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DOE OSTI2015

The compressed state Kalman filter for nonlinear state estimation: Application to large-scale reservoir monitoring

Reservoir monitoring aims to provide snapshots of reservoir conditions and their uncertainties to assist operation management and risk analysis. These snapshots may contain millions of state variables, e.g., pressures and saturations, which can be estimated by assimilating data in real time using the Kalman filter (KF). However, the KF has a computational cost that scales quadratically with the number of unknowns, m, due to the cost of computing and storing the covariance and Jacobian matrices, along with their prod-ucts. The compressed state Kalman filter (CSKF) adapts the KF for solving large-scale monitoring problems. The CSKF uses N preselected orthogonal bases to compute an accurate rank-N approximation of the covari-ance that is close to the optimal spectral approximation given by SVD. The CSKF has a computational cost that scales linearly in m and uses an efficient matrix-free approach that propagates uncertainties using N + 1 forward model evaluations, where N << m. Here in this paper we present a generalized CSKF algorithm for nonlin-ear state estimation problems such as CO 2 monitoring. For simultaneous estimation of multiple types of state variables, the algorithm allows selecting bases that represent the variability of each state type. Through synthetic numerical experiments of CO 2 monitoring, we show that the CSKF can reproduce the Kal-man gain accurately even for large compression ratios (m/N). For a given computational cost, the CSKF uses a robust and flexible compression scheme that gives more reliable uncertainty estimates than the ensemble Kalman filter, which may display loss of ensemble variability leading to suboptimal uncertainty estimates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

On the Need for Comprehensive Validation of Deformable Image Registration, Investigated With a Novel 3-Dimensional Deformable Dosimeter

Purpose: To introduce and evaluate a novel deformable 3-dimensional (3D) dosimetry system (Presage-Def/Optical-CT) and its application toward investigating the accuracy of dose deformation in a commercial deformable image registration (DIR) package. Methods and Materials: Presage-Def is a new dosimetry material consisting of an elastic polyurethane matrix doped with radiochromic leuco dye. Radiologic and mechanical properties were characterized using standard techniques. Dose-tracking feasibility was evaluated by comparing dose distributions between dosimeters irradiated with and without 27% lateral compression. A checkerboard plan of 5-mm square fields enabled precise measurement of true deformation using 3D dosimetry. Predicted deformation was determined from a commercial DIR algorithm. Results: Presage-Def exhibited a linear dose response with sensitivity of 0.0032 ΔOD/(Gy∙cm). Mass density is 1.02 g/cm{sup 3}, and effective atomic number is within 1.5% of water over a broad (0.03-10 MeV) energy range, indicating good water-equivalence. Elastic characteristics were close to that of liver tissue, with Young's modulus of 13.5-887 kPa over a stress range of 0.233-303 kPa, and Poisson's ratio of 0.475 (SE, 0.036). The Presage-Def/Optical-CT system successfully imaged the nondeformed and deformed dose distributions, with isotropic resolution of 1 mm. Comparison with the predicted deformed 3D dose distribution identified inaccuracies in the commercial DIR algorithm. Although external contours were accurately deformed (submillimeter accuracy), volumetric dose deformation was poor. Checkerboard field positioning and dimension errors of up to 9 and 14 mm, respectively, were identified, and the 3D DIR-deformed dose γ passing rate was only γ{sub 3%/3} {sub mm} = 60.0%. Conclusions: The Presage-Def/Optical-CT system shows strong potential for comprehensive investigation of DIR algorithm accuracy. Substantial errors in a commercial DIR were found in the conditions evaluated. This work highlights the critical importance of careful validation of DIR algorithms before clinical implementation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Fast Quasi-Static Time-Series (QSTS) for yearlong PV impact studies using vector quantization

