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At least 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A simulation-based model for understanding the time dependent x-ray drive asymmetries and error bars in indirectly driven implosions on the National Ignition Facility

Time-dependent low-mode asymmetries are believed to play a leading role in limiting the performance of current inertial confinement fusion implosions on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. These long wavelength modes are initiated and driven by asymmetries in the x-ray flux from the hohlraum; however, the underlying hydrodynamics of the implosion also act to modify and amplify these asymmetries. Here we present here a simulation-based model connecting the time-dependent drive asymmetry seen by the capsule to the measured inflight and hot spot symmetries. This approach is based on a Green's function analysis for which we evaluate the response of the capsule to impulses of drive asymmetry at a series of times. Our model sheds new light on the sensitivity to the drive asymmetry of an imploded capsule, giving a new tool for design. Inverting the problem and finding the drive asymmetry needed to match the experimental data allow us to tightly constrain the drive asymmetry seen by the capsule, providing an error estimate on the result. Doing so, we are able to point out when and how the complex hohlraum simulations start to deviate from what they should obtain to match the experimental data. Ultimately, we project to use this model to make some experimental recommendations to fix the time-dependent low-mode asymmetry of indirectly driven implosions and identify additional measurements to further constrain the asymmetries with a view to improving target design on the NIF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Rapid Detection of Anomalies in Battery Energy Storage System Data

Data analytics is pivotal in assessing the technical characteristics and performance of Battery Energy Storage Systems (BESS), underpinning BESS modeling, optimization, and control. However, raw datasets frequently harbor anomalies from measurement errors and equipment malfunctions, impacting BESS reliability and analysis accuracy To address the challenge, this paper presents a novel methodology for the rapid detection of anomalous charge or discharge cycles within BESS operational data, expediting the cleaning process while ensuring data integrity. We’ve collected diverse and comprehensive real-world BESS operational datasets in collaboration with the Electric Power Research Institute and multiple Washington State utilities. These datasets serve dual roles: enabling comprehensive data exploration and analysis for understanding underlying challenges and method development, while also acting as a vital validation resource, demonstrating practical effectiveness. The proposed method detects anomalies and aids in their resolution, improving system performance characterization precision. It also reveals recurring data anomaly sources, offering insights for data collection and handling enhancement. Practitioners can gain valuable insights from the identified anomalous cycles in the real-world datasets along with the investigative process for root cause analyses and essential data cleaning steps.

Crawford, Aladsair J.↗
DOE OSTI2023

Model Predictive Control-Based Trajectory Shaper for Safe and Efficient Adaptive Cruise Control

Recent studies show that commercially-available adaptive cruise control (ACC) systems are string-unstable, indicating that ACC-driven vehicles amplify speed fluctuations from downstream traffic and induce stop-and-go waves. Moreover, it is challenging to revise the original control algorithm of an ACC system to achieve string stability due to its internal complexity and powertrain uncertainties. To achieve desired control performance given a string-unstable ACC system and circumvent revising the original control algorithm, this study proposes a model predictive control-based trajectory shaper (MPC-TS), which only modifies the sensor-measured trajectory information (i.e., position and speed) of the preceding vehicle. The proposed MPC-TS leverages the input shaping technique to generate reference trajectory to improve string stability, while incorporating tracking errors and vehicle acceleration/deceleration magnitude in the MPC cost function and constraining fluctuations of vehicle speed and spacing to ensure desired car-following performance. Numerical experiments validate the control performance of ACC with the proposed MPC-TS in terms of string stability, safety, traffic efficiency, and comfort.

Zhou, Anye↗
DOE OSTI2014

Using computer-extracted image features for modeling of error-making patterns in detection of mammographic masses among radiology residents

