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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Uncertainty and Sensitivity Analysis of TREAT Transient Test no. 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). This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test no. 15. In this summary, we employ the Sobol sampling strategy implemented in RAVEN 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. The gPC coefficients are then computed via the sparse grid spectral projection method. 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.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Pushing the size limit of de novo structure ensemble prediction guided by sparse SDSL-EPR restraints to 200 residues: The monomeric and homodimeric forms of BAX

Structure determination remains a challenge for many biologically important proteins. In particular, proteins that adopt multiple conformations often evade crystallization in all biologically relevant states. Although computational de novo protein folding approaches often sample biologically relevant conformations, the selection of the most accurate model for different functional states remains a formidable challenge, in particular, for proteins with more than about 150 residues. Electron paramagnetic resonance (EPR) spectroscopy can obtain limited structural information for proteins in well-defined biological states and thereby assist in selecting biologically relevant conformations. The present study demonstrates that de novo folding methods are able to accurately sample the folds of 192-residue long soluble monomeric Bcl-2-associated X protein (BAX). The tertiary structures of the monomeric and homodimeric forms of BAX were predicted using the primary structure as well as 25 and 11 EPR distance restraints, respectively. The predicted models were subsequently compared to respective NMR/X-ray structures of BAX. EPR restraints improve the protein-size normalized root-mean-square-deviation (RMSD100) of the most accurate models with respect to the NMR/crystal structure from 5.9 Å to 3.9 Å and from 5.7 Å to 3.3 Å, respectively. Additionally, the model discrimination is improved, which is demonstrated by an improvement of the enrichment from 5% to 15% and from 13% to 21%, respectively.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Sparse optimization of two-dimensional terahertz spectroscopy

Two-dimensional terahertz spectroscopy (2DTS) is a low-frequency analog of two-dimensional optical spectroscopy that is rapidly maturing as a probe of a wide variety of condensed matter systems. However, a persistent problem with 2DTS is the long experimental acquisition times, which prevent its broader adoption. A potential solution, requiring no increase in experimental complexity, is signal reconstruction via compressive sensing. In this work, we apply the sparse exponential mode analysis (SEMA) technique to 2DTS of a cuprate superconductor. We benchmark the performance of the algorithm in reconstructing terahertz nonlinearities and find that SEMA reproduces the asymmetric photon echo line shapes at sampling rates as low as 10%, reaching the reconstruction noise floor at sampling rates beyond 20%–30%. The success of SEMA in reproducing such subtle, asymmetric line shapes confirms compressive sensing as a general method to accelerate 2DTS and multidimensional spectroscopies more broadly.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors

Abstract This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct dynamic sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.

Mathematics↗
DOE OSTI2023

Systems and methods for active learning from sparse training data

A method for active learning using sparse training data can include training a machine learning model using less than ten first training data points to generate a candidate machine learning model. The method can include performing a Monte Carlo process to sample one or more first outputs of the candidate machine learning model. The method can include testing the one or more first outputs to determine if each of the one or more first outputs satisfy a respective convergence condition. The method can include, responsive to at least one first output not satisfying the respective convergence condition, training the candidate machine learning model using at least one second training data point corresponding to the at least one first output. The method can include, responsive to the one or more first outputs each satisfying the respective convergence condition, outputting the candidate machine learning model.

Sankaranarayanan, Subramanian↗
DOE OSTI2024

Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data

Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

surrogate modeling; convolutional neural networks;↗
DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Comparison of sparse domain approaches for 4D SPECT dynamic image reconstruction

Purpose: Dynamic imaging (DI) provides additional diagnostic information in emission tomography in comparison to conventional static imaging at the cost of being computationally more challenging. Dynamic single photon emission computed tomography (SPECT) reconstruction is particularly difficult because of the limitations in the sampling geometry present in most existing scanners. We have developed an algorithm Spline Initialized Factor Analysis of Dynamic Structures (SIFADS) that is a matrix factorization method for reconstructing the dynamics of tracers in tissues and blood directly from the projections in dynamic cardiac SPECT, without first resorting to any 3D reconstruction. Methods: SIFADS is different from "pure" factor analysis in dynamic structures (FADS) in that it employs a dedicated spline-based pre-initialization. In this paper, we analyze the convergence properties of SIFADS and FADS using multiple metrics. The performances of the two approaches are evaluated for numerically simulated data and for real dynamic SPECT data from canine and human subjects. Results: For SIFADS, metrics analyzed for reconstruction algorithm convergence show better features of the metric curves vs iterations. In addition, SIAFDS provides better tissue segmentations than that from pure FADS. Measured computational times are also typically better for SIFADS implementations than those with pure FADS. Conclusion: The analysis supports the utility of the pre-initialization of a factorization algorithm for better dynamic SPECT image reconstruction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Atom probe tomography characterization of ion and neutron irradiated Alloy 800H

