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At least 19 records

Quantifying the impact of material-model error on macroscale quantities-of-interest using multiscale a posteriori error-estimation techniques

An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximate weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. Lastly, an adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.

36 MATERIALS SCIENCE↗

CAUSES: On the Role of Surface Energy Budget Errors to the Warm Surface Air Temperature Error Over the Central United States

Many weather forecasting and climate models simulate a warm surface air temperature (T2m) bias over mid-latitude continents during the summertime, especially over the Great Plains. We present here one of a series of papers from a multi-model intercomparison project (CAUSES: Cloud Above the United States and Errors at the Surface), which aims to evaluate the role of cloud, radiation, and precipitation biases in contributing to T2m bias using a short-term hindcast approach with observations mainly from the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site during the period of April to August 2011. The present study examines the contribution of surface energy budget errors to the bias. All participating models simulate higher net shortwave and longwave radiative fluxes at the surface but there is no consistency on signs of biases in latent and sensible heat fluxes over the Central U.S. and ARM SGP. Nevertheless, biases in net shortwave and downward longwave fluxes, as well as surface evaporative fraction (EF) are the main contributors to T2m bias. Radiation biases are largely affected by cloud simulations, while EF is affected by soil moisture modulated by seasonal accumulated precipitation and evaporation. An approximate equation is derived to further quantify the magnitudes of radiation and EF contributions to T2m bias. Our analysis suggests that radiation errors are always an important source of T2m error for long-term climate runs with EF errors either of equal or lesser importance. However, for the short-term hindcasts, EF errors are more important provided a model has a substantial EF bias.

Ma, H. -Y.↗

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

Here, this work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Finally, numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.

97 MATHEMATICS AND COMPUTING↗

ASSESSMENT OF SYSTEMATIC CHROMATIC ERRORS THAT IMPACT SUB-1% PHOTOMETRIC PRECISION IN LARGE-AREA SKY SURVEYS

Meeting the science goals for many current and future ground-based optical large-area sky surveys requires that the calibrated broadband photometry is both stable in time and uniform over the sky to 1% precision or better. Past and current surveys have achieved photometric precision of 1%–2% by calibrating the survey’s stellar photometry with repeated measurements of a large number of stars observed in multiple epochs. The calibration techniques employed by these surveys only consider the relative frame-by-frame photometric zeropoint offset and the focal plane position-dependent illumination corrections, which are independent of the source color. However, variations in the wavelength dependence of the atmospheric transmission and the instrumental throughput induce source color-dependent systematic errors. These systematic errors must also be considered to achieve the most precise photometric measurements. In this paper, we examine such systematic chromatic errors (SCEs) using photometry from the Dark Energy Survey (DES) as an example. We first define a natural magnitude system for DES and calculate the systematic errors on stellar magnitudes when the atmospheric transmission and instrumental throughput deviate from the natural system. We conclude that the SCEs caused by the change of airmass in each exposure, the change of the precipitable water vapor and aerosol in the atmosphere over time, and the non-uniformity of instrumental throughput over the focal plane can be up to 2% in some bandpasses. We then compare the calculated SCEs with the observed DES data. For the test sample data, we correct these errors using measurements of the atmospheric transmission and instrumental throughput from auxiliary calibration systems. The residual after correction is less than 0.3%. Moreover, we calculate such SCEs for Type Ia supernovae and elliptical galaxies and find that the chromatic errors for non-stellar objects are redshift-dependent and can be larger than those for stars at certain redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

Effects of machine learning errors on human decision-making: manipulations of model accuracy, error types, and error importance

Abstract This study addressed the cognitive impacts of providing correct and incorrect machine learning (ML) outputs in support of an object detection task. The study consisted of five experiments that manipulated the accuracy and importance of mock ML outputs. In each of the experiments, participants were given the T and L task with T-shaped targets and L-shaped distractors. They were tasked with categorizing each image as target present or target absent. In Experiment 1, they performed this task without the aid of ML outputs. In Experiments 2–5, they were shown images with bounding boxes, representing the output of an ML model. The outputs could be correct (hits and correct rejections), or they could be erroneous (false alarms and misses). Experiment 2 manipulated the overall accuracy of these mock ML outputs. Experiment 3 manipulated the proportion of different types of errors. Experiments 4 and 5 manipulated the importance of specific types of stimuli or model errors, as well as the framing of the task in terms of human or model performance. These experiments showed that model misses were consistently harder for participants to detect than model false alarms. In general, as the model’s performance increased, human performance increased as well, but in many cases the participants were more likely to overlook model errors when the model had high accuracy overall. Warning participants to be on the lookout for specific types of model errors had very little impact on their performance. Overall, our results emphasize the importance of considering human cognition when determining what level of model performance and types of model errors are acceptable for a given task.

