Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “error bound”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Evaluation of dynamic testing of full-scale wind turbine drivetrains with hardware-in-the-loop

Dynamometer testing of full-scale wind turbine drivetrains involves subjecting integrated components to extreme static loads, fatigue loads, or dynamic loads to replicate field conditions. This paper provides a detailed evaluation of the uncertainty and errors in applied loads and measured responses, and their magnitude relative to established repeatability bounds for a drivetrain subjected to static and dynamic loads on the 7.5 MW test bench at the Clemson University Wind Turbine Drivetrain Testing Facility. An ideal drivetrain simulation model is utilized to isolate the influence of load tracking errors on test article responses. It is shown that the test article response variations are mainly driven by run out and clearances inherent to the drivetrain. For the dynamic profiles, the load tracking errors are within acceptable limits. Furthermore, a frequency analysis is used to show that the test bench controller tracking performance is acceptable for profiles with frequency content up to 1.5 Hz.

17 WIND ENERGY↗
DOE OSTI2025

A new upper bound for the growth factor in Gaussian elimination with complete pivoting

Abstract The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of .

Bisain, Ankit [Department of Mathematics Massachus↗
DOE OSTI2022

Characterizing the Reproducibility of Noisy Quantum Circuits

The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Benchmarking quantum logic operations relative to thresholds for fault tolerance

Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates—defined via the diamond norm—which can differ from average error rates by orders of magnitude. One method for resolving this discrepancy is to randomize the physical implementation of quantum gates, using techniques like randomized compiling (RC). In this work, we use gate set tomography to perform precision characterization of a set of two-qubit logic gates to study RC on a superconducting quantum processor. We find that, under RC, gate errors are accurately described by a stochastic Pauli noise model without coherent errors, and that spatially correlated coherent errors and non-Markovian errors are strongly suppressed. We further show that the average and worst-case error rates are equal for randomly compiled gates, and measure a maximum worst-case error of 0.0197(3) for our gate set. Our results show that randomized benchmarks are a viable route to both verifying that a quantum processor’s error rates are below a fault-tolerance threshold, and to bounding the failure rates of near-term algorithms, if—and only if—gates are implemented via randomization methods which tailor noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Uncertainty bounds for multivariate machine learning predictions on high-strain brittle fracture

Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive. The cost increases even more if multiple simulations are needed to account for the randomness in crack length, location, and orientation, which is inherently found in real-world materials. Constructing a machine learning emulator can make the process faster by orders of magnitude. There has been little work, however, on assessing the error associated with their predictions. Estimating these errors is imperative for meaningful overall uncertainty quantification. In this work, we extend the heteroscedastic uncertainty estimates to bound a multiple output machine learning emulator. Overall, we find that the response prediction is accurate within its predicted errors, but with a somewhat conservative estimate of uncertainty.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Enhancing quantum clocks and sensors with randomization and decoherence

This letter shows how incoherent dynamics can lead to metrological advantages in quantum sensing. The results rely on the fact that incoherent dynamics lead to an additive contribution to the quantum Fisher information about time. Such an additive contribution can reduce the error of optimal estimation protocols, as implied by the quantum Cramér–Rao bound. I characterize regimes in which the estimation of a time interval or a frequency is enhanced by decoherence, thereby identifying cases in which incoherent dynamics serve as a metrological resource. The decoherence processes that yield enhanced precision of quantum sensors can be engineered by randomized Hamiltonian dynamics. I illustrate the results with protocols that display improved sensing of time intervals or global fields by qubit and photonic sensors. Enhanced precision of time intervals is achieved with Hamiltonians that include randomized global parameters. Enhanced precision in field estimation is obtained by randomized sensing times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Lower bounds on circuit depth of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which classes of problems are best suited for it. One factor in demonstrating quantum advantage is the relationship between a problem instance and the circuit depth required to implement the QAOA method. As errors in noisy intermediate-scale quantum (NISQ) devices increase exponentially with circuit depth, identifying lower bounds on circuit depth can provide insights into when quantum advantage could be feasible. In this work, we identify how the structure of problem instances can be used to identify lower bounds for circuit depth for each iteration of QAOA and examine the relationship between problem structure and the circuit depth for a variety of combinatorial optimization problems including MaxCut and MaxIndSet. Specifically, we show how to derive a graph, G, that describes a general combinatorial optimization problem and show that the depth of circuit is at least the chromatic index of G. By looking at the scaling of circuit depth, we argue that MaxCut, MaxIndSet, and some instances of vertex covering and Boolean satisfiability problems are suitable for QAOA approaches while knapsack and traveling salesperson problems are not.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the two-dimensional (2D) Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Scalable Yet Rigorous Floating-Point Error Analysis

