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DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

The DECADE cosmic shear project III: validation of analysis pipeline using spatially inhomogeneous data

We present the pipeline for the cosmic shear analysis of the Dark Energy Camera All Data Everywhere (DECADE) weak lensing dataset: a catalog consisting of 107 million galaxies observed by the Dark Energy Camera (DECam) in the northern Galactic cap. The catalog derives from a large number of disparate observing programs and is therefore more inhomogeneous across the sky compared to existing lensing surveys. First, we use simulated data-vectors to show the sensitivity of our constraints to different analysis choices in our inference pipeline, including sensitivity to residual systematics. Next we use simulations to validate our covariance modeling for inhomogeneous datasets. Finally, we show that our choices in the end-to-end cosmic shear pipeline are robust against inhomogeneities in the survey, by extracting relative shifts in the cosmology constraints across different subsets of the footprint/catalog and showing they are all consistent within 1σ to 2σ. This is done for forty-six subsets of the data and is carried out in a fully consistent manner: for each subset of the data, we re-derive the photometric redshift estimates, shear calibrations, survey transfer functions, the data vector, measurement covariance, and finally, the cosmological constraints. Our results show that existing analysis methods for weak lensing cosmology can be fairly resilient towards inhomogeneous datasets. This also motivates exploring a wider range of image data for pursuing such cosmological constraints.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Personalized, disease-stage specific, rapid identification of immunosuppression in sepsis

Introduction Data overlapping of different biological conditions prevents personalized medical decision-making. For example, when the neutrophil percentages of surviving septic patients overlap with those of non-survivors, no individualized assessment is possible. To ameliorate this problem, an immunological method was explored in the context of sepsis. Methods Blood leukocyte counts and relative percentages as well as the serum concentration of several proteins were investigated with 4072 longitudinal samples collected from 331 hospitalized patients classified as septic (n=286), non-septic (n=43), or not assigned (n=2). Two methodological approaches were evaluated: (i) a reductionist alternative, which analyzed variables in isolation; and (ii) a non-reductionist version, which examined interactions among six (leukocyte-, bacterial-, temporal-, personalized-, population-, and outcome-related) dimensions. Results The reductionist approach did not distinguish outcomes: the leukocyte and serum protein data of survivors and non-survivors overlapped. In contrast, the non-reductionist alternative differentiated several data groups, of which at least one was only composed of survivors (a finding observable since hospitalization day 1). Hence, the non-reductionist approach promoted personalized medical practices: every patient classified within a subset associated with 100% survival subset was likely to survive. The non-reductionist method also revealed five inflammatory or disease-related stages (provisionally named ‘early inflammation, early immunocompetence, intermediary immuno-suppression, late immuno-suppression, or other’). Mortality data validated these labels: both ‘suppression’ subsets revealed 100% mortality, the ‘immunocompetence’ group exhibited 100% survival, while the remaining sets reported two-digit mortality percentages. While the ‘intermediary’ suppression expressed an impaired monocyte-related function, the ‘late’ suppression displayed renal-related dysfunctions, as indicated by high concentrations of urea and creatinine. Discussion The data-driven differentiation of five data groups may foster early and non-overlapping biomedical decision-making, both upon admission and throughout their hospitalization. This approach could evaluate therapies, at personalized level, earlier. To ascertain repeatability and investigate the dynamics of the ‘other’ group, additional studies are recommended.

Immunology↗

DOE OSTI2023

Using Host Galaxy Photometric Redshifts to Improve Cosmological Constraints with Type Ia Supernovae in the LSST Era

We perform a rigorous cosmology analysis on simulated Type Ia supernovae (SNe Ia) and evaluate the improvement from including photometric host galaxy redshifts compared to using only the "z spec " subset with spectroscopic redshifts from the host or SN. We use the Deep Drilling Fields (~50 deg 2 ) from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC) in combination with a low-z sample based on Data Challenge2. The analysis includes light-curve fitting to standardize the SN brightness, a high-statistics simulation to obtain a bias-corrected Hubble diagram, a statistical+systematics covariance matrix including calibration and photo-z uncertainties, and cosmology fitting with a prior from the cosmic microwave background. Compared to using the z spec subset, including events with SN+host photo-z results in (i) more precise distances for z > 0.5, (ii) a Hubble diagram that extends 0.3 further in redshift, and (iii) a 50% increase in the Dark Energy Task Force figure of merit (FoM) based on the w 0 w a CDM model. Analyzing 25 simulated data samples, the average bias on w 0 and w a is consistent with zero. The host photo-z systematic of 0.01 reduces FoM by only 2% because (i) most z < 0.5 events are in the z spec subset, (ii) the combined SN+host photo-z has ×2 smaller bias, and (iii) the anticorrelation between fitted redshift and color self-corrects distance errors. To prepare for analyzing real data, the next SN Ia cosmology analysis with photo-zs should include non–SN Ia contamination and host galaxy misassociations.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

A bound on the rate-distortion function and application to images.

