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All sources NASA NTRS DOE OSTI

DOE OSTI2016

A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute “dual-weighted” a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Ultrafast Error-bounded Lossy Compression for Scientific Datasets

Today's scientific high-performance computing applications and advanced instruments are producing vast volumes of data across a wide range of domains, which impose a serious burden on data transfer and storage. Error-bounded lossy compression has been developed and widely used in the scientific community because it not only can significantly reduce the data volumes but also can strictly control the data distortion based on the user-specified error bound. Existing lossy compressors, however, cannot offer ultrafast compression speed, which is highly demanded by numerous applications or use cases (such as in-memory compression and online instrument data compression). In this paper, we propose a novel ultrafast error-bounded lossy compressor that can obtain fairly high compression performance on both CPUs and GPUs and with reasonably high compression ratios. The key contributions are threefold. (1) We propose a generic error-bounded lossy compression framework---called SZx---that achieves ultrafast performance through its novel design comprising only lightweight operations such as bitwise and addition/subtraction operations, while still keeping a high compression ratio. (2) We implement SZx on both CPUs and GPUs and optimize the performance according to their architectures. (3) We perform a comprehensive evaluation with six real-world production-level scientific datasets on both CPUs and GPUs. Experiments show that SZx is 2~16x faster than the second-fastest existing error-bounded lossy compressor (either SZ or ZFP) on CPUs and GPUs, with respect to both compression and decompression.

Yu, Xiaodong↗

DOE OSTI2023

Quantification and prediction of error in MIMO tests

Dynamic testing of systems is most realistic of real-world conditions when multiple input and multiple output (MIMO) techniques are used. To replicate measured environmental conditions, a series of desired outputs (responses) on the system must be realized by inverting the frequency response functions (FRF) matrix for input estimation. System identification is dependent on the number of inputs and outputs, which affect the type of solutions. In input estimation, the auto spectra of the determined inputs are affected by both the auto spectra and cross spectra of the desired outputs. This research evaluates errors and investigates two sources in an experimental setting. The first significant error source is test-to-test variability in FRFs from system identification tests, quantified by magnitude variability from long-duration tests. The second significant error source is the realization of time histories from frequency domain inputs. The spectral content of the realized random process deviates from the desired content and is also quantified. The structure is a linear three-story frame fixed at the base; two inputs are provided uniaxially with the use of suspended electrodynamic shakers. The proposed model for error sources was found to be effective in predicting errors in a SISO (single-input single-output) and a square (2-input 2-output) MIMO test.

Yousef, Odey↗

DOE OSTI2019

Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors

Stitching interferometry is performed by collecting interferometric data from overlapped sub-apertures and stitching these data together to provide a full surface map. The propagation of the systematic error in the measured subset data is one of the main error sources in stitching interferometry for accurate reconstruction of the surface topography. In this work, we propose, using the redundancy of the captured subset data, two types of two-dimensional (2D) self-calibration stitching algorithms to overcome this issue by in situ estimating the repeatable high-order additive systematic errors, especially for the application of measuring X-ray mirrors. The first algorithm, called CS short for “Calibrate, and then Stitch”, calibrates the high-order terms of the reference by minimizing the de-tilted discrepancies of the overlapped subsets and then stitches the reference-subtracted subsets. The second algorithm, called SC short for “Stitch, and then Calibrate”, stitches a temporarily result and then calibrates the reference from the de-tilted discrepancies of the measured subsets and the temporarily stitched result. In the implementation of 2D scans in $x$- and y -directions, step randomization is introduced to generate nonuniformly spaced subsets which can diminish the periodic stitching errors commonly observed in evenly spaced subsets. The regularization on low-order terms enables a highly flexible option to add the curvature and twist acquired by another system. Both numerical simulations and experiments are carried out to verify the proposed method. All the results indicate that 2D high-order repeatable additive systematic errors can be retrieved from the 2D redundant overlapped data in stitching interferometry.

