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Radar technology is used extensively by NASA for remote sensing of the Earth and other Planetary bodies. In this case study, we learn about different computational concepts for processing radar data. In particular, we learn how to correct a slanted radar image by projecting it on the surface that was sensed by a radar instrument.
In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum-of-squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD. This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world datasets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE, due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.
New procedures and software have been developed for geometric transformation of images to support digital cartography of the planets. The procedures involve the correction of spacecraft camera orientation of each image with the use of ground control and the transformation of each image to a Sinusoidal Equal-Area map projection with an algorithm which allows the number of transformation calculations to vary as the distortion varies within the image. When the distortion is low in an area of an image, few transformation computations are required, and most pixels can be interpolated. When distortion is extreme, the location of each pixel is computed. Mosaics are made of these images and stored as digital databases. Completed Sinusoidal databases may be used for digital analysis and registration with other spatial data. They may also be reproduced as published image maps by digitally transforming them to appropriate map projections.
Aquarium tests of cylindrical high-explosive charges provide optical data of the detonation front velocity and shape, propagation of the shock wave in the surrounding water, and expansion rates of the detonation products behind the front. Data from aquarium experiments is often used for calibration of reactive burn models based on phenomenological equations of state (EOS) and reaction rate laws. This paper presents a multimaterial numerical modeling framework to solve the 2D axisymmetric reactive Euler equations for high-explosive aquarium tests, in particular for ammonium nitrate - fuel oil (ANFO) explosives. An extension of the Ghost Fluid Method (GFM) is used to handle the dynamic material interfaces for the ANFO explosion products, the charge-confining material (polymethyl methacrylate PMMA), and the surrounding water. This study analyzes the sensitivity of calculations (both computational efficiency and numerical accuracy) to different algorithms for the material interface models including the original GFM versus Riemann solver-based strategies. A novel method for defining the left and right states in the interfacial Riemann problem eliminates the need for sorting or nodal interpolation during the projection along the material interface. Numerical tests indicate that populating the interface node values using the Riemann solution mitigate the overheating error observed in steady-state calculations. Solution convergence and computational efficiency are explored as a function of the spatial and temporal order of the schemes. Results from the computational model with analytical equations of state and fitted reaction rate parameters show very good quantitative agreement with experimentally observed detonation front velocity, reaction products expansion, and shock wave propagation in the surrounding water for a cylindrical ANFO charge encased in PMMA. Finally, the proposed modeling framework, in conjunction with experimental tests, provides a reliable tool to assess equations of state and reaction rate expressions for reactive burn models of confined high explosives.
This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.
Edge-Directed Radial Basis Functions (EDRBF) are used to compute super resolution(SR) image from a given set of low resolution (LR) images differing in subpixel shifts. The algorithm is tested on remote sensing images and compared for accuracy with other well-known algorithms such as Iterative Back Projection (IBP), Maximum Likelihood (ML) algorithm, interpolation of scattered points using Nearest Neighbor (NN) and Inversed Distance Weighted (IDW) interpolation, and Radial Basis Functin(RBF) . The accuracy of SR depends on various factors besides the algorithm (i) number of subpixel shifted LR images (ii) accuracy with which the LR shifts are estimated by registration algorithms (iii) and the targeted spatial resolution of SR. In our studies, the accuracy of EDRBF is compared with other algorithms keeping these factors constant. The algorithm has two steps: i) registration of low resolution images and (ii) estimating the pixels in High Resolution (HR) grid using EDRBF. Experiments are conducted by simulating LR images from a input HR image with different sub-pixel shifts. The reconstructed SR image is compared with input HR image to measure the accuracy of the algorithm using sum of squared errors (SSE). The algorithm has outperformed all of the algorithms mentioned above. The algorithm is robust and is not overly sensitive to the registration inaccuracies.
We analyze an expansion of the generalized block Krylov subspace framework of [Electron. Trans. Numer. Anal., 47 (2017), pp. 100--126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and contains, as special cases, the block GMRES method and the new block Radau--Arnoldi method. Within this general setting, we present results that extend the interpolation property from the nonblock case to a matrix polynomial interpolation property for the block case, and we relate the eigenvalues of the projected matrix to the latent roots of these matrix polynomials. Some error bounds for these modified block FOM methods for solving linear systems are presented. We then show how cospatial residuals can be preserved in the case of families of shifted linear block systems. This result is used to derive computationally practical restarted algorithms for block Krylov approximations that compute the action of a matrix function on a set of several vectors simultaneously. Finally, we prove some error bounds and present numerical results showing that two modifications of FOM, the block harmonic and the block Radau--Arnoldi methods for matrix functions, can significantly improve the convergence behavior.
