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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗
DOE OSTI2017

Error modeling for surrogates of dynamical systems using machine learning: Machine-learning-based error model for surrogates of dynamical systems

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate-model error in a quantity of interest (QoI). This eliminates the need for the user to hand-select a small number of informative features. The methodology requires a training set of parameter instances at which the time-dependent surrogate-model error is computed by simulating both the high-fidelity and surrogate models. Using these training data, the method first determines regression-model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time-instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate-model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time-dependent surrogate-model error (eg, time-integrated errors). We then apply the proposed framework to model errors in reduced-order models of nonlinear oil-water subsurface flow simulations, with time-varying well-control (bottom-hole pressure) parameters. The reduced-order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. Moreover, when the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time-instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time- and well-averaged errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Comparative Analysis of Soft-Error Detection Strategies: A Case Study with Iterative Methods

Undetected soft errors caused by transient bit flips can lead to silent data corruption (SDC), an undesirable outcome where invalid results pass for valid ones. This has motivated the design of soft error detectors to minimize SDCs. However, the detectors have been studied under different contexts, making comparative evaluation difficult. In this paper, we present the first comprehensive evaluation of four online soft error detection techniques in detecting the adverse impact of soft errors on iterative methods. We observe that, across five iterative methods, the detectors studied achieve high but not perfect detection rates. To understand the potential for improved detection, we evaluate a machine-learning based detector that takes as features that are the runtime features observed by the individual detectors to arrive at their conclusions. Our evaluation demonstrates improved but still far from perfect detection accuracy for the machine learning based detectors. This extensive evaluation demonstrates the need for designing error detectors to handle the evolutionary behavior exhibited by iterative solvers.

Silent data corruption, Soft error detection, Iter↗
DOE OSTI2019

Error field impact on mode locking and divertor heat flux in NSTX-U

During the 2016 NSTX-U experimental campaign, locked modes in the plasma edge presented clear evidence of the presence of error fields. Extensive metrology and plasma response modeling with IPEC and M3D-C1 have been conducted to understand the various sources of error fields in NSTX-U as built in 2016, and to determine which of these sources have the greatest effect on the plasma. In particular, modeling finds that the error field from misalignment of the toroidal field (TF) coils may have a significant effect on the plasma. The response to the TF error field is shown to depend on the presence of a q = 1 surface, in qualitative agreement with experimental observations. It is found that certain characteristics of the TF error field present new challenges for error field correction. Specifically, the error field spectrum differs significantly from that of coils on the low-field side (such as the NSTX-U error field correction coils), and does not resonate strongly with the dominant kink mode, thus potentially requiring a multi-mode correction. Moreover, to mitigate heat fluxes using poloidal flux expansion, the pitch angle at the divertor plates must be small (~1°). It is shown that uncorrected error fields may result in potentially significant local perturbation to the pitch angle. Estimates for coil alignment tolerances in NSTX-U are derived based on consideration of both heat flux and core resonant fields independently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Error statistics and scalability of quantum error mitigation formulas

Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(ϵN) with the gate number N before mitigation and sublinearly O(ϵ'N γ ) after mitigation, where γ ≈ 0.5, ϵ is the error rate of a quantum gate, and ϵ' is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A Comparison of Forecast Error Generators for Modeling Wind and Load Uncertainty

This paper presents four algorithms to generate random forecast error time series, including a truncated-normal distribution model, a state-space based Markov model, a seasonal autoregressive moving average (ARMA) model, and a stochastic-optimization based model. The error time series are used to create real-time (RT), hour-ahead (HA), and day-ahead (DA) wind and load forecast time series that statistically match historically observed forecasting data sets, used for variable generation integration studies. A comparison is made using historical DA load forecast and actual load values to generate new sets of DA forecasts with similar stoical forecast error characteristics. This paper discusses and compares the capabilities of each algorithm to preserve the characteristics of the historical forecast data sets.

Lu, Ning↗
DOE OSTI2013

Automated evaluation of setup errors in carbon ion therapy using PET: Feasibility study

