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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness

The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show limitations for such problems, especially when the size of the training data is limited. To address these diculties, we have developed a general framework of constructing surrogate models on spaces of stochastic input with arbitrary probability measure irrespective of the mutual dependencies between individual components of the random inputs and the analytical form. The present Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework includes a data-driven construction of multivariate polynomial basis for arbitrary mutually dependent probability measure and a sparsity enhancement rotation procedure. This sparsity-enhancing rotation method was initially proposed in our previous work [1] for Gaussian density distributions, which may not be feasible for non-Gaussian distributions due to the loss of orthogonality after the rotation. To remedy such diculties, we developed a new data-driven approach to construct orthonormal polynomials for polynomials for arbitrary mutually dependent (amdP) randomness, ensuring the constructed basis maintains the orthogonality/near-orthogonality with respect to the density of the rotated random vector, where directly applying the regular polynomial chaos including arbitrary polynomial chaos (aPC) [2] shows limitations due to the assumption of the mutual independence between the components of the random inputs. The developed DSRAR framework leads to accurate recovery, with only limited training data, of a sparse representation of the target functions. The eectiveness of our method is demonstrated in challenging problems such as PDEs and realistic molecular systems within high-dimensional conformational space (O(10)) where the underlying density is implicitly represented by a large collection of sample data, as well as systems with explicitly given non-Gaussian probabilistic measures.

Lei, Huan↗
DOE OSTI2012

Compressed sensing for phase contrast CT

Modern x-ray techniques opened the possibility to retrieve phase information. Phase-contrast computed tomography (PCCT) has the potential to significantly improve soft tissue contrast. Radiation dose, however, continues to be an issue when moving from bench to bedside. Dose reduction in this work is achieved by sparsely acquiring PCCT data. To compensate for appearing aliasing artifacts we introduce a compressed sensing (CS) reconstruction framework. We present the feasibility of CS on PCCT with numerical as well as measured phantom data. The results proof that CS compensates for under-sampling artifacts and maintains the superior soft tissue contrast and detail visibility in the reconstructed images.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Reconstructing high-dimensional Hilbert-valued functions via compressed sensing

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our theoretical framework treats the function approximation problem as a joint sparse recovery problem, where the set of jointly sparse vectors is possibly infinite. To achieve the simultaneous reconstruction of Hilbert-valued functions in both parametric domain and Hilbert space, we propose a novel mixed-norm based `1 regularization method that exploits both energy and sparsity. Our approach requires extensions of concepts such as the restricted isometry and null space properties, allowing us to prove recovery guarantees for sparse Hilbert-valued function reconstruction. We complement the enclosed theory with an algorithm for Hilbert-valued recovery, based on standard forward-backward algorithm, meanwhile establishing its strong convergence in the considered infinite-dimensional setting. Finally, we demonstrate the minimal sample complexity requirements of our approach, relative to other popular methods, with numerical experiments approximating the solutions of high-dimensional parameterized elliptic PDEs.

Dexter, Nick↗
DOE OSTI2016

Cadmium and mercury exposure over time in Swedish children

Purpose: Knowledge about changes in exposure to toxic metals over time remains very sparse, in particular for children, the most vulnerable group. Here, we assessed whether a reduction in environmental pollution with cadmium (Cd) and mercury (Hg) caused a change in exposure over time. In total, 1257 children (age 4–9) in two towns in Sweden were sampled once in 1986–2013. Blood concentrations of Cd (b-Cd; n=1120) and Hg (b-Hg; n=560) were determined. Results: The median b-Cd was 0.10 (geometric mean 0.10; range 0.010–0.61) μg/L and b-Hg was 0.91 (geometric mean 0.83; range 0.021–8.2) μg/L. Children living close to a smelter had higher b-Cd and b-Hg than those in urban and rural areas. There was no sex difference in b-Cd or b-Hg, and b-Cd and b-Hg showed no significant accumulation by age. b-Cd decreased only slightly (0.7% per year, p<0.001) over the study period. In contrast, b-Hg did show a clear decrease over the study period (3% per year, p<0.001). Conclusions: The exposure to Cd was very low but still might increase the risk of disease later in life. Moreover, b-Cd only showed a minor decrease, indicating that Cd pollution should be further restricted. b-Hg was relatively low and decreasing, probably because of reduced use of dental amalgam and lower Hg intake from fish. The b-Cd and b-Hg levels decreased much less than the levels of lead in the blood as previously found in the same children. - Highlights: • There are few studies of time trends for exposure to toxic metals, except for lead. • 1986–2013 we studied blood levels of cadmium and mercury in 1257 Swedish children. • The median blood concentration of cadmium was 0.10 μg/L, of mercury 0.83 μg/L. • Cadmium perhaps decreased by 0.7% per year, mercury by 3% per year. • Cadmium accumulation may result in toxic levels in elderly women.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles

Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do not provide uncertainty estimates, which are crucial for establishing the trustworthiness of these techniques in downstream decision making tasks and scenarios. In recent years, ensemble-based methods have achieved significant success for the uncertainty quantification in DNNs on a number of benchmark problems. However, their performance on real-world applications remains under-explored. In this work, we present an automated approach to DNN discovery and demonstrate how this may also be utilized for ensemble-based uncertainty quantification. Specifically, we propose the use of a scalable neural and hyperparameter architecture search for discovering an ensemble of DNN models for complex dynamical systems. We highlight how the proposed method not only discovers high-performing neural network ensembles for our tasks, but also quantifies uncertainty seamlessly. This is achieved by using genetic algorithms and Bayesian optimization for sampling the search space of neural network architectures and hyperparameters. Subsequently, a model selection approach is used to identify candidate models for an ensemble set construction. Afterwards, a variance decomposition approach is used to estimate the uncertainty of the predictions from the ensemble. We demonstrate the feasibility of this framework for two tasks — forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature. In conclusion, we demonstrate superior performance from the ensemble in contrast with individual high-performing models and other benchmarks.

Deep ensembles↗
DOE OSTI2020

Active Learning A Neural Network Model For Gold Clusters & Bulk From Sparse First Principles Training Data

Small metal clusters are of fundamental scientific interest and of tremendous significance in catalysis. These nanoscale clusters display diverse geometries and structural motifs depending on the cluster size; a knowledge of this size-dependent structural motifs and their dynamical evolution has been of longstanding interest. Given the high computational cost of first-principles calculations, molecular modeling and atomistic simulations such as molecular dynamics (MD) has proven to be an important complementary tool to aid this understanding. Classical MD typically employ predefined functional forms which limits their ability to capture such complex size-dependent structural and dynamical transformation. Neural Network (NN) based potentials represent flexible alternatives and in principle, well-trained NN potentials can provide high level of flexibility, transferability and accuracy on-par with the reference model used for training. A major challenge, however, is that NN models are interpolative and requires large quantities (similar to 10 4 or greater) of training data to ensure that the model adequately samples the energy landscape both near and far-from-equilibrium. A highly desirable goal is minimize the number of training data, especially if the underlying reference model is first-principles based and hence expensive. In this work, we introduce an active learning (AL) scheme that trains a NN model on-the-fly with minimal amount of first-principles based training data. Our AL workflow is initiated with a sparse training dataset (similar to 1 to 5 data points) and is updated on-the-fly via a Nested Ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and updates the training pool to improve the network performance. Using a representative system of gold clusters, we demonstrate that our AL workflow can train a NN with similar to 500 total reference calculations. Using an extensive DFT test set of similar to 1100 configurations, we show that our AL-NN is able to accurately predict both the DFT energies and the forces for clusters of a myriad of different sizes. Our NN predictions are within 30 meV/atom and 40 meV/angstrom of the reference DFT calculations. Moreover, our AL-NN model also adequately captures the various size-dependent structural and dynamical properties of gold clusters in excellent agreement with DFT calculations and available experiments. We finally show that our AL-NN model also captures bulk properties reasonably well, even though they were not included in the training data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Machine learning-based surrogate modeling for data-driven optimization: a comparison of subset selection for regression techniques

Optimization of simulation-based or data-driven systems is a challenging task, which has attracted significant attention in the recent literature. A very efficient approach for optimizing systems without analytical expressions is through fitting surrogate models. Due to their increased flexibility, nonlinear interpolating functions, such as radial basis functions and Kriging, have been predominantly used as surrogates for data-driven optimization; however, these methods lead to complex nonconvex formulations. Alternatively, commonly used regression-based surrogates lead to simpler formulations, but they are less flexible and inaccurate if the form is not known a priori. In this work, we investigate the efficiency of subset selection regression techniques for developing surrogate functions that balance both accuracy and complexity. Subset selection creates sparse regression models by selecting only a subset of original features, which are linearly combined to generate a diverse set of surrogate models. Five different subset selection techniques are compared with commonly used nonlinear interpolating surrogate functions with respect to optimization solution accuracy, computation time, sampling requirements, and model sparsity. Furthermore, our results indicate that subset selection-based regression functions exhibit promising performance when the dimensionality is low, while interpolation performs better for higher dimensional problems.

