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At least 379 records · Page 21

Identifying Nuclear Data Correlated Through Predicting Bias in Integral Experiments via Applying Principal Component Analysis to Random Forest

ABSTRACT Nuclear data (ND) are the input data for neutron‐transport simulations to answer questions related to nuclear technologies. Subsets of ND, here > 20,000 data points, are validated with respect to thousands of criticality experiments that represent various applications on a small scale. The aim of validation with these experiments is to find errors in ND or methods. The key challenge here is that several hundreds of ND are used to simulate one integral value. Hence, one cannot clearly identify what ND are leading to bias in criticality measurements. In fact, a mistake in one nuclear‐data observable can be compensated with an error in another, and the predicted criticality value would still be predicted in agreement with experimental data. Random forest (RF) was previously employed to predict bias in criticality measurements using sensitivities of simulated criticality experiments to ND. The SHapley Additive exPlanations (SHAP) metric was then applied to attribute the importance of each ND experiment and observable to bias prediction. This, however, did not highlight what ND were jointly related to predicting bias. This is important as it could inform us about where compensating errors in ND could hide. We tackle this shortcoming here by first decomposing the ND sensitivities to integral‐experiment simulations into principal components. Then we use principal component projections to predict bias via the RF and SHAP. The SHAP values and principal components are employed to reconstruct detailed SHAP values for each ND observable. We demonstrate that these extended SHAP bias predictions are more robust, less noisy, and more efficient. In addition, we show that this approach accounts for covariance in ND sensitivities and automates the identification of where compensating errors could hide in ND.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Airborne Radar for sUAS Sense and Avoid

A primary challenge for the safe integration of small UAS operations into the National Airspace System (NAS) is traffic deconfliction, both from manned and unmanned aircraft. The UAS Traffic Management (UTM) project being conducted at the National Aeronautics and Space Administration (NASA) considers a layered approach to separation provision, ranging from segregation of operations through airspace volumes (geofences) to autonomous sense and avoid (SAA) technologies for higher risk, densely occupied airspace. Cooperative SAA systems, such as Automatic Dependent Surveillance-Broadcast (ADS-B) and/or vehicle-to-vehicle communication systems provide significant additional risk mitigation but they fail to adequately mitigate collision risks for non-cooperative (non-transponder equipped) airborne aircraft. The RAAVIN (Radar on Autonomous Aircraft to Verify ICAROUS Navigation) flight test being conducted by NASA and the Mid-Atlantic Aviation Partnership (MAAP) was designed to investigate the applicability and performance of a prototype, commercially available sUAS radar to detect and track non-cooperative airborne traffic, both manned and unmanned. The radar selected for this research was a Frequency Modulated Continuous Wave (FMCW) radar with 120 degree azimuth and 80 degree elevation field of view operating at 24.55GHz center frequency with a 200 MHz bandwidth. The radar transmits 2 watts of power thru a Metamaterial Electronically Scanning Array antenna in horizontal polarization. When the radar is transmitting, personnel must be at least 1 meter away from the active array to limit nonionizing radiation exposure. The radar physical dimensions are 18.7cm by 12.1cm by 4.1cm and it weighs less than 820 grams making it well suited for installation on small UASs. The onboard, SAA capability, known as ICAROUS, (Independent Configurable Architecture for Reliable Operations of Unmanned Systems), developed by NASA to support sUAS operations, will provide autonomous guidance using the traffic radar tracks from the onboard radar. The RAAVIN set of studies will be conducted in three phases. The first phase included outdoor, ground-based radar evaluations performed at the Virginia Tech’s Kentland Farm testing range in Blacksburg, VA. The test was designed to measure how well the radar could detect and track a small UAS flying in the radar’s field of view. The radar was used to monitor 5 test flights consisting of outbound, inbound and crossing routes at different ranges and altitudes. The UAS flown during the ground test was the Inspire 2, a quad copter weighing less than 4250 grams (10 pounds) at maximum payload. The radar was set up to scan and track targets over its full azimuthal field of view from 0 to 40 degrees in elevation. The radar was configured to eliminate tracks generated from any targets located beyond 2000 meters from the radar and moving at velocities under 1.45 meters per second. For subsequent phases of the study the radar will be integrated with a sUAS platform to evaluate its performance in flight for SAA applications ranging from sUAS to manned GA aircraft detections and tracking. Preliminary data analysis from the first outdoor ground tests showed the radar performed well at tracking the vehicle as it flew outbound and repeatedly maintained a track out to 1000 meters (maximum 1387 meters) until the vehicle slowed to a stop to reverse direction to fly inbound. As the Inspire flew inbound tracks from beyond 800 meters, a reacquisition time delay was consistently observed between when the Inspire exceeds a speed of 1.45 meters per second and when the radar indicated an inbound target was present and maintained its track. The time delay varied between 6 seconds to over 37 seconds for the inbound flights examined, and typically resulted in about a 200 meter closure distance before the Inspire track was maintained. The radar performed well at both acquiring and tracking the vehicle as it flew crossing routes out past 400 meters across the azimuthal field of view. The radar and ICAROUS software will be integrated and flown on a BFD-1400-SE8-E UAS during the next phase of the RAAVIN project. The main goal at the conclusion of this effort is to determine if this radar technology can reliably support minimum requirements for SAA applications of sUAS. In particular, the study will measure the range of vehicle detections, lateral and vertical angular errors, false and missed/late detections, and estimated distance at closest point of approach after an avoidance maneuver is executed. This last metric is directly impacted by sensor performance and indicates its suitability for the task.

