Results for “algorithmic differentiation” — Page 51

NASA NTRS2020

Medics: Medical Decision Support System for Long-Duration Space Exploration

The Autonomous Medical Operations (AMO) group at NASA Ames is developing a “medical decision support system” to enable astronauts on long-duration exploration missions to operate autonomously. The system will support clinical actions by providing medical interpretation advice and procedural recommendations during emergent care and clinical work performed by crew. The current state of development of the system, called MedICS (Medical Interpretation Classification and Segmentation) includes two separate aspects: a set of machine learning diagnostic models trained to analyze organ images and patient health records, and an interface to ultrasound diagnostic hardware and to medical repositories. Three sets of images of different organs and medical records were utilized for training machine learning models for various analyses, as follows: 1. Pneumothorax condition (collapsed lung). The trained model provides a positive or negative diagnosis of the condition. 2. Carotid artery occlusion. The trained model produces a diagnosis of 5 different occlusion levels (including “normal”). 3. Ocular retinal images. The model extracts optic disc pixels (image segmentation). This is a precursor step for advanced autonomous fundus clinical evaluation algorithms to be implemented in FY20. 4. Medical health records. The model produces a differential diagnosis for any particular individual, based on symptoms and other health and demographic information. A probability is calculated for each of 25 most common conditions. The same model provides the likelihood of survival. All results are provided with a confidence level. Item 1 images were provided by the US Army and were part of a data set for the clinical treatment of injured battlefield soldiers. This condition is relevant to possible space mishaps, due to pressure management issues. Item 2 images were provided by Houston Methodist Hospital, and item 3 health records were acquired from the MIT laboratory of computational physiology. The machine learning technology utilized is deep multilayer networks (Deep Learning), and new models will continue to be produced, as relevant data is made available and specific health needs of astronaut crews are identified. The interfacing aspects of the system include a GUI for running the different models, and retrieving and storing data, as well as support for integration with an augmented reality (AR) system deployed at JSC by Tietronix Software Inc. (HoloLens). The AR system provides guidance for the placement of an ultrasound transducer that captures images to be sent to the MedICS system for diagnosis. The image captured and the associated diagnosis appear in the technician’s AR visual display.

Colombano, Silvano↗

DOE OSTI2016

On the solution of elliptic partial differential equations on regions with corners

In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

TU-EF-BRD-00: The Science of QA

Research related to quality and safety has been a staple of medical physics academic activities for a long time. From very early on, medical physicists have developed new radiation measurement equipment and analysis techniques, created ever increasingly accurate dose calculation models, and have vastly improved imaging, planning, and delivery techniques. These and other areas of interest have improved the quality and safety of radiotherapy for our patients. With the advent of TG-100, quality and safety is an area that will garner even more research interest in the future. As medical physicists pursue quality and safety research in greater numbers, it is worthwhile to consider what actually constitutes research on quality and safety. For example, should the development of algorithms for real-time EPID-based in-vivo dosimetry be defined as “quality and safety” research? How about the clinical implementation of such as system? Surely the application of failure modes and effects analysis to a clinical process would be considered quality and safety research, but is this type of research that should be included in the medical physics peer-reviewed literature? The answers to such questions are of critical importance to set researchers in a direction that will provide the greatest benefit to our field and the patients we serve. The purpose of this symposium is to consider what constitutes research in the arena of quality and safety and differentiate it from other research directions. The key distinction here is developing the tool itself (e.g. algorithms for EPID dosimetry) vs. studying the impact of the tool with some quantitative metric. Only the latter would I call quality and safety research. Issues of ‘basic’ versus ‘applied’ quality and safety research will be covered as well as how the research results should be structured to provide increasing levels of support that a quality and safety intervention is effective and sustainable. Examples from existing peer-reviewed research will be used to highlight the main points. Historical, medical physicists have leveraged many areas of applied physics, engineering and biology to improve radiotherapy. Research on quality and safety is another area where physicists can have an impact. The key to further progress is to clearly define what constitutes quality and safety research for those interested in doing such research and the reviewers of that research. Learning Objectives: List several tools of quality and safety with references to peer-reviewed literature. Describe effects of mental workload on performance. Outline research in quality and safety indicators and technique analysis. Understand what quality and safety research needs to be going forward. Understand the links between cooperative group trials and quality and safety research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-EF-BRD-01: Topics in Quality and Safety Research and Level of Evidence