Fast techniques for direct volume rendering over curvilinear grids of hexahedral cells are developed. This type of 3D grid is common in computational fluid dynamics and finite element analysis. Four new projection methods are presented and compared with each other and with previous methods for tetrahedral grids and rectilinear grids. All four methods use polygon-rendering hardware for speed. A simplified algorithm for visibility ordering, which is based on a combination of breadth-first and depth-first searches, is described. A new multi-pass blending method is described that reduces visual artifacts that are introduced by linear interpolation in hardware where exponential interpolation is needed. Multi-pass blending is of equal interest to hardware-oriented projection methods used on rectilinear grids. Visualization tools that permit rapid data banding and cycling through transfer functions, as well as region restrictions, are described.
The primary goals of this project are exploring hidden geothermal resources in the U.S.A. and designing profitable enhanced geothermal systems (EGS). Many processes and parameters control geothermal exploration and energy production from geothermal fields. Diverse datasets (e.g., geology, geochemistry, geophysics, satellite, airborne geophysics) are available to help characterize subsurface geothermal conditions. Sparse and multi-scale characteristics of these datasets prohibit properly leveraging these datasets for geothermal exploration and profitable EGS design. Recent advancements in machine learning (ML) promise to resolve these issues. The tremendous challenges and risks of geothermal exploration and production bring the demand for novel ML methods and tools that can (1) analyze large field datasets, (2) assimilate model simulations (large inputs and outputs), (3) process sparse datasets, (4) perform transfer learning (between sites with different exploratory levels), (5) extract hidden geothermal signatures in the field and simulation data, (6) label geothermal resources and processes, (7) identify high-value data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies. To address these necessities, ML-based geothermal resources exploration and enhanced geothermal systems (EGS) design tools have been developed. The exploration tool is called GeoThermalCloud and EGS design tool is called GeoDT-ML. GeoThermalCloud (https://github.com/SmartTensors/GeoThermalCloud.jl) utilizes a LANL unsupervised ML platform called SmartTensors (https://tensors.lanl.gov/) to automate data analyses and interpretations by extracting hidden signatures to identify geothermal prospects. Also, it enables the identification of critical measurements needed to identify geothermal resource signatures. Alternatively, GeoDT-ML (https://github.com/SmartTensors/GeoThermalCloud.jl/tree/master/EGS) is an ML-based alternative to GeoDT (https://github.com/GeoDesignTool/GeoDT.git), a fast, simplified multi-physics solver to evaluate EGS project designs in uncertain geologic systems. GeoDT-ML leverages recent advances in deep learning and high-performance computing. It is a faster and simpler version of GeoDT. To make this project a success, we used capabilities of LANL, PNNL, Google, Stanford, and Julia Computing. We analyzed eight datasets of the U.S.A. using GeothermalCloud and demonstrated potential highly prospective geothermal resources and identified key factors defining highly prospective sites. The first data set includes 44 locations in southwest New Mexico and 18 geological, hydrogeological, geophysical, geothermal, geochemical attributes. We defined low- and medium-temperature hydrothermal systems and discovered a new highly prospective site. The second data set analyzed 18 shallow water chemistry attributes at 14,342 locations in the Great Basin. It demarcated modestly, moderately, and highly prospective sites including key attributes for each type of prospectivity. The third data set analyzed Utah FORGE data including satellite (InSAR), geophysical (gravity, seismic), geochemical, and geothermal attributes. Here, we performed prospectivity analysis to identify future drilling locations using geological, geochemical, and geophysical attributes. Maps of temperature at depth and heat flow are constructed based on the available data. Prospectivity maps were generated, and drilling locations were proposed for future geothermal field exploration. The fourth data set analyzed 21 attributes at 120 locations in Tularosa Basin, New Mexico; data comes from past play fairway analyses in this region. ML analyses identified geothermal signatures associated with modestly, moderately, and highly hydrothermal systems. We also defined dominant attributes and spatial distribution of the geothermal signatures. The fifth, sixth, seventh, and eighth datasets include Tohatchi Springs, New Mexico, Hawaii, Brady site, Nevada, and EGS Collab, respectively. Moreover, we coupled GeothermalCloud and magnetotellurics data to pinpoint drilling locations for developing geothermal projects in the Tularosa Basin, New Mexico. GeothermalCloud found potential prospective locations for geothermal resources near White Sands Missile Range and McGregor Range at Fort Bliss. Magnetotellurics data determined the potential depth (~1800m) of geothermal prospects at McGregor Range based on apparent resistivity structures/layers in the subsurface. The McGregor Range consists of three resistivity layers and two resistivity structures. Magnetotellurics data also helps identify that the western portion of the McGregor Range has thick and low-resistivity earth materials. The low resistivity to the west is most likely for a fault system. Assuming temperature is consistent with a geothermal reservoir, the west-central part of the McGregor Range has the highest geothermal potential because