Szatkowski, George N.↗

Verification of Viscous Goal-Based Anisotropic Mesh Adaptation

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics. A key ingredient for the broader acceptance of unstructured mesh adaptation is the verification of these implementations. Anisotropic metric construction methods are evaluated with analytically defined primal fields and the corresponding entropy variables as adjoint fields. This allows the comparison of different metric formulations and different implementations of the same formulation without the complications of a flow and adjoint solution method. The convergence of the output associated with the entropy variable adjoint is studied for mesh adaptation to these fields and a manufactured solution. Mesh adapted drag output is studied for two simple wings in compressible laminar flow to show fine-mesh convergence of multiple metric construction methods to less than a single drag count. The documentation of these verification exercises helps to prepare these goal-based methods for routine use in more complex simulations for production workflows.

mesh adaptation↗

Validation of Satellite-Based Precipitation Products from TRMM to GPM

The global precipitation measurement mission (GPM) has been in operation for sevenyears and continues to provide a vast quantity of global precipitation data at finer temporospatialresolutions with improved accuracy and coverage. GPM’s signature algorithm, the integratedmultisatellite retrievals for GPM (IMERG) is a next-generation of precipitation product expectedfor wide variety of research and operational applications. This study evaluates the latest version(V06B) of IMERG and its predecessor, the tropical rainfall measuring mission (TRMM) multisatelliteprecipitation (TMPA) 3B42 (V7) using ground-based and gauge-corrected multiradar multisensorsystem (MRMS) precipitation products over the conterminous United States (CONUS). The spatialdistributions of all products are analyzed. The error characteristics are further examined for 3B42 andIMERG in winter and summer by an error decomposition approach, which partitions total bias intohit bias, biases due to missed precipitation and false precipitation. The volumetric and categoricalstatistical metrics are used to quantitatively evaluate the performance of the two satellite-basedproducts. All products show a similar precipitation climatology with some regional differences.The two satellite-based products perform better in the eastern CONUS than in the mountainousWestern CONUS. The evaluation demonstrates the clear improvement in IMERG precipitationproduct in comparison with its predecessor 3B42, especially in reducing missed precipitation inwinter and summer, and hit bias in winter, resulting in better performance in capturing lighter andheavier precipitation.

Jianxin Wang↗

Node synchronization of viterbi decoders using state metrics

The concept of node synchronization using state metrics is investigated. The branch metrics are integrated over a fixed time interval and the results are compared to the detection threshold. If the threshold is exceeded, the out-of-sync hypothesis is accepted; otherwise, the in-sync hypothesis is accepted. It is shown that the detection threshold can be chosen independent of any particular convolutional code with fixed code rate and constant length if the code has reasonably good bit error rate performance. Three node synchronization schemes are compared: (1) a scheme using the syndrome; (2) a scheme using the frame-sync patterns; and (3) a scheme using the state metrics. At very low signal to noise ratios (SNR), scheme 2 can be faster than scheme 1. For Voyager's rate 1/2 and constraint length 7 convolutional code, this happens for SNRs of less than 0.7 dB. This result is obtained by assuming that the code frame-sync pattern has good aperiodic autocorrelation properties. For a fixed false alarm probability, the sequential detection scheme based on the syndrome is faster than scheme 3 with fixed integration time. A sequential detection technique is needed to improve the speed of scheme 3.