Purpose: Mammography is the most widely accepted and utilized screening modality for early breast cancer detection. Providing high quality mammography education to radiology trainees is essential, since excellent interpretation skills are needed to ensure the highest benefit of screening mammography for patients. The authors have previously proposed a computer-aided education system based on trainee models. Those models relate human-assessed image characteristics to trainee error. In this study, the authors propose to build trainee models that utilize features automatically extracted from images using computer vision algorithms to predict likelihood of missing each mass by the trainee. This computer vision-based approach to trainee modeling will allow for automatically searching large databases of mammograms in order to identify challenging cases for each trainee. Methods: The authors’ algorithm for predicting the likelihood of missing a mass consists of three steps. First, a mammogram is segmented into air, pectoral muscle, fatty tissue, dense tissue, and mass using automated segmentation algorithms. Second, 43 features are extracted using computer vision algorithms for each abnormality identified by experts. Third, error-making models (classifiers) are applied to predict the likelihood of trainees missing the abnormality based on the extracted features. The models are developed individually for each trainee using his/her previous reading data. The authors evaluated the predictive performance of the proposed algorithm using data from a reader study in which 10 subjects (7 residents and 3 novices) and 3 experts read 100 mammographic cases. Receiver operating characteristic (ROC) methodology was applied for the evaluation. Results: The average area under the ROC curve (AUC) of the error-making models for the task of predicting which masses will be detected and which will be missed was 0.607 (95% CI,0.564-0.650). This value was statistically significantly different from 0.5 (p < 0.0001). For the 7 residents only, the AUC performance of the models was 0.590 (95% CI,0.537-0.642) and was also significantly higher than 0.5 (p = 0.0009). Therefore, generally the authors’ models were able to predict which masses were detected and which were missed better than chance. Conclusions: The authors proposed an algorithm that was able to predict which masses will be detected and which will be missed by each individual trainee. This confirms existence of error-making patterns in the detection of masses among radiology trainees. Furthermore, the proposed methodology will allow for the optimized selection of difficult cases for the trainees in an automatic and efficient manner.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Benchmark Comparisons of Lattice Physics Calculations for Thorium-Based Fuels in Pressure-Tube Heavy Water Reactors

Thorium is a fertile nuclear fuel resource that is nearly three times as abundant as uranium in the earth's crust and that can be exploited and used to extend uranium resources. The pressure tube heavy water reactor (PTHWR) is an excellent existing technology for utilizing thorium-based fuels, due to its high neutron economy achieved by using heavy water as a moderator and coolant, the ability to perform online refueling, and its flexibility in fuel management. Reactor physics studies are underway at the Canadian Nuclear Laboratories (CNL) to evaluate several types of thorium-based fuels that could be implemented in PT-HWRs in the near-term and intermediate future, building upon past experience. For preliminary, conceptual studies, deterministic lattice physics and core physics codes such as WIMS-AECL and RFSP are used to provide quick and more approximate estimates of performance and safety characteristics. The objective of this study was to perform 2D lattice physics benchmark comparisons between WIMS-AECL and MCNP5 for several types of thorium-based fuel bundle lattices for potential use in PT-HWRs. Benchmark comparisons will help confirm the validity of deterministic calculation results, and provide estimates of the potential magnitude of calculation errors and uncertainties. Areas for potential improvements in the WIMS-AECL calculations may also be identified. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Benchmark Theoretical Study of the π–π Binding Energy in the Benzene Dimer

We establish a new estimate for the binding energy between two benzene molecules in the parallel-displaced (PD) conformation by systematically converging (i) the intra- and intermolecular geometry at the minimum, (ii) the expansion of the orbital basis set, and (iii) the level of electron correlation. The calculations were performed at the second-order Møller–Plesset perturbation (MP2) and the coupled cluster including singles, doubles, and a perturbative estimate of triples replacement [CCSD(T)] levels of electronic structure theory. At both levels of theory, by including results corrected for basis set superposition error (BSSE), we have estimated the complete basis set (CBS) limit by employing the family of Dunning’s correlation-consistent polarized valence basis sets. The largest MP2 calculation was performed with the cc-pV6Z basis set (2772 basis functions), whereas the largest CCSD(T) calculation was with the cc-pV5Z basis set (1752 basis functions). The cluster geometries were optimized with basis sets up to quadruple-ζ quality, observing that both its intra- and intermolecular parts have practically converged with the triple-ζ quality sets. The use of converged geometries was found to play an important role for obtaining accurate estimates for the CBS limits. Our results demonstrate that the binding energies with the families of the plain (cc-pVnZ) and augmented (aug-cc-pVnZ) sets converge [within <0.01 kcal/mol for MP2 and <0.15 kcal/mol for CCSD(T)] to the same CBS limit. In addition, the average of the uncorrected and BSSE-corrected binding energies was found to converge to the same CBS limit much faster than either of the two constituents (uncorrected or BSSE-corrected binding energies). Due to the fact that the family of augmented basis sets (especially for the larger sets) causes serious linear dependency problems, the plain basis sets (for which no linear dependencies were found) are deemed as a more efficient and straightforward path for obtaining an accurate CBS limit. We considered extrapolations of the uncorrected (ΔE) and BSSE-corrected (ΔE cp ) binding energies, their average value (ΔE ave ), as well as the average of the latter over the plain and augmented sets (Δ~E ave ) with the cardinal number of the basis set n. Our best estimate of the CCSD(T)/CBS limit for the π–π binding energy in the PD benzene dimer is D e = -2.65 ± 0.02 kcal/mol. The best CCSD(T)/cc-pV5Z calculated value is -2.62 kcal/mol, just 0.03 kcal/mol away from the CBS limit. For comparison, the MP2/CBS limit estimate is -5.00 ± 0.01 kcal/mol, demonstrating a 90% overbinding with respect to CCSD(T). Finally, the spin-component-scaled (SCS) MP2 variant was found to closely reproduce the CCSD(T) results for each basis set, while scaled opposite spin (SOS) MP2 yielded results that are too low when compared to CCSD(T).