Purpose: To investigate the possibility of detecting patient mispositioning in carbon-ion therapy with particle therapy positron emission tomography (PET) in an automated image registration based manner. Methods: Tumors in the head and neck (H and N), pelvic, lung, and brain region were investigated. Biologically optimized carbon ion treatment plans were created with TRiP98. From these treatment plans, the reference β{sup +}-activity distributions were calculated using a Monte Carlo simulation. Setup errors were simulated by shifting or rotating the computed tomography (CT). The expected β{sup +} activity was calculated for each plan with shifts. Finally, the reference particle therapy PET images were compared to the “shifted” β{sup +}-activity distribution simulations using the Pearson's correlation coefficient (PCC). To account for different PET monitoring options the inbeam PET was compared to three different inroom scenarios. Additionally, the dosimetric effects of the CT misalignments were investigated. Results: The automated PCC detection of patient mispositioning was possible in the investigated indications for cranio-caudal shifts of 4 mm and more, except for prostate tumors. In the rather homogeneous pelvic region, the generated β{sup +}-activity distribution of the reference and compared PET image were too much alike. Thus, setup errors in this region could not be detected. Regarding lung lesions the detection strongly depended on the exact tumor location: in the center of the lung tumor misalignments could be detected down to 2 mm shifts while resolving shifts of tumors close to the thoracic wall was more challenging. Rotational shifts in the H and N and lung region of +6° and more could be detected using inroom PET and partly using inbeam PET. Comparing inroom PET to inbeam PET no obvious trend was found. However, among the inroom scenarios a longer measurement time was found to be advantageous. Conclusions: This study scopes the use of various particle therapy PET verification techniques in four indications. The automated detection of patients' setup errors was investigated in a broad accumulation of data sets. The evaluation of introduced setup errors is performed automatically, which is of utmost importance to introduce highly required particle therapy monitoring devices into the clinical routine.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Quantifying structural errors in cloud condensation nuclei activity from reduced representation of aerosol size distributions

Aerosol effects on clouds and radiation are the dominant contribution to uncertainty in radiative forcing relative to the pre-industrial atmosphere. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging by condensation of semi-volatile substances and coagulation among particles. These findings suggest that structural error in modeled aerosol properties contributes to the large inter-model variability in aerosol radiative forcing.

Fierce, Laura M.↗
DOE OSTI2021

Securing against errors in an error correcting code (ECC) implemented in an automotive system

In general, data is susceptible to errors caused by faults in hardware (i.e. permanent faults), such as faults in the functioning of memory and/or communication channels. To detect errors in data caused by hardware faults, the error correcting code (ECC) was introduced, which essentially provides a sort of redundancy to the data that can be used to validate that the data is free from errors caused by hardware faults. In some cases, the ECC can also be used to correct errors in the data caused by hardware faults. However, the ECC itself is also susceptible to errors, including specifically errors caused by faults in the ECC logic. A method, computer readable medium, and system are thus provided for securing against errors in an ECC.

Saxena, Nirmal Raj↗
DOE OSTI2015

Dependence of the compensation error on the error of a sensor and corrector in an adaptive optics phase-conjugating system

In the framework of a statistical model of an adaptive optics system (AOS) of phase conjugation, three algorithms based on an integrated mathematical approach are considered, each of them intended for minimisation of one of the following characteristics: the sensor error (in the case of an ideal corrector), the corrector error (in the case of ideal measurements) and the compensation error (with regard to discreteness and measurement noises and to incompleteness of a system of response functions of the corrector actuators). Functional and statistical relationships between the algorithms are studied and a relation is derived to ensure calculation of the mean-square compensation error as a function of the errors of the sensor and corrector with an accuracy better than 10%. Because in adjusting the AOS parameters, it is reasonable to proceed from the equality of the sensor and corrector errors, in the case the Hartmann sensor is used as a wavefront sensor, the required number of actuators in the absence of the noise component in the sensor error turns out 1.5 – 2.5 times less than the number of counts, and that difference grows with increasing measurement noise. (adaptive optics)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

On the Correspondence between Mean Forecast Errors and Climate Errors in CMIP5 Models

The present study examines the correspondence between short- and long-term systematic errors in five atmospheric models by comparing the 16 five-day hindcast ensembles from the Transpose Atmospheric Model Intercomparison Project II (Transpose-AMIP II) for July–August 2009 (short term) to the climate simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5) and AMIP for the June–August mean conditions of the years of 1979–2008 (long term). Because the short-term hindcasts were conducted with identical climate models used in the CMIP5/AMIP simulations, one can diagnose over what time scale systematic errors in these climate simulations develop, thus yielding insights into their origin through a seamless modeling approach. The analysis suggests that most systematic errors of precipitation, clouds, and radiation processes in the long-term climate runs are present by day 5 in ensemble average hindcasts in all models. Errors typically saturate after few days of hindcasts with amplitudes comparable to the climate errors, and the impacts of initial conditions on the simulated ensemble mean errors are relatively small. This robust bias correspondence suggests that these systematic errors across different models likely are initiated by model parameterizations since the atmospheric large-scale states remain close to observations in the first 2–3 days. However, biases associated with model physics can have impacts on the large-scale states by day 5, such as zonal winds, 2-m temperature, and sea level pressure, and the analysis further indicates a good correspondence between short- and long-term biases for these large-scale states. Therefore, improving individual model parameterizations in the hindcast mode could lead to the improvement of most climate models in simulating their climate mean state and potentially their future projections.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Error recovery to enable error-free message transfer between nodes of a computer network

An error-recovery method to enable error-free message transfer between nodes of a computer network. A first node of the network sends a packet to a second node of the network over a link between the nodes, and the first node keeps a copy of the packet on a sending end of the link until the first node receives acknowledgment from the second node that the packet was received without error. The second node tests the packet to determine if the packet is error free. If the packet is not error free, the second node sets a flag to mark the packet as corrupt. The second node returns acknowledgement to the first node specifying whether the packet was received with or without error. When the packet is received with error, the link is returned to a known state and the packet is sent again to the second node.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Shared Dosimetry Error in Epidemiological Dose-Response Analyses

