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NASA NTRS2010

Wavefront Control and Image Restoration with Less Computing

PseudoDiversity is a method of recovering the wavefront in a sparse- or segmented- aperture optical system typified by an interferometer or a telescope equipped with an adaptive primary mirror consisting of controllably slightly moveable segments. (PseudoDiversity should not be confused with a radio-antenna-arraying method called pseudodiversity.) As in the cases of other wavefront- recovery methods, the streams of wavefront data generated by means of PseudoDiversity are used as feedback signals for controlling electromechanical actuators of the various segments so as to correct wavefront errors and thereby, for example, obtain a clearer, steadier image of a distant object in the presence of atmospheric turbulence. There are numerous potential applications in astronomy, remote sensing from aircraft and spacecraft, targeting missiles, sighting military targets, and medical imaging (including microscopy) through such intervening media as cells or water. In comparison with prior wavefront-recovery methods used in adaptive optics, PseudoDiversity involves considerably simpler equipment and procedures and less computation. For PseudoDiversity, there is no need to install separate metrological equipment or to use any optomechanical components beyond those that are already parts of the optical system to which the method is applied. In Pseudo- Diversity, the actuators of a subset of the segments or subapertures are driven to make the segments dither in the piston, tilt, and tip degrees of freedom. Each aperture is dithered at a unique frequency at an amplitude of a half wavelength of light. During the dithering, images on the focal plane are detected and digitized at a rate of at least four samples per dither period. In the processing of the image samples, the use of different dither frequencies makes it possible to determine the separate effects of the various dithered segments or apertures. The digitized image-detector outputs are processed in the spatial-frequency (Fourier-transform) domain to obtain measures of the piston, tip, and tilt errors over each segment or subaperture. Once these measures are known, they are fed back to the actuators to correct the errors. In addition, measures of errors that remain after correction by use of the actuators are further utilized in an algorithm in which the image is phase-corrected in the spatial-frequency domain and then transformed back to the spatial domain at each time step and summed with the images from all previous time steps to obtain a final image having a greater signal-to-noise ratio (and, hence, a visual quality) higher than would otherwise be attainable.

Lyon, Richard G.↗

DOE OSTI2024

Automating Rabi & Ramsey Measurements via ML

As quantum computers scale up, the manual process of qubit tune-up becomes increasingly impractical due to its time-consuming and repetitive nature. While existing research has explored some automation techniques, many models remain underutilized for this purpose. This research aims to answer the question: can qubit tune-up be automated using the Long Short-Term Memory (LSTM) model? For the purposes of this project, only the rabi and ramsey measurement cycle was automated. These measurements are used to fine-tune a rough qubit frequency by repeating them until the optimal qubit frequency is obtained. The LSTM model uses the qubit frequency at one time step to forecast the qubit frequency at the next time step. A rabi-ramsey simulation was made to fabricate a dataset to train and test the LSTM model. As the model was trained, the error of the model decreased. Although there wasn t enough training data to generate perfect predictions, this shows it is possible to utilize forecasting models in automating the tune-up process.

Roberts, Rachel↗

DOE OSTI2024

Automating Rabi & Ramsey Measurements via Machine Learning

As quantum computers scale up, the manual process of qubit tune-up becomes increasingly impractical due to its time-consuming and repetitive nature. While existing research has explored some automation techniques, many models remain underutilized for this purpose. This research aims to answer the question: can qubit tune-up be automated using the Long Short-Term Memory (LSTM) model? For the purposes of this project, only the rabi and ramsey measurement cycle was automated. These measurements are used to fine-tune a rough qubit frequency by repeating them until the optimal qubit frequency is obtained. The LSTM model uses the qubit frequency at one time step to forecast the qubit frequency at the next time step. A rabi-ramsey simulation was made to fabricate a dataset to train and test the LSTM model. As the model was trained, the error of the model decreased. Although there wasn't enough training data to generate perfect predictions, this shows it is possible to utilize forecasting models in automating the tune-up process.

Roberts, Rachel↗

DOE OSTI2023

Online and Scalable Data Compression Pipeline with Guarantees on Quantities of Interest

Data compression is becoming critical for data-intensive scientific applications. Scientists require compression techniques that accurately preserve derived quantities of interest (QoIs). Prior work has shown that a pipeline can be built to guarantee error on the primary data (PD) within user-defined bounds and achieve near-floating point QoI errors. In this paper, we present novel computational approaches for accelerating the pipeline and demonstrate results that enable concurrent execution of compression in parallel with the simulation nodes. This allows compression, including the writing of the required compression data, for the previous time step to be completed while the simulation proceeds with the current time step. Overall, the approach presented in this paper results in a 6–8 times improvement in computational overhead compared to previous work. These results were obtained using data generated by a large-scale fusion code called XGC, which produces hundreds of terabytes of data in a single day.

