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NASA NTRS1994

An efficient system for reliably transmitting image and video data over low bit rate noisy channels

This research project is intended to develop an efficient system for reliably transmitting image and video data over low bit rate noisy channels. The basic ideas behind the proposed approach are the following: employ statistical-based image modeling to facilitate pre- and post-processing and error detection, use spare redundancy that the source compression did not remove to add robustness, and implement coded modulation to improve bandwidth efficiency and noise rejection. Over the last six months, progress has been made on various aspects of the project. Through our studies of the integrated system, a list-based iterative Trellis decoder has been developed. The decoder accepts feedback from a post-processor which can detect channel errors in the reconstructed image. The error detection is based on the Huber Markov random field image model for the compressed image. The compression scheme used here is that of JPEG (Joint Photographic Experts Group). Experiments were performed and the results are quite encouraging. The principal ideas here are extendable to other compression techniques. In addition, research was also performed on unequal error protection channel coding, subband vector quantization as a means of source coding, and post processing for reducing coding artifacts. Our studies on unequal error protection (UEP) coding for image transmission focused on examining the properties of the UEP capabilities of convolutional codes. The investigation of subband vector quantization employed a wavelet transform with special emphasis on exploiting interband redundancy. The outcome of this investigation included the development of three algorithms for subband vector quantization. The reduction of transform coding artifacts was studied with the aid of a non-Gaussian Markov random field model. This results in improved image decompression. These studies are summarized and the technical papers included in the appendices.

Costello, Daniel J., Jr.↗

DOE OSTI2024

Data Science Enabled Enabled Discovery of Superconductors (Final Progress Report)

This Final Technical Report describes efforts by 4 PIs at the University of Florida (Peter Hirschfeld, Richard Hennig, Greg Stewart and James Hamlin), over the period September 2019-August 2023, to use data science and machine learning techniques to discover new conventional superconductors. The PIs constructed a discovery loop with two theorists and two experimentalists to: develop algorithms to machine learn descriptors correlating strongly with the critical temperature Tc (PI's Peter Hirschfeld, UF Physics and Richard Hennig, UF Materials Science and En), synthesize and measure properties of promising materials, and feed back the knowledge gained into the prediction algorithm. This work was motivated by the theoretical prediction and experimental discovery of high-pressure, high-pressure hydride superconductors, and to find ways to recreate the high critical temperatures in these systems at ambient pressure. Highlights from the grant include: 1) a new equation for Tc in terms of moments of the electron-phonon spectral function, improving on the so-called Allen-Dynes equation (1975); 2) study of the metastable A15 superconductor Nb3Si, formed under explosive compression at ~1000GPa to determine the kinetic barrier to the ground state structure; 3) the development of ultra-fast machine-learned atomic potentials for molecular dynamics, and 4) the discovery of superconductivity at 19K in WB2 arising from metastable defect structures in the crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Multigroup Thermal Radiation Transport with Tensor Trains

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than 100× and speedups exceeding 2×. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as 7. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1989

A multigrid and upwind viscous flow solver on 3-D embedded and overlapped grids

A numerically efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flow about complex configurations with topologically different components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually with no significant restrictions. The Navier-Stokes equations are solved by an implicit, approximately factored, upwind, finite-volume scheme. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the holes created in the computational domain by the embedded and overlapped grids. The convergence is accelerated by a multigrid algorithm despite the existence of such holes. The solution for s supersonic flow past a blunt-nose-cylinder at high angle-of-attack is obtained using a C-O grid embedded in a global Cartesian grid.

Baysal, Oktay↗

NASA NTRS1993

Computational fluid mechanics

Two papers are included in this progress report. In the first, the compressible Navier-Stokes equations have been used to compute leading edge receptivity of boundary layers over parabolic cylinders. Natural receptivity at the leading edge was simulated and Tollmien-Schlichting waves were observed to develop in response to an acoustic disturbance, applied through the farfield boundary conditions. To facilitate comparison with previous work, all computations were carried out at a free stream Mach number of 0.3. The spatial and temporal behavior of the flowfields are calculated through the use of finite volume algorithms and Runge-Kutta integration. The results are dominated by strong decay of the Tollmien-Schlichting wave due to the presence of the mean flow favorable pressure gradient. The effects of numerical dissipation, forcing frequency, and nose radius are studied. The Strouhal number is shown to have the greatest effect on the unsteady results. In the second paper, a transition model for low-speed flows, previously developed by Young et al., which incorporates first-mode (Tollmien-Schlichting) disturbance information from linear stability theory has been extended to high-speed flow by incorporating the effects of second mode disturbances. The transition model is incorporated into a Reynolds-averaged Navier-Stokes solver with a one-equation turbulence model. Results using a variable turbulent Prandtl number approach demonstrate that the current model accurately reproduces available experimental data for first and second-mode dominated transitional flows. The performance of the present model shows significant improvement over previous transition modeling attempts.