Radiation dose reconstruction systems for large-scale epidemiological studies are sophisticated both in providing estimates of dose and in representing dosimetry uncertainty. For example, a computer program was used by the Hanford Thyroid Disease Study to provide 100 realizations of possible dose to study participants. The variation in realizations reflected the range of possible dose for each cohort member consistent with the data on dose determinates in the cohort. Another example is the Mayak Worker Dosimetry System 2013 which estimates both external and internal exposures and provides multiple realizations of "possible" dose history to workers given dose determinants. This paper takes up the problem of dealing with complex dosimetry systems that provide multiple realizations of dose in an epidemiologic analysis. In this paper we derive expected scores and the information matrix for a model used widely in radiation epidemiology, namely the linear excess relative risk (ERR) model that allows for a linear dose response (risk in relation to radiation) and distinguishes between modifiers of background rates and of the excess risk due to exposure. We show that treating the mean dose for each individual (calculated by averaging over the realizations) as if it was true dose (ignoring both shared and unshared dosimetry errors) gives asymptotically unbiased estimates (i.e. the score has expectation zero) and valid tests of the null hypothesis that the ERR slope β is zero. Although the score is unbiased the information matrix (and hence the standard errors of the estimate of β) is biased for β≠0 when ignoring errors in dose estimates, and we show how to adjust the information matrix to remove this bias, using the multiple realizations of dose. Use of these methods for several studies, including the Mayak Worker Cohort and the U.S. Atomic Veterans Study, is discussed.

epidemiological analysis↗
DOE OSTI2018

Statistical Analysis of Rounded Data: Measurement Errors vs Rounding Errors

Since data for statistical analysis are always given in a discretized form, observations contain not only measurement errors but also rounding errors which are determined by the discretization step. In this paper we consider situations where the rounding errors are considerable: they are comparable to or even greater (in average) than the measurement errors. It is shown that it can be reasonable to increase the measurement errors in order to reduce the error of the final result.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Distributed Quantum Error Correction for Chip-Level Catastrophic Errors

Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip. Here, in this work, we present a distributed error correction scheme to combat the devastating effect of such events by introducing an additional layer of quantum erasure error correcting code across separate chips. We show that our scheme is fault tolerant against chip-level catastrophic errors and discuss its experimental implementation using superconducting qubits with microwave links. Our analysis shows that in state-of-the-art experiments, it is possible to suppress the rate of these errors from 1 per 10 s to less than 1 per month.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-F-J-65: Prediction of Patient Setup Errors and Errors in the Calibration Curve from Prompt Gamma Proton Range Measurements

Purpose: To understand the extent to which the prompt gamma camera measurements can be used to predict the residual proton range due to setup errors and errors in the calibration curve. Methods: We generated ten variations on a default calibration curve (CC) and ten corresponding range maps (RM). Starting with the default RM, we chose a square array of N beamlets, which were then rotated by a random angle θ and shifted by a random vector s. We added a 5% distal Gaussian noise to each beamlet in order to introduce discrepancies that exist between the ranges predicted from the prompt gamma measurements and those simulated with Monte Carlo algorithms. For each RM, s, θ, along with an offset u in the CC, were optimized using a simple Euclidian distance between the default ranges and the ranges produced by the given RM. Results: The application of our method lead to the maximal overrange of 2.0mm and underrange of 0.6mm on average. Compared to the situations where s, θ, and u were ignored, these values were larger: 2.1mm and 4.3mm. In order to quantify the need for setup error corrections, we also performed computations in which u was corrected for, but s and θ were not. This yielded: 3.2mm and 3.2mm. The average computation time for 170 beamlets was 65 seconds. Conclusion: These results emphasize the necessity to correct for setup errors and the errors in the calibration curve. The simplicity and speed of our method makes it a good candidate for being implemented as a tool for in-room adaptive therapy. This work also demonstrates that the Prompt gamma range measurements can indeed be useful in the effort to reduce range errors. Given these results, and barring further refinements, this approach is a promising step towards an adaptive proton radiotherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Sensor Error Estimation for Reactor Coolant System with Generalization Error Equations

We consider a simplified version of the sensor error estimation problem in pressure sensors in the primary coolant system of a nuclear power plant under the condition that a majority of sensors are error-free. We present a sensor fusion method to estimate sensor errors in the primary coolant system of a power reactor by using measurements collected by multiple sensors. The underlying relationship between the measured and estimated parameters is inferred using measurements collected under controlled no-error conditions of the plant. We propose a machine learning approach to train fusers that provide an estimate of the sensor measurement by using measurements from other sensors, and the difference between the actual sensor measurement and its estimate provides the sensor estimate. We present generalization error equations for these methods that characterize the performance of their sensor error estimates on future measurements using the distribution-free machine learning formulation.

Rao, Nageswara S.↗