Cheng, U.↗

Aeroservoelastic Stability of a Floating Wind Turbine

The problem of negative damping undermines the aeroservoelastic stability of floating offshore wind turbines. The negative damping problem is most prevalent around rated wind speed, where the sensitivity of thrust to wind speed is the largest. This paper investigates the implementation of peak shaving, a controller feature that limits the rated thrust by pitching the blades before rated wind speed is reached. Two controller designs are investigated: a de-tuned controller and a nacelle-feedback controller. A time-domain metric is defined, inspired by Lyapunov theory, in order to compute and assess the stability of floating offshore wind turbines. The model of the International Energy Agency 15-MW reference wind turbine mounted on the University of Maine VolturnUS-S floater is simulated in HAWC2 with the National Renewable Energy Laboratory reference open-source controller. Peak shaving is applied to the two controller designs and stability is assessed. According to the chosen metric, peak shaving does not improve the stability of the system. This is due to the trade-off between loads and error tracking: although the loads and displacements in the fore-aft direction of the turbine are reduced, the rotor-speed tracking is poorer, which increases the shaft torsion fatigue load.

17 WIND ENERGY↗

Deep neural network uncertainty quantification for LArTPC reconstruction

We evaluate uncertainty quantification (UQ) methods for deep learning applied to liquid argon time projection chamber (LArTPC) physics analysis tasks. As deep learning applications enter widespread usage among physics data analysis, neural networks with reliable estimates of prediction uncertainty and robust performance against overconfidence and out-of-distribution (OOD) samples are critical for their full deployment in analyzing experimental data. While numerous UQ methods have been tested on simple datasets, performance evaluations for more complex tasks and datasets are scarce. Here we assess the application of selected deep learning UQ methods on the task of particle classification using the PiLArNet monte carlo 3D LArTPC point cloud dataset. We observe that UQ methods not only allow for better rejection of prediction mistakes and OOD detection, but also generally achieve higher overall accuracy across different task settings. We assess the precision of uncertainty quantification using different evaluation metrics, such as distributional separation of prediction entropy across correctly and incorrectly identified samples, receiver operating characteristic curves (ROCs), and expected calibration error from observed empirical accuracy. We conclude that ensembling methods can obtain well calibrated classification probabilities and generally perform better than other existing methods in deep learning UQ literature.

47 OTHER INSTRUMENTATION↗

MIC-DP: A Scalable Correlation-Aware Differential Privacy Framework for High-Dimensional Data

Conventional differential privacy (DP) assumes record independence, limiting effectiveness on real-world datasets with temporal, spatial, or structural correlations. These dependencies undermine privacy guarantees and degrade utility in domains like healthcare, IoT, and smart city analytics. We propose Maximum Information Correlated Differential Privacy (MIC-DP), a novel framework that dynamically calibrates noise based on statistical dependencies. MIC-DP uses the Maximum Information Coefficient (MIC) to capture both linear and nonlinear correlations without explicit modeling, enabling adaptive sensitivity adjustment and improved privacy–utility trade-offs. Evaluations on healthcare (MIMIC), demographic (ACI), and synthetic datasets show that MIC-DP reduces mean absolute error (MAE) by up to 5.2% under strict privacy budgets (ϵ≤1), with aggregate utility improvements reaching 18% across datasets and evaluation metrics. MIC-DP provides formal (ϵ,δ)-privacy guarantees, scales efficiently with feature count, and supports deployment in moderate-scale, privacy-sensitive applications. Its tunable performance and runtime efficiency make MIC-DP suitable for privacy-sensitive applications where low-latency analytics and strong privacy guarantees must coexist. These results demonstrate MIC-DP’s effectiveness as a correlation-aware solution for practical DP.

