Bootstrapping and Jackknife Resampling to Improve Sparse-Data UQ Methods for Tail Probability Estimates with Limited Samples.
Abstract not provided.
Jekel, Charles↗
SEARCH · Engineering Papers
Results for “sparse sampling”
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.
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A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media
A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Analysis of sparse recovery for Legendre expansions using envelope bound
We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ 1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m ≳ Θ 2 s x log factors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. Here, in this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s-sparse Legendre expansions, m ≳ Θs 2 x log factors, which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.
97 MATHEMATICS AND COMPUTING↗
Joint cosmic density reconstruction from photometric and spectroscopic samples
ABSTRACT We reconstruct the dark matter density field from spatially overlapping spectroscopic and photometric redshift catalogues through a field-level forward modelling approach. Instead of directly inferring the underlying density field, we find the best-fitting initial Gaussian fluctuations that will evolve into the observed cosmic volume. To account for the substantial uncertainty of photometric redshifts we employ a differentiable continuous Poisson process. As an initial test, we construct a mock based on the upcoming Prime Focus Spectrograph combined with photometric sample modelled on the Subaru Hyper Suprime-Cam. Depending on the statistic of interest, we find improvements in cosmic structure classification equivalent to 50–100 per cent more spectroscopic targets by combining relatively sparse spectroscopic with dense photometric samples.
Horowitz, B.↗
3′ RNA-seq is superior to standard RNA-seq in cases of sparse data but inferior at identifying toxicity pathways in a model organism
The application of RNA-sequencing has led to numerous breakthroughs related to investigating gene expression levels in complex biological systems. Among these are knowledge of how organisms, such as the vertebrate model organism zebrafish (Danio rerio), respond to toxicant exposure. Recently, the development of 3' RNA-seq has allowed for the determination of gene expression levels with a fraction of the required reads compared to standard RNA-seq. While 3' RNA-seq has many advantages, a comparison to standard RNA-seq has not been performed in the context of whole organism toxicity and sparse data. Here, we examined samples from zebrafish exposed to perfluorobutane sulfonamide (FBSA) with either 3' or standard RNA-seq to determine the advantages of each with regards to the identification of functionally enriched pathways. We found that 3' and standard RNA-seq showed specific advantages when focusing on annotated or unannotated regions of the genome. We also found that standard RNA-seq identified more differentially expressed genes (DEGs), but that this advantage disappeared under conditions of sparse data. We also found that standard RNA-seq had a significant advantage in identifying functionally enriched pathways via analysis of DEG lists but that this advantage was minimal when identifying pathways via gene set enrichment analysis of all genes. These results show that each approach has experimental conditions where they may be advantageous. Our observations can help guide others in the choice of 3' RNA-seq vs standard RNA sequencing to query gene expression levels in a range of biological systems.
3’ RNA-seq↗
Spectrotemporal CT data acquisition and reconstruction at low dose
Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Results: Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Conclusions: Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.
60 APPLIED LIFE SCIENCES↗
Measurement of the small-scale 3D Lyman- α forest power spectrum
Small-scale correlations measured in the Lyman-α (Lyα) forest encode information about the intergalactic medium and the primordial matter power spectrum. In this article, we present and implement a simple method to measure the 3-dimensional power spectrum, P 3D , of the Lyα forest at wavenumbers k corresponding to small, ~ Mpc scales. In order to estimate P 3D from sparsely and unevenly distributed data samples, we rely on averaging 1-dimensional Fourier Transforms, as previously carried out to estimate the 1-dimensional power spectrum of the Lyα forest, P 1D . Further, this methodology exhibits a very low computational cost. We confirm the validity of this approach through its application to Nyx cosmological hydrodynamical simulations. Subsequently, we apply our method to the eBOSS DR16 Lyα forest sample, providing as a proof of principle, a first P 3D measurement averaged over two redshift bins z = 2.2 and z = 2.4. This work highlights the potential for forthcoming P 3D measurements, from upcoming large spectroscopic surveys, to untangle degeneracies in the cosmological interpretation of P 1D .