42 ENGINEERING↗
DOE OSTI2013

Reweighted ℓ{sub 1} minimization method for stochastic elliptic differential equations

We consider elliptic stochastic partial differential equations (SPDEs) with random coefficients and solve them by expanding the solution using generalized polynomial chaos (gPC). Under some mild conditions on the coefficients, the solution is “sparse” in the random space, i.e., only a small number of gPC basis makes considerable contribution to the solution. To exploit this sparsity, we employ reweighted l{sub 1} minimization to recover the coefficients of the gPC expansion. We also combine this method with random sampling points based on the Chebyshev probability measure to further increase the accuracy of the recovery of the gPC coefficients. We first present a one-dimensional test to demonstrate the main idea, and then we consider 14 and 40 dimensional elliptic SPDEs to demonstrate the significant improvement of this method over the standard l{sub 1} minimization method. For moderately high dimensional (∼10) problems, the combination of Chebyshev measure with reweighted l{sub 1} minimization performs well while for higher dimensional problems, reweighted l{sub 1} only is sufficient. The proposed approach is especially suitable for problems for which the deterministic solver is very expensive since it reuses the sampling results and exploits all the information available from limited sources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ 1 regularization

Over the last decade or so, reconstruction methods using ℓ 1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ 1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ 1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images – even those for which TV was designed for – particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. In conclusion, we develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Enhanced detection of paramagnetic fluorine-19 magnetic resonance imaging agents using zero echo time sequence and compressed sensing

Fluorine-19 ( 19 F) magnetic resonance imaging (MRI) is an emerging technique offering specific detection of labeled cells in vivo. Lengthy acquisition times and modest signal-to-noise ratio (SNR) makes three-dimensional spin-density–weighted 19 F imaging challenging. Recent advances in tracer paramagnetic metallo-perfluorocarbon (MPFC) nanoemulsion probes have shown multifold SNR improvements due to an accelerated 19 F T 1 relaxation rate and a commensurate gain in imaging speed and averages. However, 19 F T 2 -reduction and increased linewidth limit the amount of metal additive in MPFC probes, thus constraining the ultimate SNR. To overcome these barriers, we describe a compressed sampling (CS) scheme, implemented using a “zero” echo time (ZTE) sequence, with data reconstructed via a sparsity-promoting algorithm. Our CS-ZTE scheme acquires k-space data using an undersampled spherical radial pattern and signal averaging. Image reconstruction employs off-the-shelf sparse solvers to solve a joint total variation and -norm regularized least square problem. To evaluate CS-ZTE, we performed simulations and acquired 19 F MRI data at 11.7 T in phantoms and mice receiving MPFC-labeled dendritic cells. For MPFC-labeled cells in vivo, we show SNR gains of ~6.3 × with 8-fold undersampling. We show that this enhancement is due to three mechanisms including undersampling and commensurate increase in signal averaging in a fixed scan time, denoising attributes from the CS algorithm, and paramagnetic reduction of T 1 . Importantly, 19 F image intensity analyses yield accurate estimates of absolute quantification of 19 F spins. Overall, the CS-ZTE method using MPFC probes achieves ultrafast imaging, a substantial boost in detection sensitivity, accurate 19 F spin quantification, and minimal image artifacts.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Uncertainty and Sensitivity Analysis of TREAT Transient Test #15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS) [1]. This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test #15 [2]. In this summary, we employ the Sobol sampling strategy implemented in RAVEN [3] to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest [4]. The gPC coefficients are then computed via the spectral projection method with sparse grid approach. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Machine learning-based inversion for acoustic impedance with large synthetic training data: Workflow and data characterization

