Search NASA⌕ Search

SEARCH · Search NASA

Results for “Unbiased estimator”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r 2 SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r 2 SCAN-D3. Our results show that r 2 SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Memarsadeghi, Nargess↗
NASA NTRSDate not supplied

Uncertainty Reduction With Multi-Model Monte Carlo for Crystal Plasticity Simulations of Additively Manufactured Metals

In this work, multi-model Monte Carlo estimators are developed to reduce uncertainty in quantities of interest (QoIs) extracted from crystal plasticity simulations of additively manufactured (AM) metals. A significant concern in AM parts is uncertainty in mechanical properties caused in part by complex microstructures that arise from the AM process. Quantifying uncertainty in microstructure-sensitive behavior using experiments alone is costly, especially when mechanical allowables must be established. Quantitative relationships among microstructure, micromechanical metrics like slip accumulation, crack initiation, and failure are also difficult to capture with limited experiments. Crystal plasticity material models instead enable computational prediction of micromechanical stress and strain fields given a discretized microstructure. However, high-fidelity finely discretized crystal plasticity simulations are computationally expensive, while lower-fidelity models are less accurate and generally biased, making uncertainty quantification and reduction computationally difficult as well. Multi-model Monte Carlo methods leverage correlations between high- and low-fidelity models to produce unbiased estimators for QoIs with reduced uncertainty relative to standard Monte Carlo. Crystal plasticity QoIs considered in this work include yield strength and the mean and extreme values of micromechanical fields that are relevant to crack initiation. Multi-model Monte Carlo estimators are developed for each individual QoI and several groups of QoIs. The results of this work establish relationships among model correlations, sample allocation, and uncertainty reduction for different combinations of QoIs and demonstrate a trend of less uncertainty reduction as QoIs become more sensitive to local microstructure. Limitations from using pilot samples to estimate model covariances and train low-fidelity models are also addressed. The uncertainty reduction achieved by multi-model Monte Carlo is an important step toward using computational mechanics models to predict microstructure-sensitive crack initiation and failure in AM parts.

uncertainty quantification↗
DOE OSTI2024

On the connection between least squares, regularization, and classical shadows

Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS ``shadows'' completely analogous to those in CS---namely, point estimators calculated from the empirical frequencies of single measurements---we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies---differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying ``shadow'' umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Estimating the local dark matter density in a non-axisymmetric wobbling disc

The density of dark matter near the Sun, ρDM, ⊙, is important for experiments hunting for dark matter particles in the laboratory, and for constraining the local shape of the Milky Way’s dark matter halo. Estimates to date have typically assumed that the Milky Way’s stellar disc is axisymmetric and in a steady-state. Yet the Milky Way disc is neither, exhibiting prominent spiral arms and a bar, and vertical and radial oscillations. Here, we assess the impact of these assumptions on determinations of ρDM, ⊙ by applying a free-form, steady-state, Jeans method to two different N-body simulations of Milky Way-like galaxies. In one, the galaxy has experienced an ancient major merger, similar to the hypothesized Gaia–Sausage–Enceladus; in the other, the galaxy is perturbed more recently by the repeated passage and slow merger of a Sagittarius-like dwarf galaxy. We assess the impact of each of the terms in the Jeans–Poisson equations on our ability to correctly extract ρDM, ⊙ from the simulated data. We find that common approximations employed in the literature – axisymmetry and a locally flat rotation curve – can lead to significant systematic errors of up to a factor ~1.5 in the recovered surface mass density ~2 kpc above the disc plane, implying a fractional error on ρDM, ⊙ of the order of unity. However, once we add in the tilt term and the rotation curve term in our models, we obtain an unbiased estimate of ρDM, ⊙, consistent with the true value within our 95 percent confidence intervals for realistic 20 percent uncertainties on the baryonic surface density of the disc. Other terms – the axial tilt, 2nd Poisson and time-dependent terms – contribute less than 10 percent to ρDM, ⊙ (given current data) and can be safely neglected for now. In the future, as more data become available, these terms will need to be included in the analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Unbiased primordial gravitational wave inference from the CMB with SMICA

The detection of primordial gravitational waves in Cosmic Microwave Background B-mode polarization observations requires accurate and robust subtraction of astrophysical contamination. We show, using a blind Spectral Matching Independent Component Analysis, that it is possible to infer unbiased estimates of the primordial B-mode signal from ground-based observations of a small patch of sky even for highly complex foreground contamination. This work, originally performed in the context of configuration studies for a future CMB-S4 observatory, is highly relevant for the analysis of observations by the current generation of CMB experiments.

cosmological parameters from CMBR↗
DOE OSTI2023

Resource frugal optimizer for quantum machine learning

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Beyond mass: detecting secondary halo properties with galaxy-galaxy lensing