Environmental Molecular Sciences Laboratory↗
DOE OSTI2018

A family of second-order fully explicit time integration schemes

A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗
DOE OSTI2024

Streaming Large-Scale Microscopy Data to a Supercomputing Facility

Data management is a critical component of modern experimental workflows. As data generation rates increase, transferring data from acquisition servers to processing servers via conventional file-based methods is becoming increasingly impractical. The 4D Camera at the National Center for Electron Microscopy generates data at a nominal rate of 480 Gbit s -1 (87,000 frames s -1 ⁠), producing a 700 GB dataset in 15 s. To address the challenges associated with storing and processing such quantities of data, we developed a streaming workflow that utilizes a high-speed network to connect the 4D Camera’s data acquisition system to supercomputing nodes at the National Energy Research Scientific Computing Center, bypassing intermediate file storage entirely. In this work, we demonstrate the effectiveness of our streaming pipeline in a production setting through an hour-long experiment that generated over 10 TB of raw data, yielding high-quality datasets suitable for advanced analyses. Additionally, we compare the efficacy of this streaming workflow against the conventional file-transfer workflow by conducting a postmortem analysis on historical data from experiments performed by real users. Our findings show that the streaming workflow significantly improves data turnaround time, enables real-time decision-making, and minimizes the potential for human error by eliminating manual user interactions.

4D-STEM↗
DOE OSTI2024

Forte: An Interactive Visual Analytic Tool for Trust-Augmented Net-Load Forecasting

Accurate net-load forecasting is vital for energy planning, aiding decisions on trade and load distribution. However, assessing the performance of forecasting models across diverse input variables, like temperature and humidity, remains challenging, particularly for eliciting a high degree of trust in the model outcomes. In this context, there is a growing need for data-driven technological interventions to aid scientists in comprehending how models react to both noisy and clean input variables, thus shedding light on complex behaviors and fostering confidence in the outcomes. In this paper, we present Forte, a visual analytics-based application to explore deep probabilistic net-load forecasting models across various input variables and understand the error rates for different scenarios. With carefully designed visual interventions, this web-based interface empowers scientists to derive insights about model performance by simulating diverse scenarios, facilitating an informed decision-making process. We discuss observations made using Forte and demonstrate the effectiveness of visualization techniques to provide valuable insights into the correlation between weather inputs and net-load forecasts, ultimately advancing grid capabilities by improving trust in forecasting models.