The rapidly growing penetration levels of distributed photovoltaic (PV) systems requires more comprehensive studies to understand their impact on distribution feeders. IEEE P.1547 highlights the need for Quasi-Static Time Series (QSTS) simulation in conducting distribution impact studies for distributed resource interconnection. Unlike conventional scenario-based simulation, the time series simulation can realistically assess time-dependent impacts such as the operation of various controllable elements (e.g. voltage regulating tap changers) or impacts of power fluctuations. However, QSTS simulations are still not widely used in the industry because of the computational burden associated with running yearlong simulations at a 1-s granularity, which is needed to capture device controller effects responding to PV variability. This study presents a novel algorithm that reduces the number of times that the non-linear 3-phase unbalanced AC power flow must be solved by storing and reassigning power flow solutions as it progresses through the simulation. Each unique power flow solution is defined by a set of factors affecting the solution that can easily be queried. We demonstrate a computational time reduction of 98.9% for a yearlong simulation at 1-s resolution with minimal errors for metrics including: number of tap changes, capacitor actions, highest and lowest voltage on the feeder, line losses, and ANSI voltage violations. Finally, the key contribution of this work is the formulation of an algorithm capable of: (i) drastically reducing the computational time of QSTS simulations, (ii) accurately modeling distribution system voltage-control elements with hysteresis, and (iii) efficiently compressing result time series data for post-simulation analysis.

14 SOLAR ENERGY↗

DOE OSTI2015

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

ENGINE COMBUSTION SYSTEM OPTIMIZATION USING CFD AND MACHINE LEARNING: A METHODOLOGICAL APPROACH

Gasoline compression ignition (GCI) engines are considered an attractive alternative to traditional spark-ignition and diesel engines. In this work, a Machine Learning-Grid Gradient Algorithm (ML-GGA) approach was developed to optimize the performance of internal combustion engines. Machine learning (ML) offers a pathway to transform complex physical processes that occur in a combustion engine into compact informational processes. The developed ML-GGA model was compared with a recently developed Machine learning Genetic Algorithm (ML-GA). Detailed investigations of optimization solver parameters and variables limits extension were performed in the present ML-GGA model to improve the accuracy and robustness of the optimization process. Detailed descriptions of the different procedures, optimization tools and criteria that must be followed for a successful output are provided here. The developed ML-GGA approach was used to optimize the operating conditions (case 1) and the piston bowl design (case 2) of a heavy-duty diesel engine running on a gasoline fuel with a Research Octane Number (RON) of 80. The ML-GGA approach yielded > 2% improvements in the merit function, compared to the optimum obtained from a thorough computational fluid dynamics (CFD) guided system optimization. The predictions from the ML-GGA approach were validated with engine CFD simulations. This study demonstrates the potential of ML-GGA to significantly reduce the time needed for optimization problems, without loss in accuracy compared to traditional approaches.

engine optimization↗

NASA NTRS1984

Initial postbuckling analysis of elastoplastic thin-shear structures

The design of thin shell structures with respect to elastoplastic buckling requires an extended analysis of the influence of initial imperfections. For conservative design, the most critical defect should be assumed with the maximum allowable magnitude. This defect is closely related to the initial postbuckling behavior. An algorithm is given for the quasi-static analysis of the postbuckling behavior of structures that exhibit multiple buckling points. the algorithm based upon an energy criterion allows the computation of the critical perturbation which will be employed for the definition of the critical defect. For computational efficiency, the algorithm uses the reduced basis technique with automatic update of the modal basis. The method is applied to the axisymmetric buckling of cylindrical shells under axial compression, and conclusions are given for future research.

E G Carnoy↗

NASA NTRS1985

Embedded mesh solutions of the Euler equation using a multiple-grid method

New developments make it now possible to obtain solutions to Euler equations for many problems on the basis of acceptable computing times. The possibility of an extension of these methods to more difficult flows and increasingly complex geometries can depend on obtaining suitable grid structures. Thus, an attractive approach to complex geometries involves the recasting of the problem into the framework of a multiple-grid structure. The discrete equations represented on the grid are solved as a simultaneous system. In the present investigation, this is accomplished with the aid of Ni's multiple-grid algorithm. The multiple-grid structure provided in this study represents the first step towards a completely general modular approach to the solution of the complete compressible flow problem. In the presented cases, a fine mesh resolution is obtained within the embedded mesh regions, while preserving the global coarse mesh convergence rates.