ABSTRACT Secondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter haloes. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, ΔΣ. We build an emulator trained on N-body simulations to model ΔΣ and quantify the impact of different secondary parameters on the ΔΣ profile. We focus on the impact of MAR on ΔΣ. We show that a 3σ detection of variations in MAR at fixed halo mass could be achieved with the Hyper Suprime Cam survey assuming no baryonic effects and a proxy for MAR with scatter <1.5. We show that the full radial profile of ΔΣ depends on secondary properties at fixed halo mass. Consequently, an emulator that can perform full shape fitting yields better than two times improvement upon the constraints on MAR than only using the outer part of the halo. Finally, we highlight that miscentring and MAR impact the radial profile of ΔΣ in a similar fashion, implying that miscentring and MAR need to be modelled jointly for unbiased estimates of both effects. We show that present-day lensing data sets have the statistical capability to place constraints on halo MAR within our assumptions. Our analysis opens up new possibilities for observationally measuring the assembly history of the dark matter haloes that host galaxies and clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Uniformly decaying subspaces for error-mitigated quantum computation

Here, we present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error-mitigated quantum computation. The expectation values of dynamics encoded in such subspaces are unbiased estimators of noise-free expectation values. In analogy to the decoherence free subspaces which are left invariant by the action of Lindblad operators, we show that the uniformly decaying subspaces are left invariant (up to orthogonal terms) by the action of the dissipative part of the Lindblad equation. We apply our theory to a system of qubits and qudits undergoing relaxation with varying decay rates and show that such subspaces can be used to eliminate bias up to first-order variations in the decay rates without requiring full knowledge of noise. Since such a bias cannot be corrected through standard symmetry verification, our method can improve error mitigation in dual-rail qubits and, given partial knowledge of noise, can perform better than probabilistic error cancellation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Linking Community‐Climate Disequilibrium to Ecosystem Function

Turnover in species composition often lags behind the pace of climate change, resulting in mismatches between climate and communities. However, the impact of these community‐climate disequilibria on ecosystem functions is rarely considered, and current methods for measuring disequilibria assume that species ranges were, until recently, in equilibrium with climate. Here, in this work, we develop a simple theoretical model to address both of these problems by linking community‐climate disequilibrium with ecosystem functioning. We show how disequilibrium can impair functioning in the near‐term even when climate change is expected to enhance functioning in the long‐term. Responses are most likely to change over time in communities where turnover is slow, the impact of disequilibrium counteracts the direct effects of climate on ecosystem function, and pre‐existing disequilibrium is large. These findings emphasise the importance of precise and unbiased estimates of community‐climate disequilibria for improving ecological forecasts. By fitting our model to time series of both climate and ecosystem function from a metacommunity simulation, we show the potential for community‐climate disequilibrium to be inferred without direct knowledge about species' distributions or climatic tolerances. We end by outlining a research agenda to apply dynamic disequilibrium concepts and test novel hypotheses across diverse ecosystems.

climate change↗
DOE OSTI2024

Creating Accurate Methane Emission Inventories through Data-Driven Airborne Survey Strategies: Methods and Results from the Haynesville, Anadarko, and Permian Basins

Significantly reducing methane emissions from the oil and gas sector can decrease the rate of climate change over the next two decades, buying critical time for a global energy transition. However, emissions inventories that can be used by oil and gas operators and environmental regulators to identify optimal methane emission mitigation strategies are either based on conservative emission factor methods, or are inconsistent between studies due to differences in sampling strategies or survey technologies. We developed a new approach for methane emissions survey design that yields representative basinwide methane emissions inventories by surveying a subset of total assets in a given oil and gas basin. We identify several sampling and analysis principles, including large sample sizes, balanced sampling across oil and gas production, careful survey area definition, and a unified protocol for analysis, to be vital to producing an unbiased estimate of basin-scale emissions that can be reconciled with future studies. We further present results from deploying this strategy in two oil and gas producing regions in the United States: the Haynesville Basin in Texas and Louisiana, and the Woodford Shale in the Anadarko Basin in Oklahoma. Aerial surveys were performed in 2023 using the Insight M LeakSurveyor™ technology. Preliminary results from methane emissions detected by Insight M indicate that aerially detected emissions above roughly 30 kg(CH4)/hr by themselves contribute a fractional loss rate of 1.13% of gross gas production across oil and gas operations in the Haynesville Basin, with aerially detected emissions equivalent to 2.67% of gross gas production in the Woodford Shale. We supplement these aerial estimates with modeled emissions that are below the LeakSurveyor’s survey sensitivity using a recently published inventory-based model of methane emissions, which we update for our survey areas. We then combine our aerial detections with modeled emissions to yield methane emission distributions and inventories that incorporate the full range of potential methane emissions from the smallest to the largest. These results can be used to identify the most effective methane mitigation strategies for our study areas, and can be reconciled with future methane emissions surveys that use different technologies.