Automated techniques for rigorous floating-point round-off error analysis are a prerequisite to placing important activities in HPC such as precision allocation, verification and code optimization on a formal footing. Yet existing techniques cannot provide tight bounds for expressions beyond a few dozen operators; barely enough for HPC. In this work, we offer an approach embedded in a new tool called SATIRE that scales error analysis by four orders of magnitude compared to today’s best-of-class tools. We explain how three key ideas underlying SATIRE help it attain such scale: path strength reduction, bound optimization and abstraction. SATIRE provides tight bounds and rigorous guarantees on significantly larger expressions with well over a hundred thousand operators, covering important examples including FFT, matrix multiplication and PDE stencils.

Das, Arnab↗
DOE OSTI2024

Heisenberg-limited Hamiltonian learning for interacting bosons

We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean square error ϵ using ${\mathcal{O}}(1/\epsilon )$ total evolution time, which is independent of the system size, in a way that is robust against state-preparation and measurement error. In the protocol, we only use bosonic coherent states, beam splitters, phase shifters, and homodyne measurements, which are easy to implement on many experimental platforms. A key technique we develop is to apply random unitaries to enforce symmetry in the effective Hamiltonian, which may be of independent interest.

computer science↗
DOE OSTI2024

Universal Spreading of Conditional Mutual Information in Noisy Random Circuits

For this work, we study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where CMI spreads linearly while being bounded by the light cone, we find that noisy random circuits with an error rate 𝑝 exhibit superlinear propagation of CMI, which diverges far beyond the light cone at a critical circuit depth 𝑡 𝑐 ∝ 𝑝 −1 . We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations. To analytically capture the dynamics of CMI in noisy random circuits, we introduce a coarse-graining method, and we validate our theoretical results through numerical simulations. Furthermore, we identify a universal scaling law governing the spreading of CMI.

decoherence↗
DOE OSTI2021

Quarter 4 Report: Report on Final Findings and Opportunities for Future Work in the Use of Mixed Precision in Iterative Solvers

The fourth quarter of the project was spent developing an error analysis of the s-step Lanczos and CG algorithms. Our theoretical bounds and numerical experiments show that the numerical behavior of the algorithm can be significantly improved by using extra precision in a small part of the computation related to the computation and application of the Gram matrix. We have published a technical report which includes all steps of the analysis [8]; a shortened version for journal submission is in preparation. We plan to submit this paper in the following weeks. Activities related to this also include a collaboration with Ichitaro Yamazaki on gathering performance results for these new mixed precision s-step Krylov subspace methods using single/double precision on GPUs. Namely, we would like to obtain performance results that show that the performance overhead of using double the working precision in these select computations is minimal. Other activities include attending biweekly xSDK meetings and presenting a pitch talk on this work to the group on February 25, 2021. In the remainder of the document, we summarize our findings on the potential for mixed precision in classical Krylov subspace methods and s-step Krylov subspace methods, as well as key opportunities for future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Uncovering Where Compensating Errors Could Hide in ENDF/B-VIII.0

Unconstrained physics spaces between two or more nuclear data observables in a library occur when their values can be simultaneously adjusted without violating the uncertainties in either differential information or simulations of relevant integral experiments. Differential data are often too imprecise to fully bound all nuclear data observables of interest for application simulations. Integral data are simulated with combinations of nuclear data so that an error in one observable may be hidden by a counterbalancing error in another. In this manner compensating errors may lurk within nuclear data libraries and these errors have the potential to undermine the predictive power of neutron transport simulations, particularly in situations where there is no conclusive validation experiment that resembles the application of interest. The EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) developed a preliminary workflow to identify these unconstrained physics spaces by bringing together results from a large collection of integral experiments with their simulated counter-parts as well as differential information that have a one-to-one correspondence to nuclear data. This wealth of information is processed by machine learning tools for subsequent refinement by human experts. Here, we show how the EUCLID work-flow is executed by applying it first to 239 Pu and then to 9 Be nuclear data in ENDF/B-VIII.0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Uncovering Where Compensating Errors Could Hide in ENDF/B-VIII.0