Where wells are sparse or training data are difficult to label with high-quality wireline-derived impedance logs, machine learning (ML)-based inversion of acoustic impedance typically depends on small training data sets, leading to biased prediction. We have advanced a novel workflow that applies large synthetic seismic training data to reduce facies-related bias. Using a geologically realistic model as the truth model, we randomly select sparse seed wells to perform sequential Gaussian simulation (SGS) for impedance models of the same geometry and simulate facies variability. We implement random forest regression on 30 features extracted from the synthetic volume. We observe that more seed wells tend to reduce facies-induced bias by sampling more types of facies, resulting in a better prediction. We then focus on the responses of SGS models to facies changes, the number of seed wells necessary for a useful synthetic model, and how much a synthetic model can help ML-based inversion. Here, we observe that the SGS synthetic training model outperforms well-direct training in general. For modeled clastic shore-zone systems in Miocene Gulf of Mexico, two or more seed wells are necessary for a significant reduction of root-mean-square error and outliners, and improvement of facies imaging. In a field-data test, we apply a similar workflow to quantitatively predict acoustic impedance, which is then converted to a sand-volume map at a high-frequency sequence (10–100 m), revealing detailed facies and sandstone patterns. Such results are valuable in many geologic and engineering applications, such as hydrocarbon and CO 2 reservoir prospecting, reserve estimation, simulation, etc.

3D seismic↗
DOE OSTI2016

Reducing Computation and Communication in Scientific Computing: Connecting Theory to Practice.

This report summarizes the work produced as part of a Truman Fellowship appointment and its associated LDRD project. The overall goal of the project was to develop better algorithms and implementations for key computational kernels within the field of scientific computing by designing them to be communication efficient, moving as little data as possible. The primary problem of interest was dense matrix multiplication; other computations that were addressed include sparse matrix-matrix multiplication, QR factorization, solving symmetric linear systems, and the symmetric eigendecomposition. The project also involved the study of computations at the intersection of scientific computing and data analysis, including nonnegative matrix factorization for discovering latent factors, Tucker tensor decomposition for data compression, and sampling methods for similarity search.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

On compositional variations among lunar anorthosites

Ferroan anorthosite (FAN) is the most abundant 'pristine' highlands igneous rock in the Apollo sample collection. The presence of substantial FAN in the lunar crust is one argument used in favor of a global magma ocean on which crystallizing plagioclase could float. Information about the composition of the proposed magma ocean or whatever liquids might have been parental to FAN is sparse. As a first step toward learning about the nature of the FAN parent and the processes by which FAN attained its compositional characteristics, attention is given to the concentrations for a number of major and trace elements whose behavior during magmatic processes is somewhat understood. Serious difficulties are found with both FAN and the Marcy anorthosite in interpreting incompatible trace element concentrations in the plagioclases or the whole rocks in terms of residues from parent liquids. A description is presented of the nature of these difficulties.

Haskin, L. A.↗
DOE OSTI2011

Small-Footprint Lidar Estimations of Sagebrush Canopy Characteristics

Separating lidar returns for use in determining canopy height and shape in low-height vegetation is difficult because the vegetation canopy return is often close to the ground return in time and space. In addition, height underestimation is likely exacerbated in sparsely vegetated shrub ecosystems. This study compares lidar point-cloud data to sagebrush canopy characteristics measured in the field. It was determined that cumulative prediction error could account for as much as 35.6% of the average height and 37.4% of the average canopy area of shrubs sampled. When scaling from the individual shrub scale to coarser scales, prediction error averaged over a number of shrubs decreases as observation numbers increase. High density (in this case an average of 9.46 returns per m2), small footprint lidar (in this case a footprint diameter of 18 cm at nadir) may provide sufficient accuracy for characterizing sagebrush structure and cover and estimating biomass across landscapes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Imaging electronic trap states in perovskite thin films with combined fluorescence and femtosecond transient absorption microscopy

Charge carrier trapping degrades the performance of organometallic halide perovskite solar cells. To characterize the locations of electronic trap states in a heterogeneous photoactive layer, a spatially resolved approach is essential. Here, we report a comparative study on methylammonium lead tri-iodide perovskite thin films subject to different thermal annealing times using a combined photoluminescence (PL) and femtosecond transient absorption microscopy (TAM) approach to spatially map trap states. This approach coregisters the initially populated electronic excited states with the regions that recombine radiatively. Although the TAM images are relatively homogeneous for both samples, the corresponding PL images are highly structured. The remarkable variation in the PL intensities as compared to transient absorption signal amplitude suggests spatially dependent PL quantum efficiency, indicative of trapping events. Furthermore, detailed analysis enables identification of two trapping regimes: a densely packed trapping region and a sparse trapping area that appear as unique spatial features in scaled PL maps.

36 MATERIALS SCIENCE↗