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All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Trend Detection of Atmospheric Time Series: Incorporating Appropriate Uncertainty Estimates and Handling Extreme Events

This paper is aimed at atmospheric scientists without formal training in statistical theory. Its goal is to, 1) provide a critical review of the rationale for trend analysis of the time series typically encountered in the field of atmospheric chemistry; 2) describe a range of trend-detection methods; and 3) demonstrate effective means of conveying the results to a general audience. Trend detections in atmospheric chemical composition data are often challenged by a variety of sources of uncertainty, which often behave differently to other environmental phenomena such as temperature, precipitation rate, or stream flow, and may require specific methods depending on the science questions to be addressed. Some sources of uncertainty can be explicitly included in the model specification, such as autocorrelation and seasonality, but some inherent uncertainties are difficult to quantify, such as data heterogeneity and measurement uncertainty due to the combined effect of short- and long-term natural variability, instrumental stability, and aggregation of data from sparse sampling frequency. Failure to account for these uncertainties might result in an inappropriate inference of the trends and their estimation errors. On the other hand, the variation in extreme events might be interesting for different scientific questions, for example, the frequency of extremely high surface ozone events and their relevance to human health. In this study we aim to, 1) review trend detection methods for addressing different levels of data complexity in different chemical species; 2) demonstrate that the incorporation of scientifically interpretable covariates can outperform pure numerical curve fitting techniques in terms of uncertainty reduction and improved predictability; 3) illustrate the study of trends based on extreme quantiles that can provide insight beyond standard mean or median based trend estimates; and 4) present an advanced method of quantifying regional trends based on the inter-site correlations of multi-site data. All demonstrations are based on time series of observed trace gases relevant to atmospheric chemistry, but the methods can be applied to other environmental data sets.

Trace gas↗
NASA NTRSDate not supplied

Efficient Onboard Attitude Commanding for Fast Maneuvering of Lunar Reconnaissance Orbiter

To support Lunar Reconnaissance Orbiter’s extended science missions, an algorithm for autonomous optimization of fast occultation avoidance maneuvers was developed. The fast attitude maneuvers are inserted to the spacecraft attitude control system as trajectories to be tracked. Executing maneuvers in this way requires transmission and storage of a large number of time-tagged attitude waypoints on the spacecraft. For more efficient day-to-day operations, an interpolating filter was designed to perform onboard interpolation between sparse samples of commands. The interpolating filter – called FastXMan for efficient fast maneuvering – was patched into LRO’s flight software in late 2023 and is presently operational. This paper presents an overview of the issues related to the practical implementation of the filter and illustrates the flight performance of the new scheme.

Operations↗
DOE OSTI2012

Atmospheric PSF Interpolation for Weak Lensing in Short Exposure Imaging Data

A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ({approx_equal}15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, psfent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, psfent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than {approx} 13, compared to polynomial fitting. We estimate that with psfent and for stellar densities greater than {approx_equal}1/arcmin{sup 2}, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Sparse and Random Sampling Techniques for High-Resolution, Full-Field, BSS-Based Structural Dynamics Identification from Video

Video-based techniques for identification of structural dynamics have the advantage that they are very inexpensive to deploy compared to conventional accelerometer or strain gauge techniques. When structural dynamics from video is accomplished using full-field, high-resolution analysis techniques utilizing algorithms on the pixel time series such as principal components analysis and solutions to blind source separation the added benefit of high-resolution, full-field modal identification is achieved. An important property of video of vibrating structures is that it is particularly sparse. Typically video of vibrating structures has a dimensionality consisting of many thousands or even millions of pixels and hundreds to thousands of frames. However the motion of the vibrating structure can be described using only a few mode shapes and their associated time series. As a result, emerging techniques for sparse and random sampling such as compressive sensing should be applicable to performing modal identification on video. This work presents how full-field, high-resolution, structural dynamics identification frameworks can be coupled with compressive sampling. The techniques described in this work are demonstrated to be able to recover mode shapes from experimental video of vibrating structures when 70% to 90% of the frames from a video captured in the conventional manner are removed.