An upper bound on the rate-distortion function for discrete ergodic sources with memory is developed by partitioning the source sample space into a finite number of disjoint subsets and bounding the rates for each subset. The bound depends only on the mean vectors and covariance matrices for the subsets and is easy to compute. It is tighter than the Gaussian bound for sources that exhibit clustering of either the values or covariances of successive source outputs. The bound is evaluated for a certain class of pictorial data using both one-dimensional and two-dimensional blocks of picture elements. Two-dimensional blocks yield a tighter bound than one-dimensional blocks; both result in a significantly tighter bound than the Gaussian bound.

Tasto, M.↗

NASA NTRS1974

Skylab S192 data evaluation: Comparisons with ERTS-1 results

The author has identified the following significant results. The Skylab S192 data was evaluated by: (1) comparing the classification results using S192 and ERTS-1 data over the Holt County, Nebraska agricultural study area, and (2) investigating the impact of signal-to-noise ratio on classification accuracies using registered S192 and ERTS-1 data. Results indicate: (1) The classification accuracy obtained on S192 data using its best subset of four bands can be expected to be as high as that on ERTS-1 data. (2) When a subset of four S192 bands that are spectrally similar to the ERTS-1 bands was used for classification, an obvious deterioration in the classification accuracy was observed with respect to the ERTS-1 results. (3) The thermal bands 13 and 14 as well as the near IR bands were found to be relatively important in the classification of agricultural data. Although bands 11 and 12 were highly correlated, both were invariably included in the best subsets of the band sizes, four and beyond, according to the divergence criterion. (4) The differentiation of corn from popcorn was difficult on both S192 and ERTS-1 data acquired at an early summer date. (5) The results on both sets of data indicate that it was relatively easy to differentiate grass from any other class.

Chang, C. Y.↗

NASA NTRS1975

A boundary finding algorithm and its applications

An algorithm for locating gray level and/or texture edges in digitized pictures is presented. The algorithm is based on the concept of hypothesis testing. The digitized picture is first subdivided into subsets of picture elements, e.g., 2 x 2 arrays. The algorithm then compares the first- and second-order statistics of adjacent subsets; adjacent subsets having similar first- and/or second-order statistics are merged into blobs. By continuing this process, the entire picture is segmented into blobs such that the picture elements within each blob have similar characteristics. The boundaries between the blobs comprise the boundaries. The algorithm always generates closed boundaries. The algorithm was developed for multispectral imagery of the earth's surface. Application of this algorithm to various image processing techniques such as efficient coding, information extraction (terrain classification), and pattern recognition (feature selection) are included.

Gupta, J. N.↗

NASA NTRS1976

An algorithm for selecting a radiation transport subgrid for ablation and radiation coupled hypersonic viscous shock-layer problems

An algorithm is described for selecting a grid subset for calculating radiative transport. The subset spacing is determined by using the variation in aerothermal properties across the full grid of the shock layer. Results show that a radiation grid subset of 15 to 20 points can be used for viscous-shock layer calculations where approximately 50 grid points are required to define the aerothermal profiles. Results are presented for various planetary entry conditions with and without mass injection to demonstrate both the validity and utility of the algorithm.

Bolz, C. W., Jr.↗

NASA NTRS1977

Regenerable device for scrubbing breathable air of CO2 and moisture without special heat exchanger equipment

The device concerns the circulation of cabin air through canisters which absorb and adsorb carbon dioxide, together with excess moisture, and return the scrubbed air to the cabin for recirculation. A coating on an inert substrate in granular form absorbs and adsorbs the impurities at standard temperatures and pressures, but desorbs such impurities at low pressures (vacuum) and standard temperatures. This fact is exploited by making the device in a stack of cells consisting of layers or cells which are isolated from one another flow-wise and are connected to separate manifolds and valving systems into two separate subsets. A first subset may be connected for the flow breathable air therethrough until the polyethyleneimine of its cells is saturated with CO2 and H2O. During the same period the second subset of cells is manifolded to a vacuum source.

Tepper, E. H.↗

NASA NTRS1980

A magnetohydrodynamic model for corotating interplanetary structures

A model is developed which treats interplanetary structures as a small-scale incompressible Alfvenic fluctuation superposed on a large-scale background flow, and uses the complete magnetohydrodynamic equations and the full energy equation to describe the interplanetary structures. For steady-state corotating structures the model assumes the background flow to be field aligned, and the nonlinear system is treated as being composed of two subsets: one dealing with the expansion of the solar wind in stream tubes, the other with the interaction between neighboring stream tubes. The expansion subset has a singularity at Parker's critical radius, and the interaction subset has a singularity at the Alfvenic point. Concerning the region where the flow velocity is super-Alfvenic, the characteristic equation is derived, and a general method of numerical solution for the three-dimensional problems based on the characteristics theory is discussed. In addition, a viscous WKB solution of the microscale system is presented.