Hassan, H. A.↗

DOE OSTI2018

Application of materials informatics to vapor-grown carbon nanofiber/vinyl ester nanocomposites through self-organizing maps and clustering techniques

Data mining and knowledge discovery techniques were employed herein to acquire new information on the viscoelastic, flexural, compressive, and tensile properties of vapor-grown carbon nanofiber (VGCNF)/vinyl ester (VE) nanocomposites. Formulation and processing factors (curing environment, presence or absence of dispersing agent, mixing method, VGCNF weight fraction, VGCNF type, high-shear mixing time, and sonication time) and testing temperature were utilized as inputs and the true ultimate strength, true yield strength, engineering elastic modulus, engineering ultimate strength, flexural modulus, flexural strength, storage modulus, loss modulus, and tan delta were selected as outputs. The data mining and knowledge discovery algorithms used in this study include self-organizing maps (SOMs) and clustering techniques. SOMs demonstrated that temperature and tan delta had the most significant effects on the output responses followed by the VGCNF high-shear mixing time, and sonication time. SOMs were also used to produce optimal responses using certain combination(s) of inputs. Fuzzy C-means algorithm (FCM) was also applied to discover patterns in the nanocomposite behavior subsequent to a principal component analysis (PCA), which is a dimensionality reduction technique. Utilizing these techniques, the nanocomposite specimens were separated into different clusters based on the testing temperature (30 °C and 120 °C being the most dominant responses), tan delta, high-shear mixing time, and sonication time. Furthermore, the VGCNF/VE specimens were separated into a cluster based on their viscoelastic responses (storage and loss moduli) at the same temperature. The FCM results indicate that, while all nanocomposite properties in the new framework are essential, the viscoelastic responses of the VGCNF/VE specimens are the most significant. Here this work highlights the utility of data mining and knowledge discovery techniques in the context of materials informatics for the discovery of patterns and trends in the material behavior that are not immediately known.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Lagrangian particle method for compressible fluid dynamics

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗

NASA NTRS1992

Optimum design of ninety degree bends

An algorithm for the optimum design of an internal flow component to obtain the maximum pressure rise is presented. Maximum pressure rise in a duct with simultaneous turning and diffusion is shown to be related to the control of flow separation on the passage walls. Such a flow is usually associated with downstream conditions that are desirable in turbomachinery and propulsion applications to ensure low loss and stable performance. The algorithm requires the solution of an 'adjoint' problem in addition to the 'direct' equations governing the flow in a body, which in the present analysis are assumed to be the laminar Navier-Stokes equations. The theoretical framework and computational algorithms presented in this study are for the steady Navier-Stokes equations. A procedure is developed for the numerical solution of the adjoint equations. This procedure is coupled with a direct solver in a design iteration loop, that provides a new shape with a higher pressure rise. This procedure is first validated for the design of optimum plane diffusers in two-dimensional flow. The direct Navier-Stokes and the 'adjoint' equations are solved using a finite volume formulation for spatial discretization in an artificial compressibility framework. A simplified version of the above approach is then utilized to design ninety degree diffusing bends. Calculations were carried out for a mean radius ratio at inlet of 2.5 and Reynolds numbers varying from 100 to 500. While at this stage laminar flows is assumed, it is shown that a similar approach can be conceived for turbulent flows.

Modi, Vijay↗

DOE OSTI2023

HQ-Sim: High-performance State Vector Simulation of Quantum Circuits on Heterogeneous HPC Systems

Quantum circuit simulations are applied in more and more circum- stances as the quantum computing community becomes broader. It helps researchers to evaluate quantum algorithms and relieve the burden of limited quantum computing resources. However, most of the state-of-the-art quantum simulators utilize either CPU or GPU to store and calculate the state vector, which results in resource starvation. Moreover, the maximum number of qubits supported by the simulator is bounded by the memory, since the memory utilization increases exponentially with the number of qubits. In this study, we leverage Heterogeneous computing to utilize both CPU and GPU to store and update state vectors. We also integrate lossy data compression to reduce memory requirements. Specifically, we develop a heterogeneous framework that has a dynamic scheduler to fully utilize the computing resources. We apply lossy compression to chunked state vector to make the maximum number of qubits higher than the regular simulators, the compression also benefits the data movement between CPU and GPU.

