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DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-Response Curves

X-59↗

DOE OSTI2015

A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level

An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

A SAMPLE OF OB STARS THAT FORMED IN THE FIELD

We present a sample of 14 OB stars in the Small Magellanic Cloud that meet strong criteria for having formed under extremely sparse star-forming conditions in the field. These stars are a minimum of 28 pc in projection from other OB stars, and they are centered within symmetric, round H II regions. They show no evidence of bow shocks, implying that the targets are not transverse runaway stars. Their radial velocities relative to local H I also indicate that they are not line-of-sight runaway stars. A friends-of-friends analysis shows that nine of the objects present a few low-mass companion stars, with typical mass ratios for the two highest-mass stars of around 0.1. This further substantiates that these OB stars formed in place, and that they can and do form in extremely sparse conditions. This poses strong constraints on theories of star formation and challenges proposed relations between cluster mass and maximum stellar mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Sparse Convolutional Neural Networks for particle classification in ProtoDUNE-SP events

Deep Learning (DL) methods and Computer Vision are becoming important tools for event reconstruction in particle physics detectors. In this work, we report on the use of submanifold sparse convolutional neural networks (SparseNets) for the classification of track and shower hits from a DUNE prototype liquid-argon detector at CERN (ProtoDUNE-SP). By taking advantage of the three-dimensional nature of the problem we use a set of nine input features to classify sparse and locally dense hits associated to track or shower particles. The SparseNet has been trained on a test sample and shows promising results: efficiencies and purities greater than 90%. This has also been achieved with a considerable speedup and substantially less resource utilization with respect to other DL networks such as graph neural networks. This method offers great scalability advantages for future large neutrino detectors such as the planned DUNE experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2005

Miniature Laboratory for Detecting Sparse Biomolecules

A miniature laboratory system has been proposed for use in the field to detect sparsely distributed biomolecules. By emphasizing concentration and sorting of specimens prior to detection, the underlying system concept would make it possible to attain high detection sensitivities without the need to develop ever more sensitive biosensors. The original purpose of the proposal is to aid the search for signs of life on a remote planet by enabling the detection of specimens as sparse as a few molecules or microbes in a large amount of soil, dust, rocks, water/ice, or other raw sample material. Some version of the system could prove useful on Earth for remote sensing of biological contamination, including agents of biological warfare. Processing in this system would begin with dissolution of the raw sample material in a sample-separation vessel. The solution in the vessel would contain floating microscopic magnetic beads coated with substances that could engage in chemical reactions with various target functional groups that are parts of target molecules. The chemical reactions would cause the targeted molecules to be captured on the surfaces of the beads. By use of a controlled magnetic field, the beads would be concentrated in a specified location in the vessel. Once the beads were thus concentrated, the rest of the solution would be discarded. This procedure would obviate the filtration steps and thereby also eliminate the filter-clogging difficulties of typical prior sample-concentration schemes. For ferrous dust/soil samples, the dissolution would be done first in a separate vessel before the solution is transferred to the microbead-containing vessel.

Lin, Ying↗

NASA NTRS2022

Co-leveraging Scientific Advances in Space Biology and Astrobiology Towards Achieving NASA’s Life Science Objectives