47 OTHER INSTRUMENTATION↗
DOE OSTI2011

Accelerated Gibbs Sampling for Infinite Sparse Factor Analysis

The Indian Buffet Process (IBP) gives a probabilistic model of sparse binary matrices with an unbounded number of columns. This construct can be used, for example, to model a fixed numer of observed data points (rows) associated with an unknown number of latent features (columns). Markov Chain Monte Carlo (MCMC) methods are often used for IBP inference, and in this technical note, we provide a detailed review of the derivations of collapsed and accelerated Gibbs samplers for the linear-Gaussian infinite latent feature model. We also discuss and explain update equations for hyperparameter resampling in a 'full Bayesian' treatment and present a novel slice sampler capable of extending the accelerated Gibbs sampler to the case of infinite sparse factor analysis by allowing the use of real-valued latent features.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditioned $\ell^1$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

TH-E-18A-01: Developments in Monte Carlo Methods for Medical Imaging

Monte Carlo simulation methods are widely used in medical physics research and are starting to be implemented in clinical applications such as radiation therapy planning systems. Monte Carlo simulations offer the capability to accurately estimate quantities of interest that are challenging to measure experimentally while taking into account the realistic anatomy of an individual patient. Traditionally, practical application of Monte Carlo simulation codes in diagnostic imaging was limited by the need for large computational resources or long execution times. However, recent advancements in high-performance computing hardware, combined with a new generation of Monte Carlo simulation algorithms and novel postprocessing methods, are allowing for the computation of relevant imaging parameters of interest such as patient organ doses and scatter-to-primaryratios in radiographic projections in just a few seconds using affordable computational resources. Programmable Graphics Processing Units (GPUs), for example, provide a convenient, affordable platform for parallelized Monte Carlo executions that yield simulation times on the order of 10{sup 7} xray/ s. Even with GPU acceleration, however, Monte Carlo simulation times can be prohibitive for routine clinical practice. To reduce simulation times further, variance reduction techniques can be used to alter the probabilistic models underlying the x-ray tracking process, resulting in lower variance in the results without biasing the estimates. Other complementary strategies for further reductions in computation time are denoising of the Monte Carlo estimates and estimating (scoring) the quantity of interest at a sparse set of sampling locations (e.g. at a small number of detector pixels in a scatter simulation) followed by interpolation. Beyond reduction of the computational resources required for performing Monte Carlo simulations in medical imaging, the use of accurate representations of patient anatomy is crucial to the virtual generation of medical images and accurate estimation of radiation dose and other imaging parameters. For this, detailed computational phantoms of the patient anatomy must be utilized and implemented within the radiation transport code. Computational phantoms presently come in one of three format types, and in one of four morphometric categories. Format types include stylized (mathematical equation-based), voxel (segmented CT/MR images), and hybrid (NURBS and polygon mesh surfaces). Morphometric categories include reference (small library of phantoms by age at 50th height/weight percentile), patient-dependent (larger library of phantoms at various combinations of height/weight percentiles), patient-sculpted (phantoms altered to match the patient's unique outer body contour), and finally, patient-specific (an exact representation of the patient with respect to both body contour and internal anatomy). The existence and availability of these phantoms represents a very important advance for the simulation of realistic medical imaging applications using Monte Carlo methods. New Monte Carlo simulation codes need to be thoroughly validated before they can be used to perform novel research. Ideally, the validation process would involve comparison of results with those of an experimental measurement, but accurate replication of experimental conditions can be very challenging. It is very common to validate new Monte Carlo simulations by replicating previously published simulation results of similar experiments. This process, however, is commonly problematic due to the lack of sufficient information in the published reports of previous work so as to be able to replicate the simulation in detail. To aid in this process, the AAPM Task Group 195 prepared a report in which six different imaging research experiments commonly performed using Monte Carlo simulations are described and their results provided. The simulation conditions of all six cases are provided in full detail, with all necessary data on material composition, source, geometry, scoring and other parameters provided. The results of these simulations when performed with the four most common publicly available Monte Carlo packages are also provided in tabular form. The Task Group 195 Report will be useful for researchers needing to validate their Monte Carlo work, and for trainees needing to learn Monte Carlo simulation methods. In this symposium we will review the recent advancements in highperformance computing hardware enabling the reduction in computational resources needed for Monte Carlo simulations in medical imaging. We will review variance reduction techniques commonly applied in Monte Carlo simulations of medical imaging systems and present implementation strategies for efficient combination of these techniques with GPU acceleration. Trade-offs involved in Monte Carlo acceleration by means of denoising and “sparse sampling” will be discussed. A method for rapid scatter correction in cone-beam CT (<5 min/scan) will be presented as an illustration of the simulation speeds achievable with optimized Monte Carlo simulations. We will also discuss the development, availability, and capability of the various combinations of computational phantoms for Monte Carlo simulation of medical imaging systems. Finally, we will review some examples of experimental validation of Monte Carlo simulations and will present the AAPM Task Group 195 Report. Learning Objectives: Describe the advances in hardware available for performing Monte Carlo simulations in high performance computing environments. Explain variance reduction, denoising and sparse sampling techniques available for reduction of computational time needed for Monte Carlo simulations of medical imaging. List and compare the computational anthropomorphic phantoms currently available for more accurate assessment of medical imaging parameters in Monte Carlo simulations. Describe experimental methods used for validation of Monte Carlo simulations in medical imaging. Describe the AAPM Task Group 195 Report and its use for validation and teaching of Monte Carlo simulations in medical imaging.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation

Many material and biological samples in scientific imaging are characterized by nonlocal repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a two-dimensional image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, can enable high speed data acquisition and minimize sample damage caused by the electron beam. In this paper, we present an algorithm for electron tomographic reconstruction and sparse image interpolation that exploits the nonlocal redundancy in images. We adapt a framework, termed plug-and-play priors, to solve these imaging problems in a regularized inversion setting. The power of the plug-and-play approach is that it allows a wide array of modern denoising algorithms to be used as a “prior model” for tomography and image interpolation. We also present sufficient mathematical conditions that ensure convergence of the plug-and-play approach, and we use these insights to design a new nonlocal means denoising algorithm. Finally, we demonstrate that the algorithm produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods.

47 OTHER INSTRUMENTATION↗
DOE OSTI2015

Application of High Performance Computing for Studying Cyclic Variability in Dilute Internal Combustion Engines

Combustion instabilities in dilute internal combustion engines are manifest in cyclic variability (CV) in engine performance measures such as integrated heat release or shaft work. Understanding the factors leading to CV is important in model-based control, especially with high dilution where experimental studies have demonstrated that deterministic effects can become more prominent. Observation of enough consecutive engine cycles for significant statistical analysis is standard in experimental studies but is largely wanting in numerical simulations because of the computational time required to compute hundreds or thousands of consecutive cycles. We have proposed and begun implementation of an alternative approach to allow rapid simulation of long series of engine dynamics based on a low-dimensional mapping of ensembles of single-cycle simulations which map input parameters to output engine performance. This paper details the use Titan at the Oak Ridge Leadership Computing Facility to investigate CV in a gasoline direct-injected spark-ignited engine with a moderately high rate of dilution achieved through external exhaust gas recirculation. The CONVERGE™ CFD software was used to perform single-cycle simulations with imposed variations of operating parameters and boundary conditions selected according to a sparse grid sampling of the parameter space. Using an uncertainty quantification technique, the sampling scheme is chosen similar to a design of experiments grid but uses algorithms designed to minimize the number of samples required to achieve a desired degree of accuracy. The simulations map input parameters to output metrics of engine performance for a single cycle, and by mapping over a large parameter space, results can be interpolated from within that space. This interpolation scheme forms the basis for a low-dimensional ‘metamodel’ (or model of a model) which can be used to mimic the dynamical behavior of corresponding high-dimensional simulations. Simulations of high-EGR spark-ignition combustion cycles within a parametric sampling grid were performed and analyzed statistically, and sensitivities of the physical factors leading to high CV are presented. With these results, the prospect of producing low-dimensional metamodels to describe engine dynamics at any point in the parameter space will be discussed. Additionally, modifications to the methodology to account for nondeterministic effects in the numerical solution environment are proposed.

Finney, Charles E. A.↗
NASA NTRS1995

Extracting Periodic Signals From Irregularly Sampled Data

Successive approximations formed in Fourier space. Algorithm extracts periodic signals from sparse, irregularly sampled sets of measurement data. Pertains to data processed via fast Fourier transforms (FFTs). Data represents signal components with initially unknown frequencies spanning large spectral range and includes frequencies not integer multiples of minimum FFT frequency.

