogeneous qubits and an approach to writing approximate quantum Fourier transformation and quantum phase estimation that smoothly trades off accuracy and resource use. We also illustrate that MQCC can easily encode prior one-off NISQ application designs-–multi-programming (MP), crosstalk mitigation (CM)—as well as a combination of their optimization goals (i.e., a combined MP-CM).
97 MATHEMATICS AND COMPUTING↗
Resolved Resonance Region Analysis of 206 Pb, 207 Pb, and 208 Pb for Next Generation Lead-Cooled Fast Systems
Recently, great interest has been generated in using lead as a coolant for fast neutron systems and as a result it is important to investigate the ENDF/B-VIII.0 isotopic evaluations that comprise stable le ad. To this end, resonance parameters for 206 Pb, 207 Pb, and 208 Pb were re-evaluated because their resolved resonance regions extend beyond 0.5 MeV meaning resonance parameters used in reconstructing cross sections and elastic scattering angular distributions impact fast systems. The impact of resonance parameters is demonstrated by the differences between the evaluations in predicting experimental results from the fully modeled RPI Quasi-Differential Scattering Experiment via MCNPv6.2. In addition, MCNP KCODE calculations of lead-sensitive fast spectra critical benchmarks showed variations of keff on average of 400 pcm, caused solely from differences in elastic scattering angular distributions in 208 Pb. Re-evaluation entailed fitting data with the program SAMMY.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Optimization-Driven Scenario Grouping
Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. Here, we develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.
97 MATHEMATICS AND COMPUTING↗
Source-to-Source Automatic Differentiation of OpenMP Parallel Loops
This article presents our work toward correct and efficient automatic differentiation of OpenMP parallel worksharing loops in forward and reverse mode. Automatic differentiation is a method to obtain gradients of numerical programs, which are crucial in optimization, uncertainty quantification, and machine learning. The computational cost to compute gradients is a common bottleneck in practice. For applications that are parallelized for multicore CPUs or GPUs using OpenMP, one also wishes to compute the gradients in parallel. Here, we propose a framework to reason about the correctness of the generated derivative code, from which we justify our OpenMP extension to the differentiation model. We implement this model in the automatic differentiation tool Tapenade and present test cases that are differentiated following our extended differentiation procedure. Performance of the generated derivative programs in forward and reverse mode is better than sequential, although our reverse mode often scales worse than the input programs.
97 MATHEMATICS AND COMPUTING↗
Whole-Program Adaptive Error Detection and Mitigation. Final Report
Errors in application state resulting from faults in hardware are an increasing concern on extreme-scale computing systems. Errors that escape detection and lead to silent data corruption are particularly problematic. Detecting errors is an important first step toward fault tolerant program execution. The multi-institutional project addressed a comprehensive approach to error detection and mitigation for scientific applications that combined configurable error detectors, a unified reliability specification, and whole-program detector composition.
97 MATHEMATICS AND COMPUTING↗
Livermore Computing Integrates Advanced Cognitive Simulation Resource
With the integration of the first production Cerebras CS-1 system into Lassen, Livermore Computing (LC) is preparing the way for advanced cognitive simulation (CogSim) capabilities integrated into leadership HPC systems to support Artificial Intelligence (AI) driven computational needs of the Stockpile Stewardship Program.
97 MATHEMATICS AND COMPUTING↗
Overview of Tools to Provide Support for State Energy Programs [Slides]
This "Overview of Tools to Provide Support for State Energy Programs?" is a resource to support technical assistance programs, specifically motivated by the State Energy Program Direct TA program under SCEP at the Department of Energy. It provides a general description of seven unique tools - six by NREL, one by Argonne National Lab - which may be used to benefit state energy offices either through direct use (by state offices) or through contracted support (by national lab staff via TA programs).
97 MATHEMATICS AND COMPUTING↗
Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs
A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. Here, we also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size.
97 MATHEMATICS AND COMPUTING↗
Generation of the TSL for Zirconium Hydrides from Ab Initio Methods
Zirconium hydride (ZrHx) is a moderator material used in TRIGA and other reactors that may exist in multiple phases with varying stoichiometry, which include the δ phase and the ϵ phase. Current ENDF/B-VIII.0 ZrHx thermal scattering law (TSL) evaluations do not distinguish between phases. These sub-libraries were generated with the LEAPR module of NJOY using historic phonon spectra derived from a central force model and assume incoherent elastic scattering for both bound hydrogen and zirconium, which neglects the effects of crystal structures important for scattering from zirconium bound in ZrHx. In this work, the TSLs for hydrogen and zirconium bound in δ-ZrHx and ϵ-ZrH2 were generated from phonon spectra derived from modern ab initio lattice dynamics methods and ab initio molecular dynamics. Subsequently, TSLs for hydrogen and zirconium in ZrHx and ZrH2 were generated using the Full Law Analysis Scattering System Hub (FLASSH) code. The built-in generalized coherent elastic routine was used to generate the previously neglected elastic contribution from zirconium for this material. The present TSLs provide both a re-evaluation of the current ZrH sub-libraries and expansion of the set of TSLs available for the examination of neutrons in systems with zirconium hydride, permitting explicit treatment of δ and ϵ phases.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