97 MATHEMATICS AND COMPUTING↗

Analyzing the errors of DFT approximations for compressed water systems

We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm{sup 3} where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE{sub h} ≃ 15 meV/monomer for the liquid and the clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the validity of the basis set superposition error and complete basis set limit extrapolations for the binding energy of the formic acid dimer

We report the variation of the binding energy of the Formic Acid Dimer with the size of the basis set at the Coupled Cluster with iterative Singles, Doubles and perturbatively connected Triple replacements [CCSD(T)] level of theory, estimate the Complete Basis Set (CBS) limit, and examine the validity of the Basis Set Superposition Error (BSSE)-correction for this quantity that was previously challenged by Kalescky, Kraka, and Cremer (KKC) [J. Chem. Phys. 140, 084315 (2014)]. Our results indicate that the BSSE correction, including terms that account for the substantial geometry change of the monomers due to the formation of two strong hydrogen bonds in the dimer, is indeed valid for obtaining accurate estimates for the binding energy of this system as it exhibits the expected decrease with increasing basis set size. We attribute the discrepancy between our current results and those of KKC to their use of a valence basis set in conjunction with the correlation of all electrons (i.e., including the 1s of C and O). We further show that the use of a core-valence set in conjunction with all electron correlation converges faster to the CBS limit as the BSSE correction is less than half than the valence electron/valence basis set case. The uncorrected and BSSE-corrected binding energies were found to produce the same (within 0.1 kcal/mol) CBS limits. We obtain CCSD(T)/CBS best estimates for D{sub e} = − 16.1 ± 0.1 kcal/mol and for D{sub 0} = − 14.3 ± 0.1 kcal/mol, the later in excellent agreement with the experimental value of −14.22 ± 0.12 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.

Modelling↗

Diagnosing Model Errors in Simulation of Solar Radiation on Inclined Surfaces

Transposition models have been widely used in the solar energy industry to simulate solar radiation on inclined PV panels. Following numerous studies comparing the performance of transposition models, this paper aims to understand the quantitative uncertainty in the state-of-the-art transposition models and the sources leading to the uncertainty. Our results show significant differences between two highly used isotropic transposition models with one substantially underestimating the diffuse plane-of-array (POA) irradiances when diffuse radiation is perfectly isotropic. In the empirical transposition models, the selection of empirical coefficients and land surface albedo can both result in uncertainty in the output. This study can be used as a guide for future development of physics-based transposition models.

14 SOLAR ENERGY↗

Measuring uncertainty in dose delivered to the cochlea due to setup error during external beam treatment of patients with cancer of the head and neck

Purpose: To use Cone Beam CT scans obtained just prior to treatments of head and neck cancer patients to measure the setup error and cumulative dose uncertainty of the cochlea. Methods: Data from 10 head and neck patients with 10 planning CTs and 52 Cone Beam CTs taken at time of treatment were used in this study. Patients were treated with conventional fractionation using an IMRT dose painting technique, most with 33 fractions. Weekly radiographic imaging was used to correct the patient setup. The authors used rigid registration of the planning CT and Cone Beam CT scans to find the translational and rotational setup errors, and the spatial setup errors of the cochlea. The planning CT was rotated and translated such that the cochlea positions match those seen in the cone beam scans, cochlea doses were recalculated and fractional doses accumulated. Uncertainties in the positions and cumulative doses of the cochlea were calculated with and without setup adjustments from radiographic imaging. Results: The mean setup error of the cochlea was 0.04 ± 0.33 or 0.06 ± 0.43 cm for RL, 0.09 ± 0.27 or 0.07 ± 0.48 cm for AP, and 0.00 ± 0.21 or −0.24 ± 0.45 cm for SI with and without radiographic imaging, respectively. Setup with radiographic imaging reduced the standard deviation of the setup error by roughly 1–2 mm. The uncertainty of the cochlea dose depends on the treatment plan and the relative positions of the cochlea and target volumes. Combining results for the left and right cochlea, the authors found the accumulated uncertainty of the cochlea dose per fraction was 4.82 (0.39–16.8) cGy, or 10.1 (0.8–32.4) cGy, with and without radiographic imaging, respectively; the percentage uncertainties relative to the planned doses were 4.32% (0.28%–9.06%) and 10.2% (0.7%–63.6%), respectively. Conclusions: Patient setup error introduces uncertainty in the position of the cochlea during radiation treatment. With the assistance of radiographic imaging during setup, the standard deviation of setup error reduced by 31%, 42%, and 54% in RL, AP, and SI direction, respectively, and consequently, the uncertainty of the mean dose to cochlea reduced more than 50%. The authors estimate that the effects of these uncertainties on the probability of hearing loss for an individual patient could be as large as 10%.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Fractional charge and spin errors in self-consistent Green’s function theory

