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DOE OSTI2022

An efficient decoder for a linear distance quantum LDPC code

Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear time decoder for the recent quantum Tanner codes construction of asymptotically good qLDPC codes, which can correct all errors of weight up to a constant fraction of the blocklength. Our decoder is an iterative algorithm which searches for corrections within constant-sized regions. At each step, the corrections are found by reducing a locally defined and efficiently computable cost function which serves as a proxy for the weight of the remaining error.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

Xu, Feng↗

NASA NTRSDate not supplied

Self-consistent Quantum Iteratively Sparsified Hamiltonian Algorithm (SQuISH)

Due to coherence time limitations, reducing the resources required to run quantum algorithms and simulate physical systems on a quantum computer is crucial. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the self-consistent quantum iteratively sparsified Hamiltonian (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. By utilizing this more compact Hamiltonian, our algorithm provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how it performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware.

Diana Chamaki↗

NASA NTRS1978

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Desideri, J. A.↗

DOE OSTI2024

Iterative Stress Reconstruction Algorithm to Estimate Three-Dimensional Residual Stress Fields in Manufactured Components

Residual stress (RS) significantly impacts the mechanical performance of components. Measurement of RS often provides incomplete data in terms of components of stress and spatial density. Employing such fields in finite element simulations results in significant modification of the field to achieve equilibrium and compatibility among strains. To overcome this, an iterative stress reconstruction algorithm (ISRA) is developed to estimate 3D RS fields that satisfy equilibrium, are stress component-wise complete, and represent the characterized data sampled. An Al 7075-T651 plate and an additively manufactured (AM) A36 steel wall are considered for RS reconstruction using measurement data from the literature. A maximum variation of ~2.5 MPa in the Al plate, and ~10 MPa in the steel wall are observed between the reconstructed and measured stresses. Furthermore, unknown stress components emerge and reach significant magnitudes (upto ~2.3 MPa in the Al plate and ~45 MPa in the AM wall) during ISRA. Indeed, it is found that minor errors in measurement or data processing are eliminated through the physical requirements during ISRA. Employing a reconstructed RS field is hence not just more accurate given its compatibility, but it additionally corrects for minor errors in measurement. Furthermore, it is found that spatially dense measurement data result in convergence with fewer iterations. Finally, although ISRA yields a nonunique solution dependent on boundary conditions, measurement errors, fitting errors, and mesh density, it accommodates for uncertainties and inaccuracies in measurement, as opposed to failing to reach a physically realistic converged solution.

42 ENGINEERING↗

NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

DOE OSTI2021

Iterated projected position algorithm for constructing exponentially localized generalized Wannier functions for periodic and nonperiodic insulators in two dimensions and higher

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend on a choice of unitary transform known as a gauge transformation. Over the past few decades, there have been many works that have focused on optimizing the choice of the gauge so that the corresponding Wannier functions are maximally localized or reflect some symmetry of the underlying system. In this work, we consider fully nonperiodic materials where the usual Wannier functions are not well defined and gauge optimization is impractical. To tackle the problem of calculating exponentially localized generalized Wannier functions in both periodic and nonperiodic systems, we discuss the ‘iterated projected position (IPP)” algorithm. Here, the IPP algorithm is based on matrix diagonalization and therefore unlike optimization-based approaches, it does not require initialization and cannot get stuck at a local minimum. Furthermore, the IPP algorithm is guaranteed by a rigorous analysis to produce exponentially localized functions under certain mild assumptions. We numerically demonstrate that the IPP algorithm can be used to calculate exponentially localized bases for the Haldane model, the Kane-Mele model (in both Z 2 invariant even and Z 2 invariant odd phases), and the p x + ip y model on a quasicrystal lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Chemistry↗

NASA NTRS2012

Variable Sampling Mapping

The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.

Smith, Jeffrey, S.↗

NASA NTRS1992

An iterative implicit DDADI algorithm for solving the Navier-Stokes equation

An algorithm utilizing a first order upwind split flux technique and the diagonally dominant treatment is proposed to be the temporal operator for solving the Navier-Stokes equations. Given the limit of a five point stencil, the right hand side flux derivatives are formulated by several commonly used central and upwind schemes. Their performances are studied through a test case of free vortex convection in a uniform stream. From these results, a superior treatment for evaluating the flux term is proposed and compared with the rest. The application of the proposed algorithm to the full Navier-Stokes equations is demonstrated through a calculation of flow over a backward facing step. Results are compared against the calculation done by using the fourth order central differencing scheme with artificial damping.

Chen, S. C.↗

NASA NTRS2020

Development of a Non-Iterative Balance Load Prediction Algorithm for the NASA Ames Unitary Plan Wind Tunnel

A non-iterative load prediction algorithm for strain-gage balances was developed for the NASA Ames Unitary Plan Wind Tunnels that computes balance loads from the electrical outputs of the balance bridges and a set of state variables. A state variable could be, for example, a balance temperature difference or the bellows pressure of a flow-through balance. The algorithm directly uses regression models of the balance loads for the load prediction that were obtained by applying global regression analysis to balance calibration data. This choice greatly simplifies both implementation and use of the load prediction process for complex balance configurations as no load iteration needs to be performed. The regression model of a balance load is constructed by using terms from a total of nine term groups. Four term groups are derived from a Taylor Series expansion of the relationship between the load, gage outputs, and state variables. The remaining five term groups are defined by using absolute values of the gage outputs and state variables. Terms from these groups should only be included in the regression model if calibration data from a balance with known bi-directional outputs is analyzed. It is illustrated in detail how global regression analysis may be applied to obtain the coefficients of the chosen regression model of a load component assuming that no linear or massive near-linear dependencies between the regression model terms exist. Data from the machine calibration of a six-component force balance is used to illustrate both application and accuracy of the non-iterative load prediction process.