Yang, Wenjun [Univ. of Washington, Tacoma, WA (Uni↗

Towards robust laser beam propagation in atmospheric turbulence

High-fidelity optical propagation through the atmosphere is essential for free-space optical technologies, including laser-based remote sensing and optical communication. However, atmospheric turbulence severely distorts beams and compromises system performance. In this work, we employ hypergeometric-Gaussian (HyGG) vortex beams as probes to characterize and mitigate atmospheric turbulence. Using over 250,000 experimental and simulated frames, we show that refining the power spectrum density (PSD) can reduce numerical prediction errors by up to 79.8%. Concurrently, experimental observations supported by numerical simulations demonstrate that HyGG beams exhibit superior turbulence resilience across multiple metrics compared to conventional Gaussian beams, particularly in their ability to withstand over 5 times stronger turbulence while maintaining similar intensity fluctuations. These dual investigations, on both turbulence mitigation and robust beam solutions, converge to form a unified strategy for enhancing free-space optical system performance. Collectively, our findings provide new insights into light–turbulence interactions and highlight the practical utility of vortex beams under atmospheric conditions.

Zhang, Boyu↗

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO 2 , temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

54 ENVIRONMENTAL SCIENCES↗

Performance of wind assessment datasets in United States coastal areas

The atmospheric dynamics that occur near the intersection of land and water offer exciting and challenging opportunities for wind energy deployment in coastal locations. New models and tools are continually being developed in support of wind resource assessment, and three recent products are explored in this work for their performance in representing characteristics of the wind resource at coastal locations: the Global Wind Atlas 3 (GWA3), the 2023 National Offshore Wind dataset (NOW-23), and the wind climate simulations that are a component of the Wind Integration National Dataset (WIND) Toolkit Long-Term Ensemble Dataset (WTK-LED Climate). These relatively new products are freely available and user-friendly so that anyone – from a utility-scale developer to a resident or business owner – can evaluate the potential for wind energy generation at their location of interest. The validations in this work provide guidance on the accuracy of wind resource assessments for coastal customers interested in installing small or midsize wind turbines (≤ 1 MW in capacity) to support energy needs at the residential, business, or community scale, such as the island and remotely located participants of the U.S. Department of Energy's Energy Transitions Initiative Partnership Project. At 23 coastal locations across the United States, dataset performance varies according to different evaluation metrics. All three recent datasets tend to overestimate the observed coastal wind resource. GWA3 produces the smallest annual average wind speed relative errors, whereas WTK-LED Climate is in best agreement in terms of representing diurnal wind speed cycles. NOW-23 is the highest performing of the datasets for representing seasonal and interannual trends in the coastal wind resource. While GWA3 and WTK-LED Climate are relatively insensitive to the dataset output heights selected for wind resource assessment at small and midsize wind turbine hub heights (20–60 m), significant variation in the NOW-23 representation of wind shear across the wind profile in the lowest 100 m of the atmosphere leads to notable differences in wind speed estimates according to the dataset output heights selected for evaluation. GWA3 exhibits challenges in the representation of observed wind speed diurnal cycles at small and midsize turbine hub heights, likely due to the dataset's consistent treatment of hourly wind speed trends regardless of altitude.

17 WIND ENERGY↗

Inputs and Outputs for paper "The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations"

Contains the DESC and VMEC input and output files used in the paper, as well as the plotting scripts used to create the figures in the paper (Current with the arXiv Mar 31 2022 version, https://arxiv.org/abs/2203.17173v1): 3D equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two 3D equilibrium codes, VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the MHD force error in real space directly. Accuracy as measured by final plasma energy and satisfaction of MHD force balance, as well as other metrics, will be presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near-axis. DESC's global Fourier-Zernike basis also yields the solution everywhere in the plasma volume, not just on discrete flux surfaces. Further, DESC can compute the same accuracy solution as VMEC in an order of magnitude less time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Viking relativity experiment - Verification of signal retardation by solar gravity

Analysis of 14 months of data obtained from radio ranging to the Viking spacecraft verified, to an estimated accuracy of 0.1%, the prediction of the general theory of relativity that the round-trip times of light signals traveling between the earth and Mars are increased by the direct effect of solar gravity. The corresponding value for the metric parameter gamma is 1.000 plus or minus 0.002, where the quoted uncertainty, twice the formal standard deviation, allows for possible systematic errors.