Research related to quality and safety has been a staple of medical physics academic activities for a long time. From very early on, medical physicists have developed new radiation measurement equipment and analysis techniques, created ever increasingly accurate dose calculation models, and have vastly improved imaging, planning, and delivery techniques. These and other areas of interest have improved the quality and safety of radiotherapy for our patients. With the advent of TG-100, quality and safety is an area that will garner even more research interest in the future. As medical physicists pursue quality and safety research in greater numbers, it is worthwhile to consider what actually constitutes research on quality and safety. For example, should the development of algorithms for real-time EPID-based in-vivo dosimetry be defined as “quality and safety” research? How about the clinical implementation of such as system? Surely the application of failure modes and effects analysis to a clinical process would be considered quality and safety research, but is this type of research that should be included in the medical physics peer-reviewed literature? The answers to such questions are of critical importance to set researchers in a direction that will provide the greatest benefit to our field and the patients we serve. The purpose of this symposium is to consider what constitutes research in the arena of quality and safety and differentiate it from other research directions. The key distinction here is developing the tool itself (e.g. algorithms for EPID dosimetry) vs. studying the impact of the tool with some quantitative metric. Only the latter would I call quality and safety research. Issues of ‘basic’ versus ‘applied’ quality and safety research will be covered as well as how the research results should be structured to provide increasing levels of support that a quality and safety intervention is effective and sustainable. Examples from existing peer-reviewed research will be used to highlight the main points. Historical, medical physicists have leveraged many areas of applied physics, engineering and biology to improve radiotherapy. Research on quality and safety is another area where physicists can have an impact. The key to further progress is to clearly define what constitutes quality and safety research for those interested in doing such research and the reviewers of that research. Learning Objectives: List several tools of quality and safety with references to peer-reviewed literature. Describe effects of mental workload on performance. Outline research in quality and safety indicators and technique analysis. Understand what quality and safety research needs to be going forward. Understand the links between cooperative group trials and quality and safety research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-EF-BRD-02: Indicators and Technique Analysis

Research related to quality and safety has been a staple of medical physics academic activities for a long time. From very early on, medical physicists have developed new radiation measurement equipment and analysis techniques, created ever increasingly accurate dose calculation models, and have vastly improved imaging, planning, and delivery techniques. These and other areas of interest have improved the quality and safety of radiotherapy for our patients. With the advent of TG-100, quality and safety is an area that will garner even more research interest in the future. As medical physicists pursue quality and safety research in greater numbers, it is worthwhile to consider what actually constitutes research on quality and safety. For example, should the development of algorithms for real-time EPID-based in-vivo dosimetry be defined as “quality and safety” research? How about the clinical implementation of such as system? Surely the application of failure modes and effects analysis to a clinical process would be considered quality and safety research, but is this type of research that should be included in the medical physics peer-reviewed literature? The answers to such questions are of critical importance to set researchers in a direction that will provide the greatest benefit to our field and the patients we serve. The purpose of this symposium is to consider what constitutes research in the arena of quality and safety and differentiate it from other research directions. The key distinction here is developing the tool itself (e.g. algorithms for EPID dosimetry) vs. studying the impact of the tool with some quantitative metric. Only the latter would I call quality and safety research. Issues of ‘basic’ versus ‘applied’ quality and safety research will be covered as well as how the research results should be structured to provide increasing levels of support that a quality and safety intervention is effective and sustainable. Examples from existing peer-reviewed research will be used to highlight the main points. Historical, medical physicists have leveraged many areas of applied physics, engineering and biology to improve radiotherapy. Research on quality and safety is another area where physicists can have an impact. The key to further progress is to clearly define what constitutes quality and safety research for those interested in doing such research and the reviewers of that research. Learning Objectives: List several tools of quality and safety with references to peer-reviewed literature. Describe effects of mental workload on performance. Outline research in quality and safety indicators and technique analysis. Understand what quality and safety research needs to be going forward. Understand the links between cooperative group trials and quality and safety research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-EF-BRD-03: Mental Workload and Performance

Research related to quality and safety has been a staple of medical physics academic activities for a long time. From very early on, medical physicists have developed new radiation measurement equipment and analysis techniques, created ever increasingly accurate dose calculation models, and have vastly improved imaging, planning, and delivery techniques. These and other areas of interest have improved the quality and safety of radiotherapy for our patients. With the advent of TG-100, quality and safety is an area that will garner even more research interest in the future. As medical physicists pursue quality and safety research in greater numbers, it is worthwhile to consider what actually constitutes research on quality and safety. For example, should the development of algorithms for real-time EPID-based in-vivo dosimetry be defined as “quality and safety” research? How about the clinical implementation of such as system? Surely the application of failure modes and effects analysis to a clinical process would be considered quality and safety research, but is this type of research that should be included in the medical physics peer-reviewed literature? The answers to such questions are of critical importance to set researchers in a direction that will provide the greatest benefit to our field and the patients we serve. The purpose of this symposium is to consider what constitutes research in the arena of quality and safety and differentiate it from other research directions. The key distinction here is developing the tool itself (e.g. algorithms for EPID dosimetry) vs. studying the impact of the tool with some quantitative metric. Only the latter would I call quality and safety research. Issues of ‘basic’ versus ‘applied’ quality and safety research will be covered as well as how the research results should be structured to provide increasing levels of support that a quality and safety intervention is effective and sustainable. Examples from existing peer-reviewed research will be used to highlight the main points. Historical, medical physicists have leveraged many areas of applied physics, engineering and biology to improve radiotherapy. Research on quality and safety is another area where physicists can have an impact. The key to further progress is to clearly define what constitutes quality and safety research for those interested in doing such research and the reviewers of that research. Learning Objectives: List several tools of quality and safety with references to peer-reviewed literature. Describe effects of mental workload on performance. Outline research in quality and safety indicators and technique analysis. Understand what quality and safety research needs to be going forward. Understand the links between cooperative group trials and quality and safety research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-EF-BRD-04: Summing It Up: The Future of Quality and Safety Research