42 ENGINEERING↗

DOE OSTI2018

Modeling energy balance while correcting for measurement error via free knot splines

Measurements of energy balance components (energy intake, energy expenditure, changes in energy stores) are often plagued with measurement error. Doubly-labeled water can measure energy intake (EI) with negligible error, but is expensive and cumbersome. An alternative approach that is gaining popularity is to use the energy balance principle, by measuring energy expenditure (EE) and change in energy stores (ES) and then back-calculate EI. Gold standard methods for EE and ES exist and are known to give accurate measurements, albeit at a high cost. We propose a joint statistical model to assess the measurement error in cheaper, non-intrusive measures of EE and ES. We let the unknown true EE and ES for individuals be latent variables, and model them using a bivariate distribution. We try both a bivariate Normal as well as a Dirichlet Process Mixture Model, and compare the results via simulation. Our approach, is the first to account for the dependencies that exist in individuals’ daily EE and ES. We employ semiparametric regression with free knot splines for measurements with error, and linear components for error free covariates. We adopt a Bayesian approach to estimation and inference and use Reversible Jump Markov Chain Monte Carlo to generate draws from the posterior distribution. Based on the semiparameteric regression, we develop a calibration equation that adjusts a cheaper, less reliable estimate, closer to the true value. Along with this calibrated value, our method also gives credible intervals to assess uncertainty. A simulation study shows our calibration helps produce a more accurate estimate. Furthermore, our approach compares favorably in terms of prediction to other commonly used models.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Characterizing Dynamic Test Fixtures Through the Modal Projection Error

Across many industries and engineering disciplines, physical components and systems of components are designed and deployed into their environment of intended use. It is the desire of the design agency to be able to predict whether their component or system will survive its physical environment or if it will fail due to mechanical stresses. One method to determine if the component will survive the environment is to expose the component to a simulation of the environment in a laboratory. One difficulty in doing this is that the component may not have the same boundary condition in the laboratory as is in the field configuration. This paper presents a novel method of quantifying the error in the modal domain that occurs from the impedance difference between the laboratory test fixture and the next level of assembly in the field configuration. The error is calculated from the projection from one mode shape space to the other, and the error is in terms of each mode of the field configuration. This provides insight into the effectiveness of the test fixture with respect to the ability to recreate the mode shapes of the field configuration. A case study is presented to show that the error in the modal projection between two configurations is a lower limit for the error that can be achieved by a laboratory test.

42 ENGINEERING↗

DOE OSTI2020

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↗

DOE OSTI2020

A Study on Modeled Wind Speed Errors Using the U.S. Department of Energy Buoys

Pacific Northwest National Laboratory (PNNL) operates two AXYS WindSentinel lidar buoys for the U.S. Department of Energy’s Wind Energy Technologies Office. The purpose of these buoys is to collect hub-height winds and supporting meteorological and oceanographic information to facilitate the development of wind energy in the U.S. waters. The first deployment for one buoy was off the coast of Virginia from December 2014 to May 2016, and the first deployment for the other buoy was off the coast of New Jersey from November 2015 until February 2017. This report describes recent analysis of data collected during these first two deployments. Specifically, we compare hub-height wind speed estimates using Monin-Obukhov Similarity Theory (MOST) to the lidar measurements, and examine how those errors are affected by wind direction, atmospheric stability, wind-wave direction differences, and various measures of the wave-state. The comparisons are done using standard similarity functions based on MOST; including the Businger - Dyer, the Beljaars & Holtslag and the Vickers & Mahrt similarity functions. All models produce large errors over the range of atmospheric stabilities that were observed, with the largest errors occurring for stable flows. The Vickers & Mahrt function resulted in the largest overall bias and standard deviation, while Beljaars & Holtslag function gave the smallest bias and standard deviation due to its better performance under stable conditions. The models perform best under unstable conditions, but even in this regime there is a consistent overestimation of the wind speed of between roughly 0 to 1 ms -1 compared to the lidar measurements. We identify specific metocean conditions (i.e. stability and wind and wave directions) at each of the deployment locations that lead to large errors in MOST predictions. Finally, a coupled ocean-atmosphere model framework was investigated to simulate large errors in weather research forecasting (WRF).

17 WIND ENERGY↗

DOE OSTI2021

Error Analysis on Numerical Integration Algorithms in a Hypoelasticity Framework

This report determines local truncation errors for common stress integration algorithms used in explicit finite element codes with hypoelastic material models. The hypoelastic integration algorithms in question utilize an operator splitting procedure in a rotation neutralized configuration, where the stress response is determined from de- coupling the total deformation into rotational and strain dependent components. This document analyzes the error in evolving the stress given a one-step time increment Δt and compares the errors associated with both the rotational and strain components of the operator splitting method. A slight modification to a traditional algorithm is proposed and studied, where the rate of deformation is appropriately rotated from the midstep configuration at t n+1/2 to the end step configuration at t n+1 before the constitutive evaluation. The proposed modification either completely eliminates the error associated with the rotation rate or is of the same order of magnitude as the original algorithm for the three test cases considered in this report. These cases consist of an unaxial stretch with a constant true strain rate with a rigid body rotation, an uniaxial stretch with a constant engineering strain rate with a rigid body rotation, and a simple shear deformation. All three cases are compared to a closed form solution, and in almost every test case the alternative algorithm yields the most accurate one-step local truncation error.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Assessing Cognitive Impacts of Errors from Machine Learning and Deep Learning Models: Final Report