Bhattacharjee, Kaustav↗
DOE OSTI2016

SU-F-T-230: A Simple Method to Assess Accuracy of Dynamic Wave Arc Irradiation Using An Electronic Portal Imaging Device and Log Files

Purpose: The Dynamic Wave Arc (DWA) technique, where the multi-leaf collimator (MLC) and gantry/ring move simultaneously in a predefined non-coplanar trajectory, has been developed on the Vero4DRT. The aim of this study is to develop a simple method for quality assurance of DWA delivery using an electronic portal imaging device (EPID) measurements and log files analysis. Methods: The Vero4DRT has an EPID on the beam axis, the resolution of which is 0.18 mm/pixel at the isocenter plane. EPID images were acquired automatically. To verify the detection accuracy of the MLC position by EPID images, the MLC position with intentional errors was assessed. Tests were designed considering three factors: (1) accuracy of the MLC position (2) dose output consistency with variable dose rate (160–400 MU/min), gantry speed (2.4–6°/s), ring speed (0.5–2.5°/s), and (3) MLC speed (1.6–4.2 cm/s). All the patterns were delivered to the EPID and compared with those obtained with a stationary radiation beam with a 0° gantry angle. The irradiation log, including the MLC position and gantry/ring angle, were recorded simultaneously. To perform independent checks of the machine accuracy, the MLC position and gantry/ring angle position were assessed using log files. Results: 0.1 mm intentional error can be detected by the EPID, which is smaller than the EPID pixel size. The dose outputs with different conditions of the dose rate and gantry/ring speed and MLC speed showed good agreement, with a root mean square (RMS) error of 0.76%. The RMS error between the detected and recorded data were 0.1 mm for the MLC position, 0.12° for the gantry angle, and 0.07° for the ring angle. Conclusion: The MLC position and dose outputs in variable conditions during DWA irradiation can be easily detected using EPID measurements and log file analysis. The proposed method is useful for routine verification. This research is (partially) supported by the Practical Research for Innovative Cancer Control (15Ack0106151h0001) from Japan Agency for Medical Research and development, AMED. Authors Takashi Mizowaki and Masahiro Hiraoka have consultancy agreement with Mitsubishi Heavy Industries, Ltd., Japan.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

EXAMINING THE ACCURACY OF ASTROPHYSICAL DISK SIMULATIONS WITH A GENERALIZED HYDRODYNAMICAL TEST PROBLEM

We discuss a generalization of the classic Keplerian disk test problem allowing for both pressure and rotational support, as a method of testing astrophysical codes incorporating both gravitation and hydrodynamics. We argue for the inclusion of pressure in rotating disk simulations on the grounds that realistic, astrophysical disks exhibit non-negligible pressure support. We then apply this test problem to examine the performance of various smoothed particle hydrodynamics (SPH) methods incorporating a number of improvements proposed over the years to address problems noted in modeling the classical gravitation-only Keplerian disk. We also apply this test to a newly developed extension of SPH based on reproducing kernels called CRKSPH. Counterintuitively, we find that pressure support worsens the performance of traditional SPH on this problem, causing unphysical collapse away from the steady-state disk solution even more rapidly than the purely gravitational problem, whereas CRKSPH greatly reduces this error.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Towards a wavefront-preservation X-ray crystal monochromator for high-repetition-rate FELs

The wavefront preservation of coherent X-ray free-electron laser beams is pushing the requirement on the quality and performance of X-ray optics to an unprecedented level. The Strehl ratio can be used to quantify this requirement. In this paper, the criteria for thermal deformation of the X-ray optics are formulated, especially for crystal monochromators. To preserve the X-ray wavefront, the standard deviation of the height error should be sub-nm for mirrors and less than 25 pm for crystal monochromators. Cryocooled silicon crystals combined with two techniques can be used to achieve this level of performance for monochromator crystals: (1) using a focusing element to compensate the second-order component of the thermal deformation; (2) introducing a cooling pad between the cooling block and silicon crystal and optimizing the effective cooling temperature. Each of these techniques allows the thermal deformation in standard deviation of the height error to be reduced by an order of magnitude. As an example, for the LCLS-II-HE Dynamic X-ray Scattering instrument, the criteria on thermal deformation of a high-heat-load monochromator crystal can be achieved for a 100 W SASE FEL beam. Wavefront propagation simulations confirm that the reflected beam intensity profile is satisfactory on both the peak power density and focused beam size.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Risk-Aware Framework Development for Disruption Prediction: Alcator C-Mod and DIII-D Survival Analysis