Unconstrained physics spaces between two or more nuclear data observables in a library occur when their values can be simultaneously adjusted without violating the uncertainties in either differential information or simulations of relevant integral experiments. Differential data are often too imprecise to fully bound all nuclear data observables of interest for application simulations. Integral data are simulated with combinations of nuclear data so that an error in one observable may be hidden by a counterbalancing error in another. In this manner compensating errors may lurk within nuclear data libraries and these errors have the potential to undermine the predictive power of neutron transport simulations, particularly in situations where there is no conclusive validation experiment that resembles the application of interest. The EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) developed a preliminary workflow to identify these unconstrained physics spaces by bringing together results from a large collection of integral experiments with their simulated counter-parts as well as differential information that have a one-to-one correspondence to nuclear data. This wealth of information is processed by machine learning tools for subsequent refinement by human experts. Here, we show how the EUCLID work-flow is executed by applying it first to 239 Pu and then to 9 Be nuclear data in ENDF/B-VIII.0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Error quantification and comparison of binary neutron star gravitational waveforms from numerical relativity codes

Future gravitational wave detections of merging binary neutron star systems have the possibility to tightly constrain the equation of state of dense nuclear matter. In order to extract such constraints, gravitational waveform models need to be calibrated to accurate numerical relativity simulations of the late inspiral and merger. In this work, we take an essential step toward classifying the error and potential systematics in current generation numerical relativity simulations of merging binary neutron stars. To this end, we perform a direct comparison of two codes (fil, spec), which differ in many aspects, including the numerical methods and discretizations used and equations solved. We find that despite these different approaches, the codes are—within current numerical resolution bounds—fully consistent, and broadly comparable in cost for a given accuracy level. Our results indicate that the error in the waveforms is primarily dominated by the hydrodynamic evolution, consistent with earlier findings in the literature. Finally, we also discuss current limitations and cost estimates for numerical relativity simulations to reach the accuracies required in the era of next-generation gravitational detectors.

gravitational waves↗
DOE OSTI2020

Filtering adaptive output feedback control for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics

This article synthesizes a filtering adaptive output feedback controller for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The unmodeled dynamics are bounded-input bounded-output stable. By adopting an estimation/cancellation strategy, a piecewise constant adaptive law drives the estimation error to zero at every time instant, which yields the adaptive parameters; a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, while a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. A feedforward control law is designed to track a given command. Since the virtual reference system defines the best performance that can be achieved by the closed-loop system, the uniform performance bounds are derived for the states and control signals via comparison. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed filtering adaptive output feedback control architecture, comparisons with the model reference adaptive control demonstrates the superiority of the proposed control method.

filtering adaptive control, mismatched uncertainit↗
DOE OSTI2024

Investigation of Ethane Dehydrogenation and Hydrogenolysis on Pt(111), Pt(211), and Pt(100): Bayesian Quantification and Correction of DFT-Based Enthalpic and Entropic Uncertainties

Computational investigations of heterogeneously catalyzed reactions using density functional theory (DFT) are often inaccurate, largely due to uncertainties in the choice of DFT functional (enthalpic uncertainty) and approximations for modeling adsorbate movement along the catalyst surface (entropic uncertainty). This work illustrates that both uncertainties are significant in the investigation of ethane dehydrogenation (EDH) and hydrogenolysis on Pt catalysts by considering the complete deconstruction of ethane on Pt(111), Pt(211), and Pt(100) using microkinetic modeling (MKM). Hence, this work uses both noncalibrated and Bayesian-calibrated MKMs to quantify and correct inaccuracies in macroscopic properties due to both uncertainties. A Bayesian approach to the correction of entropic errors was introduced using a “Modified Fermi Function (MFF)” to calibrate between the two bounds of entropy represented by the harmonic oscillator (HO) and free translator (FT) approximations. Regardless of enthalpic and entropic uncertainties, all three surfaces are capable of ethane activation; however, Pt(211) was found to be the most active and is largely responsible for methane production. Next, Pt(111) is largely responsible for acetylene production, and Pt(100) has the highest ethylene selectivity but is most susceptible to coking. By comparison of different calibrated models, the FT entropy approximation was found to better describe EDH under typical experimental conditions. Statistical evidence was found to support Pt(111) as the active site for EDH, assuming that one single site is responsible for the chemistry. On the three surfaces, competing second dehydrogenations to CH 2 CH 2 and CH 3 CH were observed as well as isomerization of CH 3 CH back to CH 2 CH 2 and deeper dehydrogenation of CH 3 CH. In conclusion, C–C cleavage was found to largely proceed via the CH 3 C intermediate on Pt(100) and Pt(111), while on Pt(211), it was via both CHC and CH 3 C.

Bayesian model selection↗