Due to their recent increases in performance, machine learning and deep learning models are being increasingly adopted across many domains for visual processing tasks. One such domain is international nuclear safeguards, which seeks to verify the peaceful use of commercial nuclear energy across the globe. Despite recent impressive performance results from machine learning and deep learning algorithms, there is always at least some small level of error. Given the significant consequences of international nuclear safeguards conclusions, we sought to characterize how incorrect responses from a machine or deep learning-assisted visual search task would cognitively impact users. We found that not only do some types of model errors have larger negative impacts on human performance than other errors, the scale of those impacts change depending on the accuracy of the model with which they are presented and they persist in scenarios of evenly distributed errors and single-error presentations. Further, we found that experiments conducted using a common visual search dataset from the psychology community has similar implications to a safeguards- relevant dataset of images containing hyperboloid cooling towers when the cooling tower images are presented to expert participants. While novice performance was considerably different (and worse) on the cooling tower task, we saw increased novice reliance on the most challenging cooling tower images compared to experts. These findings are relevant not just to the cognitive science community, but also for developers of machine and deep learning that will be implemented in multiple domains. For safeguards, this research provides key insights into how machine and deep learning projects should be implemented considering their special requirements that information not be missed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Systematic Errors Induced by Dipole Component Change in Quadrupole Beam-Based Alignment Measurements for Circular Accelerators

Beam-based alignment (BBA) for quadrupole magnets is now a well-established process for circular accelerators to steer beam orbit through the magnetic centers such that beam orbit is not disturbed when the gradients of quadrupoles are changed. At some facilities, the centers estimated from BBA techniques are also used as a proxy for steering beam through the centers of nearby nonlinear magnets to minimize degradation of nonlinear dynamics caused by off-centered orbit. The random errors associated with BBA are well known, but very little attention has been paid to the systematic error generated by a dipole component change, or equivalently a shift in the magnetic center, when the quadrupole strength is varied. The analytical formulas for this error and its amplification factor (potentially a few orders of magnitude) with respect to the magnetic center motion have been derived and confirmed with simulations. We address the significance of this error as well as the part that cannot be estimated from the beam-based measurement alone. Finally, the BBA measurements obtained at NSLS-II and their systematic errors on the order of hundreds of microns are discussed.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Earth-Centered, Earth-Fixed Inertial Navigation System & Error-State Kalman Filter Reference Manual

This is a self-contained reference document that derives the equations necessary to build a combined inertial navigation system and error-state Kalman filter. Coordinate transform, linear time invariant system, inertial sensing, and error-state Kalman filtering theory is built up from first principles. This theory is then leveraged to derive the system equations for two combined inertial navigation system and error-state Kalman filters: (1) a 15-state system modeling white-noise-integrating accelerometer and gyroscope biases, and (2) a 39-state system modeling static and first-order Gauss-Markov accelerometer and gyroscope biases, scale factor errors, and cross-axis sensitivity errors.

42 ENGINEERING↗

DOE OSTI2025

On the Error Covariance Correction Step of an ESKF Attitude Update

The attitude states of an error-state Kalman filter (ESKF) behave differently than most other states in the system due to their multiplicative (rather than additive) nature. One way in which they differ is an error covariance correction step after an ESKF error reset, which is not required for, for example, position and velocity states. This covariance correction step is not intuitive, and it has only been recently derived for coordinate transform matrices. The author of this memo, however, found the provided derivation in [1] confusing due to a lack of clarity surrounding the invoked reference frames, and clarity is required as there are at least 4 different ways to parameterize small-angle attitude errors in an ESKF. Furthermore, while reproducing the work, the author of this memo found a more straightforward derivation that provides additional insight into the correction step. This memo offers a derivation of the attitude error covariance correction step of an ESKF, which pays specific attention to the coordinate reference frames.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Error mitigation is an essential component of achieving a practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as other state-of-the-art methods, in mitigating observables produced from random quantum circuits and the Quantum Alternating Operator Ansatz (QAOA) applied to Max-Cut problems with various numbers of qubits, circuit depths and total numbers of shots. We find that the performance of different techniques depends strongly on shot budgets, with more powerful methods requiring more shots for optimal performance. For our largest considered shot budget (10 10 ), we find that UNITED gives the most accurate mitigation. Hence, our work represents a benchmarking of current error mitigation methods and provides a guide for the regimes when certain methods are most useful.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Error quantification of the Arrhenius blending rule for viscosity of hydrocarbon mixtures