Reasenberg, R. D.↗

Near-field Testing of the 15-meter Model of the Hoop Column Antenna

The technical results from near-field testing of the 15-meter model of the hoop column antenna at the Martin Marietta Denver Aerospace facility are documented. The antenna consists of a deployable central column and a 15 meter hoop, stiffened by cables into a structure with a high tolerance repeatable surface and offset feed location. The surface has been configured to have four offset parabolic apertures, each about 6 meters in diameter, and is made of gold plated molybdenum wire mesh. Pattern measurements were made with feed systems radiating at frequencies of 7.73, 11.60, 2.27, 2.225, and 4.26 (all in GHz). This report (Volume 1) covers the testing from an overall viewpoint and contains information of generalized interest for testing large antennas. This volume discusses the deployment of the antenna in the Martin Facility and the measurements to determine mechanical stability and trueness of the reflector surface, gives the test program outline, and gives a synopsis of antenna electromagnetic performance. Three techniques for measuring surface mechanical tolerances were used (theodolites, metric cameras, and near-field phase), but only the near-field phase approach is included. The report also includes an error analysis. A detailed listing of the antenna patterns are provided for the 2.225 Ghz feed in Volume 3 of this report, and for all other feeds in Volume 2.

Hoover, J.↗

Rapid Decimation for Direct Volume Rendering

An approach for eliminating unnecessary portions of a volume when producing a direct volume rendering is described. This reduction in volume size sacrifices some image quality in the interest of rendering speed. Since volume visualization is often used as an exploratory visualization technique, it is important to reduce rendering times, so the user can effectively explore the volume. The methods presented can speed up rendering by factors of 2 to 3 with minor image degradation. A family of decimation algorithms to reduce the number of primitives in the volume without altering the volume's grid in any way is introduced. This allows the decimation to be computed rapidly, making it easier to change decimation levels on the fly. Further, because very little extra space is required, this method is suitable for the very large volumes that are becoming common. The method is also grid-independent, so it is suitable for multiple overlapping curvilinear and unstructured, as well as regular, grids. The decimation process can proceed automatically, or can be guided by the user so that important regions of the volume are decimated less than unimportant regions. A formal error measure is described based on a three-dimensional analog of the Radon transform. Decimation methods are evaluated based on this metric and on direct comparison with reference images.

Gibbs, Jonathan↗

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO2, temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

James A Franke↗

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗

High Order Implicit Residual-Based Spatial Discretization Error Estimation for S N Neutron Transport

This work demonstrates our novel residual source spatial discretization error estimator (LeR/TEAD) for a DGFEM-1 discretization and assesses it along with two contemporary estimators, Ragusa and Wang's h -refinement estimator (RW) and Duo, Azmy, and Zikatanov's explicit residual-based estimator (DAZ), on a suite of Method of Manufactured Solutions (MMS) 2D problems and three realistic problem geometries. LeR/TE-AD is attractive because it directly estimates the local error in the angular flux, as opposed to a mere indicator of the error's behavior, on the same mesh and method order as the original numerical solution, thus typically being less computationally intensive than a refinement-based method. On the MMS suite, LeR/TE-AD consistently displayed a reduced performance versus its DGFEM-0 results in terms of accuracy and precision metrics, though it was not typically grossly inaccurate. This is attributed to the irregularities in the true solution across singular characteristics limiting the local accuracy of the numerical flux solution, leading to poor derivative approximations used in the residual approximations. The error transport problem then spreads the error in the residual to nearby cells, causing a greater degree of imprecision that did not afflict DAZ or RW. In testing the estimators on realistic problem geometries, however, LeR/TE-AD fared better. In practice, the true error is much larger in non-idealized geometries like in MMS, and a superlinear true solution means that RW and DAZ are not beneficially biased for DGFEM-1 error estimation. LeR/TE-AD was typically first or second in accuracy, primarily competing with RW, but the latter usually consumed 2-4 times the computational time as LeR/TE-AD, and requires a solution with four times as many unknowns. Furthermore, RW and LeR/TE-AD can be used to compute direct estimates of the error in any quantity of interest that is based on the angular ux solution, such as the fission rate density in a fuel pin, whereas DAZ requires a heuristic extension due to its norm-based nature.

97 MATHEMATICS AND COMPUTING↗