Usab, W. J., Jr.↗

NASA NTRS1990

Instrumentation and robotic image processing using top-down model control

A top-down image processing scheme is described. A three-dimensional model of a robotic working environment, with robot manipulators, workpieces, cameras, and on-the-scene visual enhancements is employed to control and direct the image processing, so that rapid, robust algorithms act in an efficient manner to continually update the model. Only the model parameters are communicated, so that savings in bandwidth are achieved. This image compression by modeling is especially important for control of space telerobotics. The background for this scheme lies in an hypothesis of human vision put forward by the senior author and colleagues almost 20 years ago - the Scanpath Theory. Evidence was obtained that repetitive sequences of saccadic eye movements, the scanpath, acted as the checking phase of visual pattern recognition. Further evidence was obtained that the scanpaths were apparently generated by a cognitive model and not directly by the visual image. This top-down theory of human vision was generalized in some sense to the frame in artificial intelligence. Another source of the concept arose from bioengineering instrumentation for measuring the pupil and eye movements with infrared video cameras and special-purpose hardware.

Stark, Lawrence↗

NASA NTRS1989

Computational fluid dynamics on a massively parallel computer

A finite difference code was implemented for the compressible Navier-Stokes equations on the Connection Machine, a massively parallel computer. The code is based on the ARC2D/ARC3D program and uses the implicit factored algorithm of Beam and Warming. The codes uses odd-even elimination to solve linear systems. Timings and computation rates are given for the code, and a comparison is made with a Cray XMP.

Jespersen, Dennis C.↗

NASA NTRS2010

NASA Tech Briefs, October 2010

Topics covered include: Hybrid Architecture Active Wavefront Sensing and Control; Carbon-Nanotube-Based Chemical Gas Sensor; Aerogel-Positronium Technology for the Detection of Small Quantities of Organic and/or Toxic Materials; Graphene-Based Reversible Nano-Switch/Sensor Schottky Diode; Inductive Non-Contact Position Sensor; High-Temperature Surface-Acoustic-Wave Transducer; Grid-Sphere Electrodes for Contact with Ionospheric Plasma; Enabling IP Header Compression in COTS Routers via Frame Relay on a Simplex Link; Ka-Band SiGe Receiver Front-End MMIC for Transponder Applications; Robust Optimization Design Algorithm for High-Frequency TWTs; Optimal and Local Connectivity Between Neuron and Synapse Array in the Quantum Dot/Silicon Brain; Method and Circuit for In-Situ Health Monitoring of Solar Cells in Space; BGen: A UML Behavior Network Generator Tool; Platform for Post-Processing Waveform-Based NDE; Electrochemical Hydrogen Peroxide Generator; Fabrication of Single, Vertically Aligned Carbon Nanotubes in 3D Nanoscale Architectures; Process to Create High-Fidelity Lunar Dust Simulants; Lithium-Ion Electrolytes Containing Phosphorous-Based, Flame-Retardant Additives; InGaP Heterojunction Barrier Solar Cells; Straight-Pore Microfilter with Efficient Regeneration; Determining Shear Stress Distribution in a Laminate; Self-Adjusting Liquid Injectors for Combustors; Handling Qualities Prediction of an F-16XL-Based Reduced Sonic Boom Aircraft; Tele-Robotic ATHLETE Controller for Kinematics - TRACK; Three-Wheel Brush-Wheel Sampler; Heterodyne Interferometer Angle Metrology; Aligning Astronomical Telescopes via Identification of Stars; Generation of Optical Combs in a WGM Resonator from a Bichromatic Pump; Large-Format AlGaN PIN Photodiode Arrays for UV Images; Fiber-Coupled Planar Light-Wave Circuit for Seed Laser Control in High Spectral Resolution Lidar Systems; On Calculating the Zero-Gravity Surface Figure of a Mirror; Optical Modification of Casimir Forces for Improved Function of Micro- and Nano-Scale Devices; Analysis, Simulation, and Verification of Knowledge-Based, Rule-Based, and Expert Systems; Core and Off-Core Processes in Systems Engineering; Digital Reconstruction Supporting Investigation of Mishaps; and Template Matching Approach to Signal Prediction.