Executive Summary: Distinct lines of scientific inquiry drives the separation of NASA’s fundamental life science research into Space Biology and Astrobiology. This division developed as a way to place life scientists alongside experts in the physical constraints that define the acclimation, adaptation and evolution of biology systems relevant to their respective subjects. For astrobiology, integration with disciplines such as geology, geochemistry, astronomy, planetary science, etc., enables a comprehensive assessment of the physical environment and its co-evolution with biological processes. Space Biology’s co-location with Physical Sciences places life science researchers adjacent to experts in the physical phenomena associated with microgravity and spaceflight, enabling an understanding of how the spaceflight environment affects biological systems. Despite this separation, aspects of both disciplines have converged on a similar, fundamental objective: to describe and understand the dynamics of complex living communities in the contexts of their physical environments. While the environmental systems and timescales are dramatically different, continuing to motivate the separation into distinct fields, similarities in the underlying objective present opportunities to find efficiencies, reduce overlap, and minimize duplication of effort. Space Biology and Astrobiology share a common need to understand microbial physiology in extreme environments – whether the ‘built’ spaceflight environment or the natural environments in which many astrobiology studies are conducted. In particular, open questions in each discipline require the development of quantitative frameworks, applicable at the ecosystem level, that support predictive capabilities for environments where observations are sparse. Additionally, both disciplines have a need to prepare, detect, and analyze the (potential) biological signal in complex samples-often in a completely autonomous fashion. The next decade will see NASA Space Biology moving to understand and describe the effects of the beyond low-earth orbit (BLEO) spaceflight environment on living systems. This new direction will dramatically reduce the opportunities for ground-based analysis of space-flown samples, driving space biology investigations towards fully autonomous experiments and missions. At the same time, astrobiology life detection missions aimed at detecting biosignatures on Mars and icy moons in the outer solar system could benefit from fully automated sample processing and analysis. There are opportunities to leverage instrument and method development between both disciplines within the context of these BLEO missions.

Astrobiology↗

NASA NTRS2023

Assessment of the Impact of Discontinuity in Satellite Instruments and Retrievals on Global PM2.5

Exposure to fine particulate matter (PM2.5) is the leading environmental risk factor for mortality globally. Satellite-derived estimates of surface PM2.5 developed from a combination of satellites, simulations, and ground monitor data are relied upon for health impact studies. The ability to develop satellite-derived PM2.5 estimates requires the continued availability of aerosol optical depth (AOD) sources. This work examines the impact of the addition or loss of satellite AOD data sources on global PM2.5 estimation and the impact of continuing the longterm record with AOD from the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi-National Polar orbiting Partnership (S-NPP) satellite after the loss of the MODIS (MODerate resolution Imaging Spectroradiometer) and MISR (Multi-angle Imaging Spectroradiometer) instruments on board the Terra and Aqua satellites. We find that the addition of VIIRS S-NPP AOD products to geophysical PM2.5 estimates from satellites and simulations causes regional differences that correspond to differences in the VIIRS and MODIS Deep Blue AOD algorithms and sampling. Changes in long-term trends and timeseries due to the addition or loss of AOD data sources are generally within their uncertainties. Statistical fusion with ground monitor data partially corrects for changes due to sampling differences when introducing the VIIRS AOD products, but uncertainty remains over desert regions where ground monitor coverage is sparse. This work provides promise for the sustained development of global satellite-derived PM2.5 estimates, despite discontinuities in instruments and retrieval methods.

Remote sensing↗

DOE OSTI2020

A Particle-Based Conditional Sampling Scheme for the Simulation of Transport in Fractured Rock With Diffusion Into Stagnant Water and Rock Matrix

In situ experiments and field-scale characterization studies have pointed out that, in fractured crystalline media, groundwater flow is highly channelized. This implies that, at the scale of a single fracture, only part of the fracture surface area is in contact with flowing water, while the rest of in-plane water is essentially stagnant and can be accessed by solutes via molecular diffusion. Despite their importance for contaminant retention, to date, there are no numerical or analytical approaches that could be used to assess the implication of stagnant water zones on solute transport in realistic large-scale Discrete Fracture Network-based models. In this study, we present an efficient and flexible algorithm for the simulation of transport in fractured rock with diffusion into stagnant water and rock matrix. The algorithm is a generalization of a previously developed numerical framework for time domain particle tracking in sparsely fractured rock. The key of the generalization is that total time in fracture (τ f ) is first evaluated using a Monte Carlo sampling and then a second sampling is performed conditioned on τ f . The algorithm has been successfully validated against existing independent solutions and the implication of diffusion into stagnant water and secondary diffusion into the matrix has been assessed for a realistic modeling scenario. The results show that, due to diffusion into stagnant water, contaminants are more strongly retarded. This increased retention is more significant for sorbing species, as a larger number of sorption sites is accessible. A high sensitivity to the flowing channel/stagnant water zone geometry has also been observed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Simultaneous event-specific estimates of transport, loss, and source rates for relativistic outer radiation belt electrons: Event-Specific 1-D Modeling