Wilcox, Jaroslava Z.↗
DOE OSTI2026

Improving statistical precision in Monte Carlo samples with negative weights via reweighting and uncertainty quantification

High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight distributions of any sample, allowing the reduction of statistical uncertainty by reweighting kinematically equivalent events with the same sign. A robust uncertainty quantification method is required for the practical application of such method. Two methods for the estimation of the reweighting uncertainty are developed: one at the event and another one at the final observable level. The latter method is strongly favored. The gains in statistical precision are then quantified. The method is demonstrated on Sherpa vector boson plus jets samples when using all generated events and when restricted to the signal region of a mock analysis. It is demonstrated to significantly reduce stochastic behavior in sparse MC samples while decreasing the overall uncertainty with a sufficiently well-known reweighting function.

Monte Carlo methods↗
DOE OSTI2013

Mineral Association Changes the Secondary Structure and Dynamics of Murine Amelogenin

Biomineralization proteins, present during the formation of hard tissues including bones, teeth, egg shells and nacre, result in the exquisite structures and properties of the resulting materials.[1] The structure of these proteins is often implicated in the control of the mineral properties, however very little structural data is available for the bulk of these proteins due to the difficulty in determining structures of immobilized proteins. Solid-state NMR is uniquely suited to the study of the structure of proteins bound to surfaces, demonstrated with the structural and orientation insights provided for the hydroxyapatite mineralization proteins statherin and the amelogenin, LRAP.[2] While these data are some of the only structural data available for this important class of protein, the experiments are often expensive and time consuming, due to the need to prepare and measure samples with isolated spin pairs, and are limited to a size of ~60 residues. In this work, we utilized a combination of 1D and recent 2D[3] solid-state NMR techniques along with a sparsely labelled sample to characterize the structure and dynamics of potential HAP binding residues of the 180 residue enamel protein, amelogenin. Amelogenin nanospheres and mineral bound amelogenin were investigated and a shift from unstructured to β-sheet structure was observed, along with a decrease in protein flexibility. This work provides the first molecular level structure and dynamic information of full-length amelogenin on the surface of hydroxyapatite (HAP) and within nanospheres, and demonstrates the ability to evaluate structural characteristics of large biomineralization proteins bound to their physiologically relevant surface. The research was performed at the Pacific Northwest National Laboratory (PNNL), a facility operated by Battelle for the U.S. Department of Energy, with a portion of it performed at the W.R. Wiley Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the U.S. DOE Biological and Environmental Research program.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1995

Multiwavelength monitoring of the BL Lacertae object PKS 2155-304. 4: Multiwavelength analysis

Simultaneous X-ray, ultraviolet, optical, infrared, and radio monitoring data were used to test and constrain models of continuum emission from the BL Lacertae object PKS 2155-304. Intensively sampled ultraviolet and soft X-ray light curves showed a clear temporal correlation with the X-rays leading the ultraviolet by 2-3 hr. This lag was found to be significantly different from zero after an exhaustive comparison of four different techniques for measuring temporal correlations. Variations in the ultraviolet trough optical wave bands were also strongly correlated, with no measurable lag down to limiting timescales of approximately less than 1-2 hr. This strong correlation extends to the near-infrared, but the less intensive sampling precludes measurement of any lag beyomnd an upper limit of approximately less than 1 day. These lags and limits of the order of hours are much shorter than most rapid observed single-band variations. Because of the very sparse radio sampling, it was not possible to measure quantitatively the correlation and lag with shorter wavelengths, but the data do suggest that the radio may lag the optical/ultraviolet by approximately 1 week, with longer delays and weaker variations to longer radio wavelengths. The epoch-folding Q(exp 2) statistic was used to test for periodicity, and no evidence for strict or quasi-periodicity was found in any of the light curves. Because they lead the lower frequencies, the soft X-rays (approximately less than 1 keV) cannot arise from synchrotron self-Compton scattering. These results also rule out the accretion disk model, which predicts a measurable lag between ultraviolet/optical wavelength bands and a correlation between hardness and brightness, neither of which were seen. They are consistent with the entire radio through X-ray continuum arising from direct synchrotron emission from a relativistic jet. However, the tapered jet model, in which the X-ray emission is produced closer in, has problems explaining the magnitude of the ultraviolet/X-ray lag, because the X-ray-emitting electrons have very short lifetimes (t(sub 1/2) much less than 1 s). The result that the lag is much smaller than the variability timescale suggests instead that the radiation may be produced in a flattened region such as a shock front.

Edelson, R.↗
DOE OSTI2019

Randomized methods to characterize large-scale vortical flow networks

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Sparsifying priors for Bayesian uncertainty quantification in model discovery

We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.

97 MATHEMATICS AND COMPUTING↗