Zhang, Boyuan↗

DOE OSTI2019

Reconstructing high-dimensional Hilbert-valued functions via compressed sensing

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our theoretical framework treats the function approximation problem as a joint sparse recovery problem, where the set of jointly sparse vectors is possibly infinite. To achieve the simultaneous reconstruction of Hilbert-valued functions in both parametric domain and Hilbert space, we propose a novel mixed-norm based `1 regularization method that exploits both energy and sparsity. Our approach requires extensions of concepts such as the restricted isometry and null space properties, allowing us to prove recovery guarantees for sparse Hilbert-valued function reconstruction. We complement the enclosed theory with an algorithm for Hilbert-valued recovery, based on standard forward-backward algorithm, meanwhile establishing its strong convergence in the considered infinite-dimensional setting. Finally, we demonstrate the minimal sample complexity requirements of our approach, relative to other popular methods, with numerical experiments approximating the solutions of high-dimensional parameterized elliptic PDEs.

Dexter, Nick↗

DOE OSTI2022

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗

NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations.

Mavriplis, Dimitri J.↗

NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

Mavriplis, Dimitri J.↗

DOE OSTI2016

Global Sensitivity Analysis with Small Sample Sizes: Ordinary Least Squares Approach

A new version of global sensitivity analysis is developed in this paper. This new version coupled with tools from statistics, machine learning, and optimization can devise small sample sizes that allow for the accurate ordering of sensitivity coefficients for the first 10-30 most sensitive chemical reactions in complex chemical-kinetic mechanisms, and is particularly useful for studying the chemistry in realistic devices. A key part of the paper is calibration of these small samples. Because these small sample sizes are developed for use in realistic combustion devices, the calibration is done over the ranges of conditions in such devices, with a test case being the operating conditions of a compression ignition engine studied earlier. Compression ignition engines operate under low-temperature combustion conditions with quite complicated chemistry making this calibration difficult, leading to the possibility of false positives and false negatives in the ordering of the reactions. So an important aspect of the paper is showing how to handle the trade-off between false positives and false negatives using ideas from the multiobjective optimization literature. The combination of the new global sensitivity method and the calibration are sample sizes a factor of approximately 10 times smaller than were available with our previous algorithm.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Modeling of wave processes in blocky media with porous and fluid-saturated interlayers

The wave processes in blocky media are analyzed by applying different mathematical models, wherein the elastic blocks interact with each other via pliant interlayers with the complex mechanical properties. Four versions of constitutive equations are considered. In the first version, an elastic interaction between the blocks is simulated within the framework of linear elasticity theory, and the model of elastic–plastic interlayers is constructed to take into account the appearance of irreversible deformation of interlayers at short time intervals. In the second one, the effects of viscoelastic shear in the interblock interlayers are taken into the consideration using the Poynting–Thomson rheological scheme. In the third option, the model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. In the fourth case, the model of a fluid-saturated material with open pores is examined based on Biot's equations. The collapse of pores is modeled by the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact, which is used to describe the behavior of materials with the different resistance to tension and compression. It was shown that the thermodynamically consistent model is provided, which means that the energy balance equation is fulfilled for an entire blocky structure, where the kinetic and potential energy of the system is the sum of the kinetic and potential energies of the blocks and interlayers. Under numerical implementation of the interlayers models, the dissipationless finite difference Ivanov's method was used. The splitting method by spatial variables in the combination with the Godunov gap decay scheme was applied in the blocks. As a result, robust and stable computational algorithms are built and tested. Using MPI technology, the parallel software was designed for the modeling of wave processes in 2D setting. The numerical results are presented, discussed and future studies are outlined. - Highlights: • We model the propagation of waves in a blocky medium with compliant interlayers. • Models of porous and fluid saturated interlayers are proposed using Biot's approach. • A parallel computational algorithm is developed for supercomputers of cluster type. • Problems of instant rotation of central and boundary blocks are solved numerically. • Wave motions are compared in the cases of elastic and fluid-saturated interlayers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1987

An engineering study of hybrid adaptation of wind tunnel walls for three-dimensional testing

Solid wall tunnels having only upper and lower walls flexing are described. An algorithm for selecting the wall contours for both 2 and 3 dimensional wall flexure is presented and numerical experiments are used to validate its applicability to the general test case of 3 dimensional lifting aircraft models in rectangular cross section wind tunnels. The method requires an initial approximate representation of the model flow field at a given lift with wallls absent. The numerical methods utilized are derived by use of Green's source solutions obtained using the method of images; first order linearized flow theory is employed with Prandtl-Glauert compressibility transformations. Equations are derived for the flexed shape of a simple constant thickness plate wall under the influence of a finite number of jacks in an axial row along the plate centerline. The Green's source methods are developed to provide estimations of residual flow distortion (interferences) with measured wall pressures and wall flow inclinations as inputs.

Brown, Clinton↗