of the increase in porosity and associated permeability attributed to the interpreted fault system. Also, we devised a coupling strategy between a process model and GeothermalCloud to characterize hydrogeological conditions and geothermal conditions, respectively. The process model characterizes hydrogeological and geothermal conditions on highly prospective geothermal sites provided by GeothermalCloud. We developed a physics-informed neural network (PINN) version of the Burns equation that can be easily coupled with GeothermalCloud. Furthermore, we performed an optimal design decision maximizing the economic value of an EGS power plant. This study optimized the range of well spacing between injection and production wells maximizing net present value in dollars (NPV). For this task, we used the GeoDT to simulate the Utah FORGE EGS development cycle from the initial well design to the end of production. Next, we accomplished another crucial task, which is predicting permeability of geothermal reservoirs. Predicting permeability of geothermal reservoirs is a non-trivial task because of huge computational runtime of simulation and lack of measurements. To avoid these limitations, we used easy-to-measure chemical concentrations in the subsurface as measurement data and convolutional neural network based ML model of a high-fidelity model. Next, we predicted permeability using Markov chain Monte Carlo simulation. We found that Markov chain Monte Carlo simulation predicts permeability with a high certainty if the prediction zone in the simulation area has chemical concentration data. Finally, we analyzed the DOE funded INGENIOUS and GeoDAWN projects data. For discovering hidden geothermal systems in the Great Basin, the INGENIOUS project accumulated old data, collected new data, and released them in 2022. The dataset includes a total of 24 geological, geophysical, and geochemical attributes. Data resolution and scale significantly vary prohibiting an appropriate usage. To avoid such limitations, we brought all data in the same resolution and scale by applying the inverse distance weighting interpolation technique for predicting data in unsampled locations. Subsequently, we analyzed LiDAR data of the GeoDAWN project. We received data in tiles format. The DOE’s overarching goal is to use ML on LiDAR data for finding favorable geological structures (e.g., step up faults in Brady, Nevada). To serve the purpose, we need to label favorable geologic structures that correspond to LiDAR data. We wrote an algorithm to label the LiDAR data with the favorable geologic structures.
Interaction with tumbling objects will become more common as human activities in space expand. Attempting to interact with a large complex object translating and rotating in space, a human operator using only his visual and mental capacities may not be able to estimate the object motion, plan actions or control those actions. A robot system (RAMBO) equipped with a camera, which, given a sequence of simple tasks, can perform these tasks on a tumbling object, is being developed. RAMBO is given a complete geometric model of the object. A low level vision module extracts and groups characteristic features in images of the object. The positions of the object are determined in a sequence of images, and a motion estimate of the object is obtained. This motion estimate is used to plan trajectories of the robot tool to relative locations rearby the object sufficient for achieving the tasks. More specifically, low level vision uses parallel algorithms for image enhancement by symmetric nearest neighbor filtering, edge detection by local gradient operators, and corner extraction by sector filtering. The object pose estimation is a Hough transform method accumulating position hypotheses obtained by matching triples of image features (corners) to triples of model features. To maximize computing speed, the estimate of the position in space of a triple of features is obtained by decomposing its perspective view into a product of rotations and a scaled orthographic projection. This allows use of 2-D lookup tables at each stage of the decomposition. The position hypotheses for each possible match of model feature triples and image feature triples are calculated in parallel. Trajectory planning combines heuristic and dynamic programming techniques. Then trajectories are created using dynamic interpolations between initial and goal trajectories. All the parallel algorithms run on a Connection Machine CM-2 with 16K processors.
A well-documented problem in the analysis of data collected by spacecraft instruments is the need for an accurate, efficient representation of the data set. The data may suffer from several problems, including additive noise, data dropouts, an irregularly-spaced sampling grid, and time-delayed sampling. These data irregularities render most traditional signal processing techniques unusable, and thus the data must be interpolated onto an even grid before scientific analysis techniques can be applied. In addition, the extremely large volume of data collected by scientific instrumentation presents many challenging problems in the area of compression, visualization, and analysis. Therefore, a representation of the data is needed which provides a structure which is conducive to these applications. Wavelet representations of data have already been shown to possess excellent characteristics for compression, data analysis, and imaging. The main goal of this project is to develop a new adaptive filtering algorithm for image restoration and compression. The algorithm should have low computational complexity and a fast convergence rate. This will make the algorithm suitable for real-time applications. The algorithm should be able to remove additive noise and reconstruct lost data samples from images.
Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.
We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.
The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction Π will almost certainly be nonorthogonal (and divergent) in any known standard product, meaning ∥Π∥ > 1. This introduces a new consideration, that one wants coarse-grid correction to be as close to orthogonal as possible, in an appropriate norm. In addition, due to nonorthogonality, Π may actually amplify certain error modes that are in the range of interpolation. Relaxation must then not only be complementary to interpolation, but also rapidly eliminate any error amplified by the nonorthogonal correction, or the algorithm may diverge. Here this paper develops analytic formulae on how to construct “compatible” transfer operators in nonsymmetric AMG such that ∥Π∥ = 1 in some standard matrix-induced norm. Discussion is provided on different options for the norm in the nonsymmetric setting, the relation between “ideal” transfer operators in different norms, and insight into the convergence of nonsymmetric reduction-based AMG.
Recent developments in algorithms and software tools for generating overset grids for complex configurations are described. These include the overset surface grid generation code SURGRD and version 2.0 of the hyperbolic volume grid generation code HYPGEN. The SURGRD code is in beta test mode where the new features include the capability to march over a collection of panel networks, a variety of ways to control the side boundaries and the marching step sizes and distance, a more robust projection scheme and an interpolation option. New features in version 2.0 of HYPGEN include a wider range of boundary condition types. The code also allows the user to specify different marching step sizes and distance for each point on the surface grid. A scheme that takes into account of the overlapped zones on the body surface for the purpose of forces and moments computation is also briefly described, The process involves the following two software modules: MIXSUR - a composite grid generation module to produce a collection of quadrilaterals and triangles on which pressure and viscous stresses are to be integrated, and OVERINT - a forces and moments integration module.
Abstract Cities need climate information to develop resilient infrastructure and for adaptation decisions. The information desired is at the order of magnitudes finer scales relative to what is typically available from climate analysis and future projections. Urban downscaling refers to developing such climate information at the city (order of 1 – 10 km) and neighborhood (order of 0.1 – 1 km) resolutions from coarser climate products. Developing these higher resolution (finer grid spacing) data needed for assessments typically covering multiyear climatology of past data and future projections is complex and computationally expensive for traditional physics-based dynamical models. In this study, we develop and adopt a novel approach for urban downscaling by generating a general-purpose operator using deep learning. This ‘DownScaleBench’ tool can aid the process of downscaling to any location. The DownScaleBench has been generalized for both in situ (ground- based) and satellite or reanalysis gridded data. The algorithm employs an iterative super-resolution convolutional neural network (Iterative SRCNN) over the city. We apply this for the development of a high-resolution gridded precipitation product (300 m) from a relatively coarse (10 km) satellite-based product (JAXA GsMAP). The high-resolution gridded precipitation datasets is compared against insitu observations for past heavy rain events over Austin, Texas, and shows marked improvement relative to the coarser datasets relative to cubic interpolation as a baseline. The creation of this Downscaling Bench has implications for generating high-resolution gridded urban meteorological datasets and aiding the planning process for climate-ready cities.
Radiation therapy plays an essential role in the treatment of cancer. In radiation therapy, the ideal radiation doses are delivered to the observed tumor while not affecting neighboring normal tissues. In three-dimensional computed tomography (3D-CT) scans, the contours of tumors and organs-at-risk (OARs) are often manually delineated by radiologists. The task is complicated and time-consuming, and the manually delineated results will be variable from different radiologists. We propose a semi-supervised contour detection algorithm, which firstly uses a few points of region of interest (ROI) as an approximate initialization. Then the data sequences are achieved by the closed polygonal line (CPL) algorithm, where the data sequences consist of the ordered projection indexes and the corresponding initial points. Finally, the smooth lung contour can be obtained, when the data sequences are trained by the backpropagation neural network model (BNNM). We use the private clinical dataset and the public Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) dataset to measure the accuracy of the presented method, respectively. To the private dataset, experimental results on the initial points which are as low as 15% of the manually delineated points show that the Dice coefficient reaches up to 0.95 and the global error is as low as 1.47 × 10{sup −2}. The performance of the proposed algorithm is also better than the cubic spline interpolation (CSI) algorithm. While on the public LIDC-IDRI dataset, our method achieves superior segmentation performance with average Dice of 0.83.
The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.