Ulbrich, Norbert M.↗

DOE OSTI2023

An Iterative Bidirectional Gradient Boosting Algorithm for CVR Baseline Estimation

This paper presents a novel iterative, bidirectional, gradient boosting (bidirectional-GB) algorithm for estimating the baseline of the Conservation Voltage Reduction (CVR) program. We define the CVR baseline as the load profile during the CVR period if the substation voltage is not lowered. The proposed algorithm consists of two key steps: selection of similar days and iterative bidirectional-GB training. In the first step, preand post-event temperature profiles of the targeted CVR day are used to select similar days from historical non-CVR days. In the second step, the pre-event and post-event similar days are used to train two GBMs iteratively: a forward-GBM and a backwardGBM. After each iteration, the two generated CVR baselines are reconciled and only the first and the last points on the reconciled baseline are kept. The iteration repeats until all CVR baseline points are generated. We tested two gradient boosting methods (i.e., GBM and LighGBM) with two data resolutions (i.e., 15and 30-minute). The results demonstrate that both the accuracy and performance of the algorithm are satisfactory.

Lee, Han Pyo↗

NASA NTRS1989

Scheduling Tasks In Parallel Processing

Algorithms sought to minimize time and cost of computation. Report describes research on scheduling of computations tasks in system of multiple identical data processors operating in parallel. Computational intractability requires use of suboptimal heuristic algorithms. First algorithm called "list heuristic", variation of classical list scheduling. Second algorithm called "cluster heuristic" applied to tightly coupled tasks and consists of four phases. Third algorithm called "exchange heuristic", iterative-improvement algorithm beginning with initial feasible assignment of tasks to processors and periods of time. Fourth algorithm is iterative one for optimal assignment of tasks and based on concept called "simulated annealing" because of mathematical resemblance to aspects of physical annealing processes.

Price, Camille C.↗

NASA NTRS1983

Space shuttle propulsion parameter estimation using optimal estimation techniques

The first twelve system state variables are presented with the necessary mathematical developments for incorporating them into the filter/smoother algorithm. Other state variables, i.e., aerodynamic coefficients can be easily incorporated into the estimation algorithm, representing uncertain parameters, but for initial checkout purposes are treated as known quantities. An approach for incorporating the NASA propulsion predictive model results into the optimal estimation algorithm was identified. This approach utilizes numerical derivatives and nominal predictions within the algorithm with global iterations of the algorithm. The iterative process is terminated when the quality of the estimates provided no longer significantly improves.

Source record↗

NASA NTRS2003

Optimal Area Profiles for Ideal Single Nozzle Air-Breathing Pulse Detonation Engines

The effects of cross-sectional area variation on idealized Pulse Detonation Engine performance are examined numerically. A quasi-one-dimensional, reacting, numerical code is used as the kernel of an algorithm that iteratively determines the correct sequencing of inlet air, inlet fuel, detonation initiation, and cycle time to achieve a limit cycle with specified fuel fraction, and volumetric purge fraction. The algorithm is exercised on a tube with a cross sectional area profile containing two degrees of freedom: overall exit-to-inlet area ratio, and the distance along the tube at which continuous transition from inlet to exit area begins. These two parameters are varied over three flight conditions (defined by inlet total temperature, inlet total pressure and ambient static pressure) and the performance is compared to a straight tube. It is shown that compared to straight tubes, increases of 20 to 35 percent in specific impulse and specific thrust are obtained with tubes of relatively modest area change. The iterative algorithm is described, and its limitations are noted and discussed. Optimized results are presented showing performance measurements, wave diagrams, and area profiles. Suggestions for future investigation are also discussed.

Paxson, Daniel E.↗

DOE OSTI2025

Accelerating iterative ptychography with an integrated neural network

Electron ptychography is a powerful and versatile tool for high-resolution and dose-efficient imaging. Iterative reconstruction algorithms are powerful but also computationally expensive due to their relative complexity and the many hyperparameters that must be optimised. Gradient descent-based iterative ptychography is a popular method, but it may converge slowly when reconstructing low spatial frequencies. Here, in this work, we present a method for accelerating a gradient descent-based iterative reconstruction algorithm by training a neural network (NN) that is applied in the reconstruction loop. The NN works in Fourier space and selectively boosts low spatial frequencies, thus enabling faster convergence in a manner similar to accelerated gradient descent algorithms. We discuss the difficulties that arise when incorporating a NN into an iterative reconstruction algorithm and show how they can be overcome with iterative training. We apply our method to simulated and experimental data of gold nanoparticles on amorphous carbon and show that we can significantly speed up ptychographic reconstruction of the nanoparticles.

4DSTEM↗

NASA NTRS2009

Three Dimensional Sector Design with Optimal Number of Sectors

The concept of dynamic sector design suggests a strategic approach to ease air traffic congestion, which is predicted to become a serious problem in the national airspace system by 2025. Considerable research has been conducted to address the sectorization problem. In previous work, an approach that combines the Voronoi diagrams, Genetic Algorithms (GA), and the iterative deepening algorithm was proposed. However, as originally formulated, the number of sectors used was predefined and only two-dimensional partitions were allowed, which constrained the method's ability to achieve good designs. The current work extends the earlier Voronoi-based method by treating the number of sectors as an additional decision variable, allowing 3D partitions, and developing more comprehensive costs.

Xue, Min↗