79 ASTRONOMY AND ASTROPHYSICS↗
Wavefront shaping with a Hadamard basis for scattering soil imaging
Here, soil is a scattering medium that inhibits imaging of plant-microbial-mineral interactions that are essential to plant health and soil carbon sequestration. However, optical imaging in the complex medium of soil has been stymied by the seemingly intractable problems of scattering and contrast. Here, we develop a wavefront shaping method based on adaptive stochastic parallel gradient descent optimization with a Hadamard basis to focus light through soil mineral samples. Our approach allows a sparse representation of the wavefront with reduced dimensionality for the optimization. We further divide the used Hadamard basis set into subsets and optimize a certain subset at once. Simulation and experimental optimization results demonstrate our method has an approximately seven times higher convergence rate and overall better performance compared to that with optimizing all pixels at once. The proposed method can benefit other high-dimensional optimization problems in adaptive optics and wavefront shaping.
47 OTHER INSTRUMENTATION↗
Integration of Large-Scale Electrical Imaging into Geological Framework Development and Refinement
Geologic framework models (GFMs) are critical to the construction of reliable simulation models of groundwater flow and contaminant transport. To support GFM development, direct information (e.g., core samples, fluid samples, hydraulic testing) tends to be sparse and separated by large distances relative to the spatial scales of aquifer heterogeneity. There are additional challenges associated with highly contaminated legacy waste sites, where drilling is particularly costly, and invasive sampling requires specialized handling and disposal of hazardous materials. At these sites in particular, non-invasive geophysical imaging can play an important role in filling spatial gaps between boreholes and reducing characterization costs by optimizing and minimizing the number of necessary boreholes. Here this paper presents a case study demonstrating the use of large-scale (> 30 km 2 ) electrical mapping to identify hydrostratigraphy and potential paleochannels at the Hanford Site, located in Washington State, USA. In two field campaigns, over 36 line-kilometers of electrical resistivity tomography (ERT) data were collected along 14 transects. ERT surveys were sited and performed to image critical aspects (e.g., paleochannels, stratigraphic contacts) of the subsurface, demonstrating a general workflow for integrating ERT with GFM development. Inconsistencies between the GFM and ERT were catalogued to provide a basis for future site characterization using complementary geophysical methods and (or) direct sampling.
58 GEOSCIENCES↗
Dispersion-enhanced sequential batch sampling for adaptive contour estimation
In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two-dimensional four-branch function, a four-dimensional function with a disjoint contour of interest and a time-delay dynamic system.
97 MATHEMATICS AND COMPUTING↗
Advanced Material Studies for High Intensity Proton Production Targets and Windows
The titanium alloy Ti6Al4V is widely used in accelerator facilities as beam windows, which are exposed to high cycle compressive stress waves from intense pulsed proton beams. Such materials interacting with the beam are subject to various forms of radiation damage, which can adversely affect their endurance limit. However, no fatigue data is currently available for high energy proton irradiated titanium alloy. Due to limitations in proton irradiation facilities, only miniature flat samples can be used for irradiation. To address this issue, we have developed a custom-made bend fatigue tester at Fermilab specifically for testing proton irradiated titanium alloy. In this presentation, we report on the fatigue test results obtained from this custom-fatigue tester using a non-ASTM standard specimen design. We plan to validate these sparse fatigue data with ASTM standard samples using standard fatigue samples. Furthermore, we have modified another commercial bend fatigue tester to accommodate miniature samples, and discuss some inherent deficiencies of the commercial fatigue tester to test miniature samples. To overcome this issue, a new fixture design is presented, which enables satisfactory fatigue testing on miniature samples over long periods. Finally, we present an upgrade to the custom-fatigue tester, featuring this new fixture design.
