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At least 1,261 records · Page 70

All sources NASA NTRS DOE OSTI

DOE OSTI2020

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution; thus, avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2022

A Quantum Algorithm to Simulate Open Quantum Systems

Given the advent of quantum algorithms for a wide array of problems in linear algebra and machine learning, it is important to develop general methods for the simulation of arbitrary (ie non-unitary) operators on quantum hardware. In this talk, we present a novel quantum algorithm based on the quantum singular value transformation (QSVT) to apply an arbitrary operator K to some input state and subsequently estimate the expectation value of some observable. Our construction then immediately yields a route to estimating observables of states undergoing open quantum dynamics, whose effect is captured by a set of non-unitary Kraus operators. Our algorithm succeeds deterministically given the Sz-Nagy dilation, and we provide details on the algorithm's query and gate complexity, numerical verification, and comparisons with prior methods.

Quantum computing↗

NASA NTRS2003

An algorithm for neurite outgrowth reconstruction

We present a numerical method which provides the ability to analyze digitized microscope images of retinal explants and quantify neurite outgrowth. Few parameters are required as input and limited user interaction is necessary to process an entire experiment of images. This eliminates fatigue related errors and user-related bias common to manual analysis. The method does not rely on stained images and handles images of variable quality. The algorithm is used to determine time and dose dependent, in vitro, neurotoxic effects of 1 GeV per nucleon iron particles in retinal explants. No neurotoxic effects are detected until 72 h after exposure; at 72 h, significant reductions of neurite outgrowth occurred at doses higher than 10 cGy.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS1987

Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Balakrishnan, A.↗

NASA NTRS1988

A stiffly-stable implicit Runge-Kutta algorithm for CFD applications

A stiffly-stable implicit Runge-Kutta integration algorithm is derived for CFD applications spanning the range of semidiscrete theories. The algorithm family contains the one-step 'theta' algorithms, including backwards Euler and the trapezoidal rule, and provides a versatile framework to identify expressions governing algorithm stability characteristics. Parameters of a Runge-Kutta optimal implicit algorithm, second-order accurate in time and stiffly-stable, are established. This algorithm is implemented within a weak statement finite element semidiscrete formulation for one- and two-dimensional conservation law systems. Numerical results are compared to theta-algorithm solutions, for unsteady quasi-one-dimensional Euler predictions with shocks, and for a specially derived two-dimensional conservation law system modeling the Euler equations.

Baker, A. J.↗

DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Nonlinear dimension reduction for surrogate modeling using gradient information

We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm uses a sample $\{{\textbf{x}}^{(i)},u({\textbf{x}}^{(i)}),\nabla u({\textbf{x}}^{(i)})\}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1994

A mathematical model for simulating noise suppression of lined ejectors

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

Watson, Willie R.↗

NASA NTRS2003

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental tool in numerous image processing and remote sensing applications. For example, unsupervised clustering is often used to obtain vegetation maps of an area of interest. This approach is useful when reliable training data are either scarce or expensive, and when relatively little a priori information about the data is available. Unsupervised clustering methods play a significant role in the pursuit of unsupervised classification. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points (or samples) in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute a set of cluster centers in d-space. Although there is no specific optimization criterion, the algorithm is similar in spirit to the well known k-means clustering method in which the objective is to minimize the average squared distance of each point to its nearest center, called the average distortion. One significant feature of ISOCLUS over k-means is that clusters may be merged or split, and so the final number of clusters may be different from the number k supplied as part of the input. This algorithm will be described in later in this paper. The ISOCLUS algorithm can run very slowly, particularly on large data sets. Given its wide use in remote sensing, its efficient computation is an important goal. We have developed a fast implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm, the filtering algorithm, by Kanungo et al.. They showed that, by storing the data in a kd-tree, it was possible to significantly reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm. For technical reasons, which are explained later, it is necessary to make a minor modification to the ISOCLUS specification. We provide empirical evidence, on both synthetic and Landsat image data sets, that our algorithm's performance is essentially the same as that of ISOCLUS, but with significantly lower running times. We show that our algorithm runs from 3 to 30 times faster than a straightforward implementation of ISOCLUS. Our adaptation of the filtering algorithm involves the efficient computation of a number of cluster statistics that are needed for ISOCLUS, but not for k-means.