The most significant unknown regarding relativistic electrons in Earth’s outer Van Allen radiation belt is the relative contribution of loss, transport, and acceleration processes within the inner magnetosphere. Detangling each individual process is critical to improve the understanding of radiation belt dynamics, but determining a single component is challenging due to sparse measurements in diverse spatial and temporal regimes. However, there are currently an unprecedented number of spacecraft taking measurements that sample different regions of the inner magnetosphere. With the increasing number of varied observational platforms, system dynamics can begin to be unraveled. In this work, we employ in-situ measurements during the 13-14 January 2013 enhancement event to isolate transport, loss, and source dynamics in a one dimensional radial diffusion model. We then validate the results by comparing them to Van Allen Probes and THEMIS observations, indicating that the three terms have been accurately and individually quantified for the event. Finally, a direct comparison is performed between the model containing event-specific terms and various models containing terms parameterized by geomagnetic index. Models using a simple 3/Kp loss timescale show deviation from the event specific model of nearly two orders of magnitude within 72 hours of the enhancement event. However, models using alternative loss timescales closely resemble the event specific model.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Multi-fidelity classification using Gaussian processes: Accelerating the prediction of large-scale computational models

We report that machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational models which typically take days to run, thus hindering the potential of machine learning tools. In this work, we present a novel classifier that takes advantage of lower fidelity models and inexpensive approximations to predict the binary output of expensive computer simulations. We postulate an autoregressive model between the different levels of fidelity with Gaussian process priors. We adopt a fully Bayesian treatment for the hyper-parameters and use Markov Chain Monte Carlo samplers. We take advantage of the probabilistic nature of the classifier to implement active learning strategies. We also introduce a sparse approximation to enhance the ability of the multi-fidelity classifier to handle a large amount of low fidelity samples. We test these multi-fidelity classifiers against their single-fidelity counterpart with synthetic data, showing a median computational cost reduction of 23% for a target accuracy of 90%. In an application to cardiac electrophysiology, the multi-fidelity classifier achieves an F1 score, the harmonic mean of precision and recall, of 99.6% compared to 74.1% of a single-fidelity classifier when both are trained with 50 samples. In general, our results show that the multi-fidelity classifiers outperform their single-fidelity counterpart in terms of accuracy in all cases. Finally, we envision that this new tool will enable researchers to study classification problems that would otherwise be prohibitively expensive. Source code is available at https://github.com/fsahli/MFclass.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Quickest Detection for Changes in Maximal kNN Coherence of Random Matrices

This paper addresses the problem of quickest detection of a change in the maximal coherence between columns of a n p random matrix based on a sequence of matrix observations having a single unknown change point. The random matrix is assumed to have identically distributed rows and the maximal coherence is defined as the largest of the ( 2 p) correlation coefficients associated with any row. Likewise the κ nearest neighbor (kNN) coherence is defined as the κ-th largest of these correlation coefficients. The forms of the preand postchange distributions of the observed matrices are assumed to belong to the family of elliptically contoured densities with sparse dispersion matrices but are otherwise unknown. A nonparametric stopping rule is proposed that is based on the maximal kNN sample coherence between columns of each observed random matrix. This is a summary statistic that is related to a test of existence of a hub vertex in a sample correlation graph having degree at least κ. Performance bounds on the delay and false alarm performance of the proposed stopping rule are obtained in the purely high-dimensional regime where p → ∞ and n is fixed. When the prechange dispersion matrix is diagonal it is shown that, among all functions of the proposed summary statistic, the proposed stopping rule is asymptotically optimal under a minimax quickest change detection model as the stopping threshold approaches infinity. Furthermore, the theory developed also applies to sequential hypothesis testing and fixed sample size tests.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