Source record↗

NASA NTRS2005

Real-Time Principal-Component Analysis

A recently written computer program implements dominant-element-based gradient descent and dynamic initial learning rate (DOGEDYN), which was described in Method of Real-Time Principal-Component Analysis (NPO-40034) NASA Tech Briefs, Vol. 29, No. 1 (January 2005), page 59. To recapitulate: DOGEDYN is a method of sequential principal-component analysis (PCA) suitable for such applications as data compression and extraction of features from sets of data. In DOGEDYN, input data are represented as a sequence of vectors acquired at sampling times. The learning algorithm in DOGEDYN involves sequential extraction of principal vectors by means of a gradient descent in which only the dominant element is used at each iteration. Each iteration includes updating of elements of a weight matrix by amounts proportional to a dynamic initial learning rate chosen to increase the rate of convergence by compensating for the energy lost through the previous extraction of principal components. In comparison with a prior method of gradient-descent-based sequential PCA, DOGEDYN involves less computation and offers a greater rate of learning convergence. The sequential DOGEDYN computations require less memory than would parallel computations for the same purpose. The DOGEDYN software can be executed on a personal computer.

Duong, Vu↗

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.↗

DOE OSTI2022

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗

DOE OSTI2020

Provable Convergence of Plug-and-Play Priors With MMSE Denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. Here we address this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Aperture‐Synthesis Radar Imaging With Compressive Sensing for Ionospheric Research

Abstract Inverse methods involving compressive sensing are tested in the application of two‐dimensional aperture‐synthesis imaging of radar backscatter from field‐aligned plasma density irregularities in the ionosphere. We consider basis pursuit denoising, implemented with the fast iterative shrinkage thresholding algorithm, and orthogonal matching pursuit (OMP) with a wavelet basis in the evaluation. These methods are compared with two more conventional optimization methods rooted in entropy maximization (MaxENT) and adaptive beamforming (linearly constrained minimum variance or often “Capon's Method.”) Synthetic data corresponding to an extended ionospheric radar target are considered. We find that MaxENT outperforms the other methods in terms of its ability to recover imagery of an extended target with broad dynamic range. Fast iterative shrinkage thresholding algorithm performs reasonably well but does not reproduce the full dynamic range of the target. It is also the most computationally expensive of the methods tested. OMP is very fast computationally but prone to a high degree of clutter in this application. We also point out that the formulation of MaxENT used here is very similar to OMP in some respects, the difference being that the former reconstructs the logarithm of the image rather than the image itself from basis vectors extracted from the observation matrix. MaxENT could in that regard be considered a form of compressive sensing.

Hysell, D. L.↗

DOE OSTI2018

The basic matrix library (BML) for quantum chemistry

The basic matrix library package (BML) provides a common application programming interface (API) for linear algebra and matrix functions in C and Fortran for quantum chemistry codes. The BML API is matrix format independent. Currently the dense, compressed sparse row, and ELLPACK-R sparse matrix data types are available, each with different implementations. We show how the second-order spectral projection (SP2) algorithm used to compute the electronic structure of a molecular system represented with a tight-binding Hamiltonian can be successfully implemented with the aid of this library.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies

Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.

Rudi, Johann↗

DOE OSTI2022

Pairwise connected tensor network representation of path integrals

It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. A generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.

36 MATERIALS SCIENCE↗