Memarsadeghi, Nargess↗

NASA NTRS1990

Modeling supersonic combustion using a fully-implicit numerical method

A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.

Maccormack, Robert W.↗

DOE OSTI2025

Solving k –SAT problems with generalized quantum measurement

We generalize the projection–based quantum measurement–driven k –SAT algorithm of Benjamin, Zhao, and Fitzsimons to arbitrary strength quantum measurements, including the limit of continuous monitoring. In doing so, we clarify that this algorithm is a particular case of the measurement–driven quantum control strategy elsewhere referred to as “Zeno dragging”. We argue that the algorithm is most efficient with finite time and measurement resources in the continuum limit, where measurements have an infinitesimal strength and duration. Moreover, for solvable k -SAT problems, the dynamics generated by the algorithm converge deterministically towards target dynamics in the long–time (Zeno) limit, implying that the algorithm can successfully operate autonomously via Lindblad dissipation, without detection. We subsequently study both the conditional and unconditional dynamics of the algorithm implemented via generalized measurements, quantifying the advantages of detection for heralding errors. These strategies are investigated first in a computationally–trivial 2-qubit 2-SAT problem to build intuition, and then we consider the scaling of the algorithm on 3-SAT problems encoded with 4–10 qubits. We numerically investigate the scaling of 3-SAT with respect to algorithmic runtime and find that the optimized time to solution scales with qubit number n as λ n , where λ is slightly larger than $\sqrt{2}$ for unconditional dynamics and less than $\sqrt{2}$ for conditional dynamics. We assess the implications for using this analog measurement–driven approach to quantum computing in practice.

quantum information↗

NASA NTRS1989

Parallel multi-time step integration on a transputer system

An algorithm which allows different nodes of the finite element mesh to be integrated with different time steps is presented for second order finite element systems. The implementation of this algorithm on a system of transputer processors is discussed and a numerical example is used to evaluate the efficiency of the algorithm.

Smolinski, P.↗

NASA NTRS1976

A technique for pole-zero placement for dual-input control systems

A technique is presented for determining state variable feedback gains that will place both the poles and zeros of a selected transfer function of a dual-input control system at pre-determined locations in the s-plane. Leverrier's algorithm is used to determine the numerator and denominator coefficients of the closed-loop transfer function as functions of the feedback gains. The values of gain that match these coefficients to those of a pre-selected model are found by solving two systems of linear simultaneous equations. The algorithm has been used in a computer simulation of the CH-47 helicopter to control longitudinal dynamics.

Reid, G. F.↗

NASA NTRS1973

A parallel variable metric optimization algorithm

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Straeter, T. A.↗

NASA NTRS1997

Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

Kontinos, Dean A.↗

NASA NTRS1989

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Lin, Tsung-Chieh↗

NASA NTRS1992

A generalized reusable guidance algorithm for optimal aerobraking

A practical real-time guidance algorithm was developed for guiding aerobraking vehicles in such a way that the maximum heating rate, the maximum structural loads, and the post-aeropass delta-V requirements (for post-aeropass orbit insertion) are all minimized. The algorithm is general and reusable in the sense that a minimum of assumptions are made, thus minimizing the number of gains and mission-dependent parameters that must be laboriously determined prior to a particular mission. A particularly interesting feature is that inplane guidance performance is tuned by simply adjusting one mission-dependent parameter, the bank margin; similarly, the out-of-plane guidance performance is turned by simply adjusting a plane controller time constant. Other objectives in the algorithm development are simplicity, efficiency, and ease of use. The algorithm is developed for, but not necessarily restricted to, a single pass mission and a trimmed vehicle with a bank angle modulation as the method of trajectory control. Guidance performance is demonstrated via results obtained using this algorithm integrated into an aerobraking test-bed program. Comparisons are made with numerical results from a version of the aerobraking guidance algorithm that was to be flown onboard NASA's aeroassist flight experiment (AFE) vehicle. Promising results are obtained with a minimum of development effort.

Dukeman, G. A.↗