Alloy 800H is a high temperature and creep resistant alloy, and is considered as a candidate alloy for use in Generation IV nuclear reactor systems. To clarify the alloy's behavior under irradiation, samples were subjected to single ion irradiations up to 20 dpa at 440°C, a dual ion/He irradiation to 17 dpa at 460°C, and a neutron irradiation to 17 dpa at 385°C. The irradiated microstructures were characterized using atom probe tomography to complement previously published transmission electron microscopy studies. Additionally, after single ion irradiation, sparse fine Al and Ti clusters were observed after 1dpa, while high number densities of nanoscale Ni-Al-Ti clusters, Cr-Ti rich carbides, and Si-decorated dislocation loops developed after 10 and 20 dpa. The microstructure formed during single ion irradiation exhibited a strong depth dependence. No significant differences were observed between the single and dual ion irradiations. While Ni-Al-Ti clusters, Cr-Ti rich carbides, and Si-decorated dislocation loops were also observed after neutron irradiation, the neutron-irradiated microstructure differed from those found in the ion-irradiated samples.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Gravity Gradiometry: A Novel Application for Compressed Sensing

During the past decade, compressed sensing (CS) has proven to be extremely useful for sparse signal reconstruction. Here the method of CS is applied to fast mass distribution determination based on cold atom gravity gradiometer measurements. Specifically we consider an array of M gradiometers placed around a 2D target area in order to determine the interior mass distribution in cases where the set of (M) sensor measurements under samples the distribution. This was done by assuming that the system’s sparsity comes from the mass distributions only having K non-zero masses, which led to a non-orthogonal basis dictionary. This lack of orthogonality caused interesting behaviors, including weakened noise performance, and breaking of the typical CS motivated logarithmic scaling of required M values for larger K values. However, for low K values M scaled as expected. Modifications to the gravity sensor model to promote orthogonality and test its impact on signal recovery postponed the onset of anomalous scaling; suggesting that lack of orthogonality is the primary cause. While CS works for this sparse, but intrinsically ill-posed problem, this sensor system displayed increased noise sensitivity and a smaller upper bound on the size of recoverable K sets. However, while these limitations decrease CS performance, significant improvements over traditional sensing approaches are still possible.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

RARE EARTH AND CRITICAL ELEMENT RELATIONSHIPS TO COAL DEPOSIT LITHOLOGIES IN SOUTHWEST WYOMING AND NORTHWEST COLORADO

Rare earth elements (REE) and critical minerals (CM) are vital components in a wide variety of applications, not only in the renewable energy sector but also in military, telecommunication, and other civilian uses. The association of REE and CM with coal deposits is widely known but not thoroughly understood. While individual coal samples or beds themselves might not host significant concentrations of REE, recent studies indicate temporal relationships among some REE with coal beds and their immediately adjacent non-coal bounding strata, including interbeds. These strata most commonly include clays, carbonaceous shales, and ash beds, but other related strata are possible in different coal-bearing settings. Variations in REE and CM concentrations and their direct or indirect association with coal beds are not always predictable. This study presents recent findings from studying different associations between coal beds and adjacent rocks to identify possible relationships between REE-CM concentrations and the coals and adjacent rocks. For this study we collected and analyzed several dozen samples from the U.S. Geological Survey’s Core Research Center (CRC). Additionally, a small number of coal mine outcrops and their adjacent non-coal rocks were included. Most samples are of Cretaceous age. Previous work has shown a potential link between coals in the Upper Cretaceous Williams Fork Formation and REE occurrences in the Yampa ash bed in northwest Colorado. While data are uncommon and sparse, this possible link may suggest REE or CM enrichment from leaching or reworking of the ash bed. Trace element geochemistry, whole rock data, and microscopic examinations are used here to explore these relationships and guide future studies.

REE, CM, ash, volcanic ash, coal↗
DOE OSTI2022

Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel -statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion () with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Acquisition of STEM Images by Adaptive Compressive Sensing

Compressive Sensing (CS) allows a signal to be sparsely measured first and accurately recovered later in software [1]. In scanning transmission electron microscopy (STEM), it is possible to compress an image spatially by reducing the number of measured pixels, which decreases electron dose and increases sensing speed [2,3,4]. The two requirements for CS to work are: (1) sparsity of basis coefficients and (2) incoherence of the sensing system and the representation system. However, when pixels are missing from the image, it is difficult to have an incoherent sensing matrix. Nevertheless, dictionary learning techniques such as Beta-Process Factor Analysis (BPFA) [5] are able to simultaneously discover a basis and the sparse coefficients in the case of missing pixels. On top of CS, we would like to apply active learning [6,7] to further reduce the proportion of pixels being measured, while maintaining image reconstruction quality. Suppose we initially sample 10% of random pixels. We wish to select the next 1% of pixels that are most useful in recovering the image. Now, we have 11% of pixels, and we want to decide the next 1% of “most informative” pixels. Active learning methods are online and sequential in nature. Our goal is to adaptively discover the best sensing mask during acquisition using feedback about the structures in the image. In the end, we hope to recover a high quality reconstruction with a dose reduction relative to the non-adaptive (random) sensing scheme. In doing this, we try three metrics applied to the partial reconstructions for selecting the new set of pixels: (1) variance, (2) Kullback-Leibler (KL) divergence using a Radial Basis Function (RBF) kernel, and (3) entropy. Figs. 1 and 2 display the comparison of Peak Signal-to-Noise (PSNR) using these three different active learning methods at different percentages of sampled pixels. At 20% level, all the three active learning methods underperform the original CS without active learning. However, they all beat the original CS as more of the “most informative” pixels are sampled. One can also argue that CS equipped with active learning requires less sampled pixels to achieve the same value of PSNR than CS with pixels randomly sampled, since all the three PSNR curves with active learning grow at a faster pace than that without active learning. For this particular STEM image, by observing the reconstructed images and the sensing masks, we find that while the method based on RBF kernel acquires samples more uniformly, the one on entropy samples more areas of significant change, thus less uniformly. The KL-divergence method performs the best in terms of reconstruction error (PSNR) for this example [8].