Abstract Survival regression models can achieve longer warning times at similar receiver operating characteristic performance than previously investigated models. Survival regression models are also shown to predict the time until a disruption will occur with lower error than other predictors. Time-to-event predictions from time-series data can be obtained with a survival analysis statistical framework, and there have been many tools developed for this task which we aim to apply to disruption prediction. Using the open-source Auton-Survival package we have implemented disruption predictors with the survival regression models Cox Proportional Hazards, Deep Cox Proportional Hazards, and Deep Survival Machines. To compare with previous work, we also include predictors using a Random Forest binary classifier, and a conditional Kaplan-Meier formalism. We benchmarked the performance of these five predictors using experimental data from the Alcator C-Mod and DIII-D tokamaks by simulating alarms on each individual shot. We find that developing machine-relevant metrics to evaluate models is an important area for future work. While this study finds cases where disruptive conditions are not predicted, there are instances where the desired outcome is produced. Giving the plasma control system the expected time-to-disruption will allow it to determine the optimal actuator response in real time to minimize risk of damage to the device.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Long-term nitrogen dioxide exposure assessment using back-extrapolation of satellite-based land-use regression models for Australia

Highlights: • We assessed how well a year-2006 satellite-based LUR model captures historical NO{sub 2}. • We used three methods to estimate annual mean NO{sub 2} during 1990–2005. • We measured their performance using standard LUR validation techniques. • Back-extrapolated 2006 levels captured up to 76% of spatial variability (90–05). Assessing historical exposure to air pollution in epidemiological studies is often problematic because of limited spatial and temporal measurement coverage. Several methods for modelling historical exposures have been described, including land-use regression (LUR). Satellite-based LUR is a recent technique that seeks to improve predictive ability and spatial coverage of traditional LUR models by using satellite observations of pollutants as inputs to LUR. Few studies have explored its validity for assessing historical exposures, reflecting the absence of historical observations from popular satellite platforms like Aura (launched mid-2004). We investigated whether contemporary satellite-based LUR models for Australia, developed longitudinally for 2006–2011, could capture nitrogen dioxide (NO{sub 2}) concentrations during 1990–2005 at 89 sites around the country. We assessed three methods to back-extrapolate year-2006 NO{sub 2} predictions: (1) ‘do nothing’ (i.e., use the year-2006 estimates directly, for prior years); (2) change the independent variable ‘year’ in our LUR models to match the years of interest (i.e., assume a linear trend prior to year-2006, following national average patterns in 2006–2011), and; (3) adjust year-2006 predictions using selected historical measurements. We evaluated prediction error and bias, and the correlation and absolute agreement of measurements and predictions using R{sup 2} and mean-square error R{sup 2} (MSE-R{sup 2}), respectively. We found that changing the year variable led to best performance; predictions captured between 41% (1991; MSE-R{sup 2} = 31%) and 80% (2003; MSE-R{sup 2} = 78%) of spatial variability in NO{sub 2} in a given year, and 76% (MSE-R{sup 2} = 72%) averaged over 1990–2005. We conclude that simple methods for back-extrapolating prior to year-2006 yield valid historical NO{sub 2} estimates for Australia during 1990–2005. These results suggest that for the time scales considered here, satellite-based LUR has a potential role to play in long-term exposure assessment, even in the absence of historical predictor data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Modal Field Reconstruction in Resonant Cavities in the Fundamental and Undermoded Frequency Regimes

Theory, simulations, and experiments are presented that demonstrate reconstruction of electromagnetic fields in a cavity from sparse probe measurements. Such techniques are often referred to as virtual sensing, allowing fields at unobserved locations to be predicted. These methods are appropriate for the fundamental and undermoded regimes, providing the ability to estimate fields (and shielding effectiveness) throughout an arbitrarily shaped cavity from a few judiciously spaced probes. A modal simulation method is implemented that allows the response of arbitrarily shaped cavities to be rapidly computed with respect to varying probe locations and slot parameters, enabling statistical analysis of probe placement on reconstruction performance. A cylindrical vessel with numerous probe holes is developed for experiments, referred to as Perforated Vessel 2 (PV2). Experiments are performed on the vessel with and without a steel box inside, where transmit power is delivered into the vessel either through probes (probe injection) or through slots using an external antenna (slot excitation). Simulations and experiments illustrate that when the number of probes is minimal (equal to the number of mode coefficients to be estimated at each frequency), probe placement is critical to avoid missed peaks and to have acceptable reconstruction error. Probe placement becomes less important as the number of probes is increased, but care is still required to avoid probe locations giving poor performance.

42 ENGINEERING↗