Research related to quality and safety has been a staple of medical physics academic activities for a long time. From very early on, medical physicists have developed new radiation measurement equipment and analysis techniques, created ever increasingly accurate dose calculation models, and have vastly improved imaging, planning, and delivery techniques. These and other areas of interest have improved the quality and safety of radiotherapy for our patients. With the advent of TG-100, quality and safety is an area that will garner even more research interest in the future. As medical physicists pursue quality and safety research in greater numbers, it is worthwhile to consider what actually constitutes research on quality and safety. For example, should the development of algorithms for real-time EPID-based in-vivo dosimetry be defined as “quality and safety” research? How about the clinical implementation of such as system? Surely the application of failure modes and effects analysis to a clinical process would be considered quality and safety research, but is this type of research that should be included in the medical physics peer-reviewed literature? The answers to such questions are of critical importance to set researchers in a direction that will provide the greatest benefit to our field and the patients we serve. The purpose of this symposium is to consider what constitutes research in the arena of quality and safety and differentiate it from other research directions. The key distinction here is developing the tool itself (e.g. algorithms for EPID dosimetry) vs. studying the impact of the tool with some quantitative metric. Only the latter would I call quality and safety research. Issues of ‘basic’ versus ‘applied’ quality and safety research will be covered as well as how the research results should be structured to provide increasing levels of support that a quality and safety intervention is effective and sustainable. Examples from existing peer-reviewed research will be used to highlight the main points. Historical, medical physicists have leveraged many areas of applied physics, engineering and biology to improve radiotherapy. Research on quality and safety is another area where physicists can have an impact. The key to further progress is to clearly define what constitutes quality and safety research for those interested in doing such research and the reviewers of that research. Learning Objectives: List several tools of quality and safety with references to peer-reviewed literature. Describe effects of mental workload on performance. Outline research in quality and safety indicators and technique analysis. Understand what quality and safety research needs to be going forward. Understand the links between cooperative group trials and quality and safety research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

An Adaptive Reference Scheme to Extend the Functional Range of Optical Backscatter Reflectometry in Extreme Environments

Optical frequency domain reflectometry (OFDR) measurements are performed by recording the interference pattern of light backscattered by density fluctuations or Bragg gratings along the length of an optical fiber. Changes in local temperature or strain in the fiber cause shifts in the backscattered light spectrum, which can be calibrated to the applied temperature or strain. Comparing the backscattered optical spectra from each reflection site with a reference (unstrained) spectrum allows for quantification of local spectral shifts. While mature OFDR-based technologies can provide high-precision spatially distributed measurements over kilometer lengths, the post-processing approaches used to recover spectral shifts from raw optical intensity data can limit the use of OFDR in harsh environments. This paper presents a novel approach to post-processing OFDR data which extends the usability of optical fibers exposed to harsh environments. This approach is the first to use the spectral shift quality, calculated for two OFDR measurements, to identify an appropriate reference scan from which the spectral shift can be determined. Here, three experimental data sets are used to test the algorithm: (1) an optical fiber heated to >950°C, (2) an aluminum-embedded optical fiber under strain from differential thermal expansion, and (3) an optical fiber exposed to a total neutron flux of 2×10 13 n/cm 2 /s over 40 hours in a nuclear test reactor. Results show that using a metric of quality to select an appropriate reference measurement extends the functional range of OFDR strain and temperature sensors. Furthermore, this algorithm can be applied to existing OFDR data.