Six hundred and seventy-five measurements of dynamic viscosity and density have been used to assess the prediction error of the Arrhenius blending rule for kinematic viscosity of hydrocarbon mixtures. Major trends within the data show that mixture complexity–binary to hundreds of components—and temperature are more important determinants of prediction error than differences in molecular size or hydrogen saturation between the components of the mixtures. Over the range evaluated, no correlation between prediction error and mole fractions was observed, suggesting the log of viscosity truly is linear in mole fraction, as indicated by the Arrhenius blending rule. Mixture complexity and temperature also impact molar volume and its prediction. However, a linear regression between the two model errors explains less than 20% of the observed variation, indicating that mixture viscosity and/or molar volume are not linear with respect to temperature and/or mixture complexity. Extensive discussion of the intermolecular forces and the geometric arrangement of molecules and vacancies in liquids, which ultimately determines its viscosity, is brought into context with the implicit approximations behind the Arrhenius blending rule. The complexity of this physics is not compatible with a simple algebraic correction to the model. However, sufficient data is now available to determine confidence intervals around the prediction of fuel viscosity based on its component mole fractions and viscosities. At -40°C, when all identified components are pure molecules the modeling error is 13.2% of the predicted (nominal) viscosity times the root mean square of the component mole fractions.

10 SYNTHETIC FUELS↗

DOE OSTI2016

A NEW METHOD TO QUANTIFY AND REDUCE THE NET PROJECTION ERROR IN WHOLE-SOLAR-ACTIVE-REGION PARAMETERS MEASURED FROM VECTOR MAGNETOGRAMS

Projection errors limit the use of vector magnetograms of active regions (ARs) far from the disk center. In this Letter, for ARs observed up to 60° from the disk center, we demonstrate a method for measuring and reducing the projection error in the magnitude of any whole-AR parameter that is derived from a vector magnetogram that has been deprojected to the disk center. The method assumes that the center-to-limb curve of the average of the parameter’s absolute values, measured from the disk passage of a large number of ARs and normalized to each AR’s absolute value of the parameter at central meridian, gives the average fractional projection error at each radial distance from the disk center. To demonstrate the method, we use a large set of large-flux ARs and apply the method to a whole-AR parameter that is among the simplest to measure: whole-AR magnetic flux. We measure 30,845 SDO /Helioseismic and Magnetic Imager vector magnetograms covering the disk passage of 272 large-flux ARs, each having whole-AR flux >10{sup 22} Mx. We obtain the center-to-limb radial-distance run of the average projection error in measured whole-AR flux from a Chebyshev fit to the radial-distance plot of the 30,845 normalized measured values. The average projection error in the measured whole-AR flux of an AR at a given radial distance is removed by multiplying the measured flux by the correction factor given by the fit. The correction is important for both the study of the evolution of ARs and for improving the accuracy of forecasts of an AR’s major flare/coronal mass ejection productivity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

This study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Second, using a newly developed proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors< ~2°, than those from the three empirical models with averaged errors >~5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. This study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.

58 GEOSCIENCES↗

NASA NTRS1972

A Monte Carlo error analysis program for near-Mars, finite-burn, orbital transfer maneuvers

A computer program was developed which performs an error analysis of a minimum-fuel, finite-thrust, transfer maneuver between two Keplerian orbits in the vicinity of Mars. The method of analysis is the Monte Carlo approach where each off-nominal initial orbit is targeted to the desired final orbit. The errors in the initial orbit are described by two covariance matrices of state deviations and tracking errors. The function of the program is to relate these errors to the resulting errors in the final orbit. The equations of motion for the transfer trajectory are those of a spacecraft maneuvering with constant thrust and mass-flow rate in the neighborhood of a single body. The thrust vector is allowed to rotate in a plane with a constant pitch rate. The transfer trajectory is characterized by six control parameters and the final orbit is defined, or partially defined, by the desired target parameters. The program is applicable to the deboost maneuver (hyperbola to ellipse), orbital trim maneuver (ellipse to ellipse), fly-by maneuver (hyperbola to hyperbola), escape maneuvers (ellipse to hyperbola), and deorbit maneuver.

Green, R. N.↗