Sherwin, Evan (ORCID:0000000321804297)↗
DOE OSTI2022

Integrating Deep Learning and Hydrodynamic Modeling to Improve the Great Lakes Forecast

The Laurentian Great Lakes, one of the world’s largest surface freshwater systems, pose a modeling challenge in seasonal forecast and climate projection. While physics-based hydrodynamic modeling is a fundamental approach, improving the forecast accuracy remains critical. In recent years, machine learning (ML) has quickly emerged in geoscience applications, but its application to the Great Lakes hydrodynamic prediction is still in its early stages. This work is the first one to explore a deep learning approach to predicting spatiotemporal distributions of the lake surface temperature (LST) in the Great Lakes. Our study shows that the Long Short-Term Memory (LSTM) neural network, trained with the limited data from hypothetical monitoring networks, can provide consistent and robust performance. The LSTM prediction captured the LST spatiotemporal variabilities across the five Great Lakes well, suggesting an effective and efficient way for monitoring network design in assisting the ML-based forecast. Furthermore, we employed an explainable artificial intelligence (XAI) technique named SHapley Additive exPlanations (SHAP) to uncover how the features impact the LSTM prediction. Our XAI analysis shows air temperature is the most influential feature for predicting LST in the trained LSTM. The relatively large bias in the LSTM prediction during the spring and fall was associated with substantial heterogeneity of air temperature during the two seasons. In contrast, the physics-based hydrodynamic model performed better in spring and fall yet exhibited relatively large biases during the summer stratification period. Finally, we developed a statistical integration of the hydrodynamic modeling and deep learning results based on the Best Linear Unbiased Estimator (BLUE). The integration further enhanced prediction accuracy, suggesting its potential for next-generation Great Lakes forecast systems.

Xue, Pengfei (ORCID:000000025702421X)↗
DOE OSTI2025

Measurement and Modeling of Polarized Atmosphere at the South Pole with SPT-3G

We present the detection and characterization of fluctuations in linearly polarized emission from the atmosphere above the South Pole. These measurements make use of data from the SPT-3G receiver on the South Pole Telescope in three frequency bands centered at 95, 150, and 220 GHz. We use the cross-correlation between detectors to produce an unbiased estimate of the power in Stokes I, Q, and U parameters on large angular scales. Our results are consistent with the polarized signal being produced by the combination of Rayleigh scattering of thermal radiation from the ground and thermal emission from a population of horizontally aligned ice crystals with an anisotropic distribution described by Kolmogorov turbulence. The measured spatial scaling, frequency scaling, and elevation dependence of the polarized emission are explained by this model. Polarized atmospheric emission has the potential to significantly impact observations on the large angular scales being targeted by searches for inflationary B-mode CMB polarization. We present the distribution of measured angular power spectrum amplitudes in Stokes Q and I for 4 yr of Austral winter observations, which can be used to simulate the impact of atmospheric polarization and intensity fluctuations at the South Pole on a specified experiment and observation strategy. We present a mitigation strategy that involves both downweighting significantly contaminated observations and subtracting a polarized atmospheric signal from the 150 GHz band maps. In observations with the SPT-3G instrument, the polarized atmospheric signal is a well-understood and subdominant contribution to the measured noise after implementing the mitigation strategies described here.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

Minimum variance system identification with application to digital adaptive flight control

A new on-line minimum variance filter for the identification of systems with additive and multiplicative noise is described which embodies both accuracy and computational efficiency. The resulting filter is shown to use both the covariance of the parameter vector itself and the covariance of the error in identification. A bias reduction scheme can be used to yield asymptotically unbiased estimates. Experimental results for simulated linearized lateral aircraft motion in a digital closed loop mode are presented, showing the utility of the identification schemes.

Kotob, S.↗
NASA NTRS1977

An improved digital algorithm for fast amplitude approximations of quadrature pairs

A computationally fast algorithm for approximating the amplitude (A) of a quadrature pair (I,Q) has been discovered. The piecewise linear formula, the unbiased estimate of A=X+1/8y when X or = 3Y and 7/8X + 1/2Y when X or = 3Y applies where X is congruent to the maximum absolute value of (I,Q) and Y is congruent to the minimum absolute value of (I,Q). This algorithm has been proven to be far more accurate then currently used approximations. An immediate application is the wideband digital spectrum analyzer under development for monitoring radio frequency interference at Deep Space Network stations.

Levitt, B. K.↗