47 OTHER INSTRUMENTATION↗

NASA NTRS1975

Fixed-range optimum trajectories for short-haul aircraft

An algorithm, based on the energy-state method, is derived for calculating optimum trajectories with a range constraint. The basis of the algorithm is the assumption that optimum trajectories consist of, at most, three segments: an increasing energy segment (climb); a constant energy segment (cruise); and a decreasing energy segment (descent). This assumption allows energy to be used as the independent variable in the increasing and decreasing energy segments, thereby eliminating the integration of a separate adjoint differential equation and simplifying the calculus of variations problem to one requiring only pointwise extremization of algebraic functions. The algorithm is used to compute minimum fuel, minimum time, and minimum direct-operating-cost trajectories, with range as a parameter, for an in-service CTOL aircraft and for an advanced STOL aircraft. For the CTOL aircraft and the minimum-fuel performance function, the optimum controls, consisting of air-speed and engine power setting, are continuous functions of the energy in both climb and descent as well as near the maximum or cruise energy. This is also true for the STOL aircraft except in the descent where at one energy level a nearly constant energy dive segment occurs, yielding a discontinuity in the airspeed at that energy. The reason for this segment appears to be the relatively high fuel flow at idle power of the engines used by this STOL aircraft. Use of a simplified trajectory which eliminates the dive increases the fuel consumption of the total descent trajectory by about 10 percent and the time to fly the descent by about 19 percent compared to the optimum.

Erzberger, H.↗

NASA NTRS1983

Robust penalty method for structural synthesis

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

Kamat, M. P.↗

DOE OSTI2021

MADLens, a python package for fast and differentiable non-Gaussian lensing simulations

Here, we present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as possible. A MADLens simulation with only particles produces convergence maps whose power agrees with theoretical lensing power spectra up to within the accuracy limits of HaloFit. This is made possible by a combination of a highly parallelizable particle-mesh algorithm, a sub-evolution scheme in the lensing projection, and a machine-learning inspired sharpening step. Further, MADLens is fully differentiable with respect to the initial conditions of the underlying particle-mesh simulations and a number of cosmological parameters. These properties allow MADLens to be used as a forward model in Bayesian inference algorithms that require optimization or derivative-aided sampling. Another use case for MADLens is the production of large, high resolution simulation sets as they are required for training novel deep-learning-based lensing analysis tools. We make the MADLens package publicly available under a Creative Commons License

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Machine Learning to Select Experiments Driven by Fundamental Science and Applications for Targeted Nuclear Data Improvement

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in 239 Pu nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to 239 Pu fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate 63 Cu and 239 Pu total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with Al 2 ⁢O 3 and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

Block-Iterative Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs

Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient smoother algorithms suitable for current and evolving GPU and multicore CPU systems is a significant challenge. We address this issue in the case of constant-coefficient stencils arising in the solution of elliptic partial differential equations on structured 3D uniform and adaptively refined block structured grids. Robust, highly parallel implementations of block Jacobi and chaotic block Gauss-Seidel algorithms with exact inversion of the blocks are developed using different parallelization techniques. Experimental results for NVIDIA Fermi/Kepler GPUs and AMD multicore systems are presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide the first rigorous analysis of the behavior of the multigrid algorithm in the presence of faults. Specifically, we prove estimates on the behavior of the Two Grid Method similar to the classical asymptotic results. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations, and it is of considerable importance to anticipate its behavior on an exascale machine. The analysis of resilience of algorithms is in its infancy, and the current work is perhaps the first to provide a mathematical model for faults and analyze the behavior of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

Mathematics↗

DOE OSTI2023

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗

DOE OSTI2014

Noise propagation in hybrid models of nonlinear systems: The Ginzburg–Landau equation

Every physical phenomenon can be described by multiple models with varying degrees of fidelity. The computational cost of higher fidelity models (e.g., molecular dynamics simulations) is invariably higher than that of their lower fidelity counterparts (e.g., a continuum model based on differential equations). While the former might not be suitable for large-scale simulations, the latter are not universally valid. Hybrid algorithms provide a compromise between the computational efficiency of a coarse-scale model and the representational accuracy of a fine-scale description. This is achieved by conducting a fine-scale computation in subdomains where it is absolutely required (e.g., due to a local breakdown of a continuum model) and coupling it with a coarse-scale computation in the rest of a computational domain. We analyze the effects of random fluctuations generated by the fine-scale component of a nonlinear hybrid on the hybrid's overall accuracy and stability. Two variants of the time-dependent Ginzburg–Landau equation (GLE) and their discrete representations provided by a nearest-neighbor Ising model serve as a computational testbed. Our analysis shows that coupling these descriptions in a one-dimensional simulation leads to erroneous results. Adding a random source term to the GLE provides accurate prediction of the mean behavior of the quantity of interest (magnetization). It also allows the two GLE variants to correctly capture the strength of the microscale fluctuations. Our work demonstrates the importance of fine-scale noise in hybrid simulations, and suggests the need for replacing an otherwise deterministic coarse-scale component of the hybrid with its stochastic counterpart.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

Mathematical algorithms to maximize performance in numerical weather prediction

Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized.

Foreman, A.↗