Xie, Weiyi↗
DOE OSTI2023

Automated piezoresponse force microscopy domain tracking during fast thermally stimulated phase transition in CuInP 2 S 6

Real-time tracking of dynamic nanoscale processes such as phase transitions by scanning probe microscopy is a challenging task, typically requiring extensive and laborious human supervision. Smart strategies to track specific regions of interest (ROI) in the system during such transformations in a fast and automated manner are necessary to study the evolution of the microscopic changes in such dynamic systems. In this work, we realize automated ROI tracking in piezoresponse force microscopy during a fast (≈0.8 °C s –1 ) thermally stimulated ferroelectric-to-paraelectric phase transition in CuInP 2 S 6 . We use a combination of fast (1 frame per second) sparse scanning with compressed sensing image reconstruction and real-time offset correction via phase cross correlation. The applied methodology enables in situ fast and automated functional nanoscale characterization of a certain ROI during external stimulation that generates sample drift and changes local functionality.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Loamy sand soil approaches organic carbon saturation after 37 years of conservation tillage

Conservation tillage is reported to increase soil organic carbon (SOC) and total nitrogen (TN) contents, but long-term (>30 yr) field results quantifying the responses in Coastal Plain Ultisols are sparse. The distribution, accumulation, and topsoil storage of SOC and TN after 37 yr of crop production using conventional (CvT) or conservation tillage (CnT) on a Norfolk loamy sand (fine-loamy, kaolinitic, thermic, Typic Kandiudults) were quantified. Soil samples were collected annually from the 0-5-, 5-10-, and 10-15-cm depth increments beneath corn (Zea mays L.), soybean [Glycine max (L.) Merr.], and cotton (Gossypium hirsutum L.) crops. Overall, SOC and TN accumulation in the 0-5-cm depth were highest for Norfolk soil under CnT. Focusing on total long-term changes for the 0-15-cm sampling depth beneath various corn crops shows that CnT and CvT sequestered 24.7 and 21.4 Mg C ha -1 , respectively. Between 1978 and 2016, there was a highly significant (P < .0001) exponential increase in SOC within the top 5-cm soil depth. However, the exponential curves began to plateau suggesting the Norfolk topsoil was approaching its organic carbon (OC) storage capacity. These field measurements strongly indicate that additional topsoil SOC increases with current tillage and crop management practices are limited.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

A novel coupling of noise reduction algorithms for particle flow simulations

Proper orthogonal decomposition (POD) and its extension based on time-windows have been shown to greatly improve the effectiveness of recovering smooth ensemble solutions from noisy particle data. However, to successfully de-noise any molecular system, a large number of measurements still need to be provided. In order to achieve a better efficiency in processing time-dependent fields, we have combined POD with a well-established signal processing technique, wavelet-based thresholding. In this novel hybrid procedure, the wavelet filtering is applied within the POD domain and referred to as WAVinPOD. The algorithm exhibits promising results when applied to both synthetically generated signals and particle data. In this work, the simulations compare the performance of our new approach with standard POD or wavelet analysis in extracting smooth profiles from noisy velocity and density fields. Numerical examples include molecular dynamics and dissipative particle dynamics simulations of unsteady force- and shear-driven liquid flows, as well as phase separation phenomenon. Simulation results confirm that WAVinPOD preserves the dimensionality reduction obtained using POD, while improving its filtering properties through the sparse representation of data in wavelet basis. This paper shows that WAVinPOD outperforms the other estimators for both synthetically generated signals and particle-based measurements, achieving a higher signal-to-noise ratio from a smaller number of samples. The new filtering methodology offers significant computational savings, particularly for multi-scale applications seeking to couple continuum informations with atomistic models. It is the first time that a rigorous analysis has compared de-noising techniques for particle-based fluid simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantifying uncertainties on fission fragment mass yields with mixture density networks

Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we explore the use of one such probabilistic network, the mixture density network (MDN), to reproduce fission yields and their uncertainties. In this paper, we study mass yields for the spontaneous fission of 252 Cf, exploring the number of training samples needed for converged predictions, how different levels of uncertainty propagate from the training set to the MDN predictions, and how well physical constraints of the yields—such as normalization and symmetry—are upheld by the algorithm. Finally, we test the ability of the MDN to interpolate between and extrapolate beyond samples in the training set using energy-dependent mass yields for the neutron-induced fission on 235 U. The MDN provides a reliable way to include and predict uncertainties and is a promising path forward for supplementing sparse sets of nuclear data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