Whang, Y. C.↗

NASA NTRS1984

A Preliminary Analysis of LANDSAT-4 Thematic Mapper Radiometric Performance

Analysis was performed to characterize the radiometry of three Thematic Mapper (TM) digital products of a scene of Arkansas. The three digital products examined were the NASA raw (BT) product, the radiometrically corrected (AT) product and the radiometrically and geometrically corrected (PT) product. The frequency distribution of the digital data; the statistical correlation between the bands; and the variability between the detectors within a band were examined on a series of image subsets from the full scene. The results are presented from one 1024 x 1024 pixel subset of Realfoot Lake, Tennessee which displayed a representative range of ground conditions and cover types occurring within the full frame image. Bands 1, 2 and 5 of the sample area are presented. The subsets were extracted from the three digital data products to cover the same geographic area. This analysis provides the first step towards a full appraisal of the TM radiometry being performed as part of the ESA/CEC contribution to the NASA/LIDQA program.

Justice, C.↗

NASA NTRS1985

An algorithm for computing the number of distinct spectral vectors in thematic mapper data

A computationally efficient method was developed to compute the number of distinct spectral vectors and their frequency of occurrence in Landsat-4 Thematic Mapper (TM) data. The algorithm first partitions the image into spectrally disjoint subsets and then computes the frequency distribution of distinct spectral vectors within each subset from a multidimensional histogram. The overall frequency distribution is tabulated by accumulating the results from each subset. The number of distinct spectral vectors could be used as a measure of potential storage compaction of alternate data representations for data compression, or as a measure of information content in the comparison of spectral band combinations and/or spatial resolutions for an image. Results from processing three 512 x 512 pixel Landsat-4 TM images and one Landsat-4 Multispectral Scanner (MSS) image are presented as examples. An algorithm for computing the frequency distribution of distinct spectral vectors in MSS data is given in the Appendix.

Wharton, S. W.↗

NASA NTRS1986

The SIMRAND methodology: Theory and application for the simulation of research and development projects

A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions.

Miles, R. F., Jr.↗

NASA NTRS1992

Encoding spatial images: A fuzzy set theory approach

As the use of fuzzy set theory continues to grow, there is an increased need for methodologies and formalisms to manipulate obtained fuzzy subsets. Concepts involving relative position of fuzzy patterns are acknowledged as being of high importance in many areas. In this paper, we present an approach based on the concept of dominance in fuzzy set theory for modelling relative positions among fuzzy subsets of a plane. In particular, we define the following spatial relations: to the left (right), in front of, behind, above, below, near, far from, and touching. This concept has been implemented to define spatial relationships among fuzzy subsets of the image plane. Spatial relationships based on fuzzy set theory, coupled with a fuzzy segmentation, should therefore yield realistic results in scene understanding.

Sztandera, Leszek M.↗

NASA NTRS1992

Validation and upgrading of physically based mathematical models

The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.

Duval, Ronald↗

NASA NTRS1993

The signature of the cosmological redshift in population studies of gamma-ray burst spectra

The slope of a gamma-ray burst spectrum determines how the burst flux decreases as the cosmological redshift z increases. This provides a test for the presence of a cosmological redshift in a sample of gamma-ray bursts. Many bursts have spectra characterized by a frequency-dependent power-law index, so a burst subset can be created by requiring that each subset member have a power-law index of the given value at a low frequency and an index of a different given value at a high frequency. If all bursts in this subset are at z much less than 0.1, then the flux at low frequency will change proportionally with the flux at high frequency. If, however, z greater than 0.1 for most bursts, then the linear dependence of the high-frequency flux on the low-frequency flux disappears at the flux characterizing the spatial cutoff in the log N-log C(max)/C(min) diagram. This signature of the cosmological redshift generally persists when gamma-ray bursts are given a broad distribution of intrinsic fluxes and spectral shapes. The characteristics that a burst distribution must have to mask the cosmological redshift are discussed. The limitations of this test are observational, arising primarily from errors in measuring the photon flux and in determining the spectral index of the burst spectrum.

Brainerd, J. J.↗

NASA NTRS1993

A formal language for the specification and verification of synchronous and asynchronous circuits

A formal hardware description language for the intended application of verifiable asynchronous communication is described. The language is developed within the logical framework of the Nqthm system of Boyer and Moore and is based on the event-driven behavioral model of VHDL, including the basic VHDL signal propagation mechanisms, the notion of simulation deltas, and the VHDL simulation cycle. A core subset of the language corresponds closely with a subset of VHDL and is adequate for the realistic gate-level modeling of both combinational and sequential circuits. Various extensions to this subset provide means for convenient expression of behavioral circuit specifications.

Russinoff, David M.↗