We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

PRESAGE: Protecting Structured Address Generation against Soft Errors

Modern computer scaling trends in pursuit of larger component counts and power efficiency have, unfortunately, lead to less reliable hardware and consequently soft errors escaping into application data ("silent data corruptions"). Techniques to enhance system resilience hinge on the availability of efficient error detectors that have high detection rates, low false positive rates, and lower computational overhead. Unfortunately, efficient detectors to detect faults during address generation (to index large arrays) have not been widely researched. We present a novel lightweight compiler-driven technique called PRESAGE for detecting bit-flips affecting structured address computations. A key insight underlying PRESAGE is that any address computation scheme that flows an already incurred error is better than a scheme that corrupts one particular array access but otherwise (falsely) appears to compute perfectly. Enabling the flow of errors allows one to situate detectors at loop exit points, and helps turn silent corruptions into easily detectable error situations. Our experiments using PolyBench benchmark suite indicate that PRESAGE-based error detectors have a high error-detection rate while incurring low overheads.

Sharma, Vishal C.↗

Characterizing NWP Model Errors Using Doppler-Lidar Measurements of Recurrent Regional Diurnal Flows: Marine-Air Intrusions into the Columbia-River Basin

Ground-based Doppler-lidar instrumentation provides atmospheric wind data at dramatically improved accuracies and spatial/temporal resolutions. These capabilities have provided new insights into atmospheric flow phenomena, but they also should have a strong role in NWP model improvement. Insight into the nature of model errors can be gained by studying recurrent atmospheric flows, here a regional summertime diurnal sea breeze and subsequent marine-air intrusion into the arid interior of Oregon-Washington, where these winds are an important windenergy resource. These marine intrusions were sampled by three scanning Doppler lidars in the Columbia-River Basin as part of the Second Wind Forecast Improvement Project (WFIP2), using data from summer 2016. Lidar time-height cross sections of wind speed identified eight days when the diurnal-flow cycle, (peak wind speeds at midnight, afternoon minima) was obvious and strong. Eight-day composite time-height cross sections of lidar wind speeds are used to validate those generated by the operational NCEP-HRRR model. HRRR simulated the diurnal wind cycle, but produced errors in the timing of onset and significant errors due to a premature nighttime demise of the intrusion flow, producing low-bias errors of 6 m s-1 . Day-to-day and in the composite, whenever a marine intrusion occurred, HRRR made these same errors. The errors occurred under a range of gradient wind conditions indicating that they resulted from the misrepresentation of physical processes within a limited region around the measurement locations. Because of their generation within a limited geographical area, field-measurement programs can be designed to find and address the sources of these NWP errors.

Banta, Robert M.↗

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model

Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. Here, we investigate the impact of model structural error on calibration and prediction of a real-world groundwater flow model, using a Bayesian method with a data-driven error model to explicitly account for model structural error. The error-explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error-explicit Bayesian method gives signficantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error-explicit Bayesian approach provides a solution to real-world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.

