Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematics of computing”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

Strengthening LLNL Missions through Laboratory Directed Research and Development in High Performance Computing

High performance computing (HPC) has been a defining strength of Lawrence Livermore National Laboratory (LLNL) since its founding. Livermore scientists have designed and used some of the world’s most powerful computers to drive breakthroughs in nearly every mission area. Today, the Laboratory is recognized as a world leader in the application of HPC to complex science, technology, and engineering challenges. Most importantly, HPC has been integral to the National Nuclear Security Administration’s (NNSA’s) Stockpile Stewardship Program—designed to ensure the safety, security, and reliability of our nuclear deterrent without nuclear testing. A critical factor behind Lawrence Livermore’s preeminence in HPC is the ongoing investments made by the Laboratory Directed Research and Development (LDRD) Program in cutting-edge concepts to enable efficient utilization of these powerful machines. Congress established the LDRD Program in 1991 to maintain the technical vitality of the Department of Energy (DOE) national laboratories. Since then, LDRD has been, and continues to be, an essential tool for exploring anticipated needs that lie beyond the planning horizon of our programs and for attracting the next generation of talented visionaries. Through LDRD, Livermore researchers can examine future challenges, propose and explore innovative solutions, and deliver creative approaches to support our missions. The present scientific and technical strengths of the Laboratory are, in large part, a product of past LDRD investments in HPC. Here, we provide seven examples of LDRD projects from the past decade that have played a critical role in building LLNL’s HPC, computer science, mathematics, and data science research capabilities, and describe how they have impacted LLNL’s mission.

97 MATHEMATICS AND COMPUTING↗

Parameter Estimation for Thurstone Choice Models

We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates the well-known choice models such as the Luce choice model for comparison sets of two or more items and the Bradley-Terry model for pair comparisons. We provide a tight characterization of the mean squared error of the maximum likelihood parameter estimator. We also provide similar characterizations for parameter estimators defined by a rank-breaking method, which amounts to deducing one or more pair comparisons from a comparison of two or more items, assuming independence of these pair comparisons, and maximizing a likelihood function derived under these assumptions. We also consider a related binary classification problem where each individual parameter takes value from a set of two possible values and the goal is to correctly classify all items within a prescribed classification error. The results of this paper shed light on how the parameter estimation accuracy depends on given Thurstone choice model and the structure of comparison sets. In particular, we found that for unbiased input comparison sets of a given cardinality, when in expectation each comparison set of given cardinality occurs the same number of times, for a broad class of Thurstone choice models, the mean squared error decreases with the cardinality of comparison sets, but only marginally according to a diminishing returns relation. On the other hand, we found that there exist Thurstone choice models for which the mean squared error of the maximum likelihood parameter estimator can decrease much faster with the cardinality of comparison sets. We report empirical evaluation of some claims and key parameters revealed by theory using both synthetic and real-world input data from some popular sport competitions and online labor platforms.

97 MATHEMATICS AND COMPUTING↗

iVPIC: A low-­dispersion, energy-­conserving relativistic PIC solver for LPI simulations

We have developed a novel low-­dispersion, exactly energy-­conserving PIC algorithm for the relativistic Vlasov-­Maxwell system. The approach features an exact energy conservation theorem while preserving the favorable performance and numerical dispersion properties of explicit PIC. The new algorithm has the potential to enable much longer laser-­plasma-­interaction (LPI) simulations than are currently possible.

97 MATHEMATICS AND COMPUTING↗

Sensitivity Analysis and Uncertainty Quantification for the LAMMPS Molecular Dynamics Simulation Code

We examine sensitivity analysis and uncertainty quantification for molecular dynamics simulation. Extreme (large or small) output values for the LAMMPS code often occur at the boundaries of input regions, and uncertainties in those boundary values are overlooked by common SA methods. Similarly, input values for which code outputs are consistent with calibration data can also occur near boundaries. Upon applying approaches in the literature for imprecise probabilities (IPs), much more realistic results are obtained than for the complacent application of standard SA and code calibration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Final Technical Report of the project "Controlling Quantum Information by Quantum Correlations"

The report describes hypotheses, aims, methods and results of the project 20170675PRD2, “Controlling Quantum Information by Quantum Correlations”, which has been run from July 31, 2017 to January 7, 2018. The technical work has been performed by Director’s Fellow Davide Girolami of the T-4 Division, Physics of Condensed Matter and Complex Systems, under the supervision of Wojciech Zurek (T-4), Lukasz Cincio (T-4), and Marcus Daniels (CCS-7). The project ended as Davide Girolami has been converted to J. R. Oppenheimer Fellow to work on the project 20180702PRD1, “Optimal Control of Quantum Machines”, started on January 8, 2018.

97 MATHEMATICS AND COMPUTING↗

Corrections to the General (2,4) and (4,4) FDTD Schemes

The sampling weights associated with two general higher order FDTD schemes were derived by Smith, et al. and published in a IEEE Transactions on Antennas and Propagation article in 2012. Inconsistencies between governing equations and their resulting solutions were discovered within the article. In an effort to track down the root cause of these inconsistencies, the full three-dimensional, higher order FDTD dispersion relation was re-derived using Mathematica TM . During this process, two errors were identi ed in the article. Both errors are highlighted in this document. The corrected sampling weights are also provided. Finally, the original stability limits provided for both schemes are corrected, and presented in a more precise form. It is recommended any future implementations of the two general higher order schemes provided in the Smith, et al. 2012 article should instead use the sampling weights and stability conditions listed in this document.

97 MATHEMATICS AND COMPUTING↗

Design, analysis and preliminary numerical results for the nonconforming VEM for parabolic problems

The virtual element method (VEM) is a numerical methodology for solving partial differential equations on unstructured polytopal meshes. In this work, we extend the nonconforming high-order formulation suitable to time-dependent diffusion problems with possibly nonlinear forcing terms. Coupling high-order virtual element formulations in space with time-marching schemes based on Backward Differention Formulas (BDFs) makes a fully discrete method with optimal order of convergence in the Method of Lines framework. We investigate and assess the performance of the method through theoretical analysis and a set of numerical experiments.

97 MATHEMATICS AND COMPUTING↗

EpiCast: Simulating Epidemics with Extreme Detail

In early 2020, COVID-19 swept the globe. Governments attempted to “flatten the curve” through business shutdowns and stay-at-home orders, but the United States was hit hard. By the end of March, mere months after the virus first emerged in humans 7,000 miles away, the U.S. had recorded 192,300 cases and 5,300 deaths. While this unprecedented disaster sent shockwaves through every level of society and clouded an uncertain future, state and local governments turned to computational and mathematical epidemiology researchers to help formulate intervention strategies to limit the spread of the disease. Traditional forecasting models provided a reasonable understanding of how the near future was likely to look, but local policy makers and public health communities still struggled to understand how potential mitigations ought to be implemented. Decision makers needed a way to measure the impact of their policy choices—they needed better technology. EpiCast answered the call, bringing urgently needed answers to policymakers grappling with how to adjust school and business schedules. EpiCast is modeling software that generates a synthetic, representative population to simulate infectious disease transmission in the United States with extreme detail and granularity. The software models human behavior combined with community-specific information to provide a fine-grained preview of the effect of potential mitigation strategies for decision makers.

60 APPLIED LIFE SCIENCES↗

Disease Precognition [Slides]

How can we reduce the health and economic impacts future epidemics and pandemics? Global Real-Time Disease Forecasting is not just for weather anymore! Disease precognition technology is discussed.

59 BASIC BIOLOGICAL SCIENCES↗