NASA NTRS2001

A TRMM-Calibrated Infrared Rainfall Algorithm Over Brazil

An improved version of the Convective/Stratiform Technique (CST) and its application over Brazil are presented. Keeping the major components of traditional CST, we have modified the scheme for classing convective and stratiform rainfall and tested various schemes to eliminate non-raining cirrus clouds. The parameters of the technique are calibrated using Tropical Rainfall Measuring Mission (TRMM) multi-sensor observations, including TMI, PR and Visible Infrared Scanner (VIRS). This technique takes advantage of the high temporal sampling rate of geosynchronous infrared channel and the better instantaneous rain observation of TRMM Microwave Imager (TMI) and PR. Moreover, sparse TMI rain estimates are used to dynamically calibrate the parameters of the technique to improve its performance. The technique is applied to make rainfall estimates on various time scales and to study rainfall statistics such as the distributions of rain intensity and storm duration over a four-month period beginning January 1999. The study period coincides with the TRMM/Large-Scale Biosphere-Atmosphere experiment in Amazonia (LBA) ground validation experiment, and observations from the LBA radar are used to validate the technique. Results show the mean diurnal cycle of precipitation over the LBA area, and are compared to radar data from the Tropical Oceans and Global Atmosphere (TOGA) radar. When the larger geographic region is considered, the analysis of the mean hourly estimates revealed the pronounced effects of rivers, topography and local circulations on the rainfall.

Negri, Andrew J.↗

DOE OSTI2020

Modeling of Hidden Structures Using Sparse Chemical Shift Data from NMR Relaxation Dispersion

NMR relaxation dispersion measurements report on conformational changes occurring on the μs-ms timescale. Chemical shift information derived from relaxation dispersion can be used to generate structural models of weakly populated alternative conformational states. Current methods to obtain such models rely on determining the signs of chemical shift changes between the conformational states, which are difficult to obtain in many situations. Here, we use a “sample and select” method to generate relevant structural models of alternative conformations of the C-terminal-associated region of Escherichia coli dihydrofolate reductase (DHFR), using only unsigned chemical shift changes for backbone amides and carbonyls ( 1 H, 15 N, and 13 C'). We find that CS-Rosetta sampling with unsigned chemical shift changes generates a diversity of structures that are sufficient to characterize a minor conformational state of the C-terminal region of DHFR. The excited state differs from the ground state by a change in secondary structure, consistent with previous predictions from chemical shift hypersurfaces and validated by the x-ray structure of a partially humanized mutant of E. coli DHFR (N23PP/G51PEKN). The results demonstrate that the combination of fragment modeling with sparse chemical shift data can determine the structure of an alternative conformation of DHFR sampled on the μs-ms timescale. Such methods will be useful for characterizing alternative states, which can potentially be used for in silico drug screening, as well as contributing to understanding the role of minor states in biology and molecular evolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Posiform planting: generating QUBO instances for benchmarking

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing quadratic unconstrained binary optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting , for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) and the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to 5, 627 qubits.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Th-230 - U-238 series disequilibrium of the Olkaria basalts Gregory Rift Valley, Kenya

U-Th disequilibrium analyses of the Naivasha basalts show a very small (U-238/Th-230) ratios which are lower than any previously analyzed basalts. The broadly positive internal isochron trend from one sample indicates that the basalts may have source heterogeneities, this is supported by earlier work. The Naivasha complex comprises a bimodal suite of basalts and rhyolites. The basalts are divided into two stratigraphic groups each of a transitional nature. The early basalt series (EBS) which were erupted prior to the Group 1 comendites and, the late basalt series (LBS) which erupted temporally between the Broad Acres and the Ololbutot centers. The basalts represent a very small percentage of the overall eruptive volume of material at Naivasha (less than 2 percent). The analyzed samples come from four stratigraphic units in close proximity around Ndabibi, Hell's Gate and Akira areas. The earliest units occur as vesicular flows from the Ndabibi plain. These basalts are olivine-plagioclase phyric with the associated hawaiites being sparsely plagioclase phyric. An absolute age of 0.5Ma was estimated for these basalts. The next youngest basalts flows occur as younger tuft cones in the Ndabibi area and are mainly olivine-plagioclase-clinopyroxcene phyric with one purely plagioclase phyric sample. The final phase of activity at Ndabibi resulted in much younger tuft cones consisting of air fall ashes and lapilli tufts. Many of these contain resorbed plagioclase phenocrysts with sample number 120c also being clinopyroxene phyric. The isotopic evidence for the basalt formation is summarized.

Black, S.↗

DOE OSTI2011

A non-adapted sparse approximation of PDEs with stochastic inputs

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