54 ENVIRONMENTAL SCIENCES↗

Sources of errors in the simulation of south Asian summer monsoon in the CMIP5 GCMs

Accurate simulation of the South Asian summer monsoon (SAM) is still an unresolved challenge. There has not been a benchmark effort to decipher the origin of undesired yet virtually invariable unsuccessfulness of general circulation models (GCMs) over this region. This study analyzes a large ensemble of CMIP5 GCMs to show that most of the simulation errors in the precipitation distribution and their driving mechanisms are systematic and of similar nature across the GCMs, with biases in meridional differential heating playing a critical role in determining the timing of monsoon onset over land, the magnitude of seasonal precipitation distribution and the trajectories of monsoon depressions. Errors in the pre-monsoon heat low over the lower latitudes and atmospheric latent heating over the slopes of Himalayas and Karakoram Range induce significant errors in the atmospheric circulations and meridional differential heating. Lack of timely precipitation further exacerbates such errors by limiting local moisture recycling and latent heating aloft from convection. Most of the summer monsoon errors and their sources are reproducible in the land–atmosphere configuration of a GCM when it is configured at horizontal grid spacing comparable to the CMIP5 GCMs. While an increase in resolution overcomes many modeling challenges, coarse resolution is not necessarily the primary driver in the exhibition of errors over South Asia. These results highlight the importance of previously less well known pre-monsoon mechanisms that critically influence the strength of SAM in the GCMs and highlight the importance of land–atmosphere interactions in the development and maintenance of SAM.

CMIP5↗

Correlated charge noise and relaxation errors in superconducting qubits

In This report, the central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits (“qubits”) are susceptible to two types of error, corresponding to flips of the qubit state about the X- and Z-directions. While the Heisenberg Uncertainty Principle precludes simultaneous monitoring of X- and Z-flips on a single qubit, it is possible to encode quantum information in large arrays of entangled qubits that enable accurate monitoring of all errors in the system, provided the error rate is low. Another crucial requirement is that errors cannot be correlated. Here, we characterize a superconducting multiqubit circuit and find that charge fluctuations are highly correlated on a length scale over 600 µm; moreover, discrete charge jumps are accompanied by a strong transient suppression of qubit energy relaxation time across the millimeter-scale chip. The resulting correlated errors are explained in terms of the charging event and phonon-mediated quasiparticle poisoning associated with absorption of gamma rays and cosmic-ray muons in the qubit substrate. Robust quantum error correction will require the development of mitigation strategies to protect multiqubit arrays from correlated errors due to particle impacts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An error reduction algorithm to improve lidar turbulence estimates for wind energy

Abstract. Remote-sensing devices such as lidars are currently being investigated as alternatives to cup anemometers on meteorological towers for the measurement of wind speed and direction. Although lidars can measure mean wind speeds at heights spanning an entire turbine rotor disk and can be easily moved from one location to another, they measure different values of turbulence than an instrument on a tower. Current methods for improving lidar turbulence estimates include the use of analytical turbulence models and expensive scanning lidars. While these methods provide accurate results in a research setting, they cannot be easily applied to smaller, vertically profiling lidars in locations where high-resolution sonic anemometer data are not available. Thus, there is clearly a need for a turbulence error reduction model that is simpler and more easily applicable to lidars that are used in the wind energy industry. In this work, a new turbulence error reduction algorithm for lidars is described. The Lidar Turbulence Error Reduction Algorithm, L-TERRA, can be applied using only data from a stand-alone vertically profiling lidar and requires minimal training with meteorological tower data. The basis of L-TERRA is a series of physics-based corrections that are applied to the lidar data to mitigate errors from instrument noise, volume averaging, and variance contamination. These corrections are applied in conjunction with a trained machine-learning model to improve turbulence estimates from a vertically profiling WINDCUBE v2 lidar. The lessons learned from creating the L-TERRA model for a WINDCUBE v2 lidar can also be applied to other lidar devices. L-TERRA was tested on data from two sites in the Southern Plains region of the United States. The physics-based corrections in L-TERRA brought regression line slopes much closer to 1 at both sites and significantly reduced the sensitivity of lidar turbulence errors to atmospheric stability. The accuracy of machine-learning methods in L-TERRA was highly dependent on the input variables and training dataset used, suggesting that machine learning may not be the best technique for reducing lidar turbulence intensity (TI) error. Future work will include the use of a lidar simulator to better understand how different factors affect lidar turbulence error and to determine how these errors can be reduced using information from a stand-alone lidar.

17 WIND ENERGY↗