43 PARTICLE ACCELERATORS↗
Advanced Material Studies for High Intensity Proton Production Targets and Windows
The titanium alloy Ti6Al4V is widely used in accelerator facilities as beam windows, which are exposed to high cycle compressive stress waves from intense pulsed proton beams. Such materials interacting with the beam are subject to various forms of radiation damage, which can adversely affect their endurance limit. However, no fatigue data is currently available for high energy proton irradiated titanium alloy. Due to limitations in proton irradiation facilities, only miniature flat samples can be used for irradiation. To address this issue, we have developed a custom-made bend fatigue tester at Fermilab specifically for testing proton irradiated titanium alloy. In this presentation, we report on the fatigue test results obtained from this custom-fatigue tester using a non-ASTM standard specimen design. We plan to validate these sparse fatigue data with ASTM standard samples using standard fatigue samples. Furthermore, we have modified another commercial bend fatigue tester to accommodate miniature samples, and discuss some inherent deficiencies of the commercial fatigue tester to test miniature samples. To overcome this issue, a new fixture design is presented, which enables satisfactory fatigue testing on miniature samples over long periods. Finally, we present an upgrade to the custom-fatigue tester, featuring this new fixture design.
43 PARTICLE ACCELERATORS↗
Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems
Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.
Mukherjee, Sayak↗
FAST (FAST AUTONOMOUS SCANNING TOOLKIT)
SF-23-006 FAST (FAST AUTONOMOUS SCANNING TOOLKIT)The software is deployed on an edge computing device at the beamline computer attached to a scanning microscope. It iteratively analyzes the data collected, then identifies new scan positions to scan next and directs the positioners that move the sample (or probe beam) to these positions. Overall, it identifies a sparse set of scan positions that are sufficient to image the full sample. This can reduce the scan time by >60%.
KANDEL, SAUGAT↗
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ{sub 1}-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids
We present a new approach to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed: (1) stochastic collocation based on dimension-adaptive sparse grids (SGs), which approximates the stochastic objective function with a limited number of quadrature nodes, and (2) projection-based reduced-order models (ROMs), which generate efficient approximations to PDE solutions. These two sources of inexactness lead to inexact objective function and gradient evaluations, which are managed by a trust-region method that guarantees global convergence by adaptively refining the SG and ROM until a proposed error indicator drops below a tolerance specified by trust-region convergence theory. A key feature of the proposed method is that the error indicator---which accounts for errors incurred by both the SG and ROM---must be only an asymptotic error bound, i.e., a bound that holds up to an arbitrary constant that need not be computed. This allows the approach to be applicable to a wide range of problems, including those where sharp, computable error bounds are not available; this distinguishes the proposed method from previous works. Numerical experiments performed on a model problem from optimal flow control under uncertainty verify global convergence of the method and demonstrate the method's ability to outperform previously proposed alternatives.
97 MATHEMATICS AND COMPUTING↗
Uncertainty Quantification in Dynamic Simulations of Large-scale Power System Models using the High-Order Probabilistic Collocation Method on Sparse Grids
This paper proposes a probabilistic collocation method (PCM) to quantify the uncertainties with dynamic simulations in power systems. The appraoch was tested on a single-machine-infinite-bus system and the over 15,000 -bus Western Electricity Coordinating Council (WECC) system. Comparing to classic Monte-Carlo (MC) method, the proposed PCM applies the Smolyak algorithm to reduce the number of simulations that have to be performed. Therefore, the computational cost can be greatly reduced using PCM. The algorithm and procedures are described in the paper. Comparison was made with MC method on the single machine as well as the WECC system. The simulation results shows that using PCM only a small number of sparse grid points need to be sampled even when dealing with systems with a relatively large number of uncertain parameters. PCM is, therefore, computationally more efficient than MC method.
Uncertainty quantification, parameter estimation, ↗
Algorithms for X-Ray Imaging of Single Particles
Our group develops image reconstruction algorithms and applies them to data collected with x-ray sources (synchrotron, XFEL) and electron microscopes. Some of the challenges we face are (1) extremely low signal levels and noise, (2) missing information (phase, sample orientation), and (3) large, very sparse datasets. We have made significant progress in all three of these areas in our DOE project. This final report highlights two results produced during the extension of the project that proved to be spectacular successes. Publications and software products generated over the entire project period are listed at the end of the report.
97 MATHEMATICS AND COMPUTING↗