Banerjee, Tania↗

DOE OSTI2024

A Semi-Analytical Approach for State-Space Electromagnetic Transient Simulation

Here, this paper proposes a semi-analytical approach for efficient and accurate electromagnetic transient (EMT) simulation of a power grid. The approach first derives a high-order semi-analytical solution (SAS) of the grid’s state-space EMT model using the differential transformation (DT), and then evaluates the solution over enlarged, variable time steps to significantly accelerate the simulations while maintaining its high accuracy on detailed fast EMT dynamics. The approach also addresses switches during large time steps by using a limit violation detection algorithm with a binary search-enhanced quadratic interpolation. Case studies are conducted on EMT models of the IEEE 39-bus system and large-scale systems to demonstrate the merits of the new simulation approach against traditional numerical methods.

electromagnetic transient↗

DOE OSTI2020

High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

In this work, we present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrix-free operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrix-free operator evaluations utilize GPU-accelerated sum-factorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a low-order refined methodology with parallel subspace corrections, as described for diffusion problems in [1]. The saddle-point Stokes system is solved using block-preconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible Navier-Stokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Neural Network for Principle of Least Action

The principle of least action is the cornerstone of classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. Here, we describe how a neural network (NN) learns to find the trajectory for a Lennard-Jones (LJ) system that maintains balance in minimizing the Onsager–Machlup (OM) action and maintaining the energy conservation. The phase-space trajectory thus calculated is in excellent agreement with the corresponding results from the “ground-truth” molecular dynamics (MD) simulation. Furthermore, we show that the NN can easily find structural transformation pathways for LJ clusters, for example, the basin-hopping transformation of an LJ 38 from an incomplete Mackay icosahedron to a truncated face-centered cubic octahedron. Unlike MD, the NN computes atomic trajectories over the entire temporal domain in one fell swoop, and the NN time step is a factor of 20 larger than the MD time step. The NN approach to OM action is quite general and can be adapted to model morphometrics in a variety of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Hybrid quantum-classical approach for coupled-cluster Green's function theory

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number of T gates that grows as O ( N 5 ) per time step to calculate the impurity Green's function in the time domain, where N is the total number of energy levels in the AIM. Since the number of T gates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requires O ( N 6 ) computational resources per time step.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1987

Smoothing and the second law

The technique of obtaining second-order oscillation-free total -variation-diminishing (TVD), scalar difference schemes by adding a limited diffusive flux ('smoothing') to a second-order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell-by-cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second-order spatial accuracy was found to have extremely restrictive time-step limitation. Switching to an implicit scheme removed the time-step limitation.

Merriam, Marshal L.↗

NASA NTRS1991

A fast upwind solver for the Euler equations on three-dimensional unstructured meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a novel cell reconstruction process which results in computational times per cell comparable to those of structured codes. The approach yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicit limiting. Solutions are advanced in time by a 3-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Solutions are presented for a range of configurations in the transonic speed regime to demonstrate code accuracy, speed, and robustness. The results include an assessment of grid sensitivity and convergence acceleration by mesh sequencing.

Frink, Neal T.↗

NASA NTRS1992

Upwind scheme for solving the Euler equations on unstructured tetrahedral meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a multidimensional linear reconstruction process. The solution gradients required for the higher-order differenes are computed by a novel approach that yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicitly applying a limiter. Solutions are advanced in time by a three-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Transonic solutions are presented for two meshes around the ONERA M6 wing and demonstrate substantial accuracy and insensitivity to mesh size.

Frink, Neal T.↗

NASA NTRS2004

A Fast Upwind Solver for the Euler Equations on Three-Dimensional Unstructured Meshes

Frink, Neal T.↗

NASA NTRS1991

Comparison of SMAC, PISO, and iterative time-advancing schemes for unsteady flows

Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PSIO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PSIO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

Kim, Sang-Wook↗

NASA NTRS1992

Comparison of the SMAC, PISO, and iterative time-advancing schemes for unsteady flows

Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PISO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PISO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

Kim, S.-W.↗

NASA NTRS2001

HITEMP Material and Structural Optimization Technology Transfer

The feasibility of adding viscoelasticity and the Generalized Method of Cells (GMC) for micromechanical viscoelastic behavior into the commercial HyperSizer structural analysis and optimization code was investigated. The viscoelasticity methodology was developed in four steps. First, a simplified algorithm was devised to test the iterative time stepping method for simple one-dimensional multiple ply structures. Second, GMC code was made into a callable subroutine and incorporated into the one-dimensional code to test the accuracy and usability of the code. Third, the viscoelastic time-stepping and iterative scheme was incorporated into HyperSizer for homogeneous, isotropic viscoelastic materials. Finally, the GMC was included in a version of HyperSizer. MS Windows executable files implementing each of these steps is delivered with this report, as well as source code. The findings of this research are that both viscoelasticity and GMC are feasible and valuable additions to HyperSizer and that the door is open for more advanced nonlinear capability, such as viscoplasticity.

Collier, Craig S.↗

NASA NTRS1990

A user guide for the EMTAC-MZ CFD code

The computer code (EMTAC-MZ) was applied to investigate the flow field over a variety of very complex three-dimensional (3-D) configurations across the Mach number range (subsonic, transonic, supersonic, and hypersonic flow). In the code, a finite volume, multizone implementation of high accuracy, total variation diminishing (TVD) formulation (based on Roe's scheme) is used to solve the unsteady Euler equations. In the supersonic regions of the flow, an infinitely large time step and a space-marching scheme is employed. A finite time step and a relaxation or 3-D approximate factorization method is used in subsonic flow regions. The multizone technique allows very complicated configurations to be modeled without geometry modifications, and can easily handle combined internal and external flow problems. An elliptic grid generation package is built into the EMTAC-MZ code. To generate the computational grid, only the surface geometry data are required. Results obtained for a variety of configurations, such as fighter-like configurations (F-14, AVSTOL), flow through inlet, multi-bodies (shuttle with external tank and SRBs), are reported and shown to be in good agreement with available experimental data.

Szema, Kuo-Yen↗

NASA NTRS1996

Computation of Acoustic Waves Through Sliding-Zone Interfaces Using an Euler/Navier-Stokes Code

The effect of a patched sliding-zone interface on the transmission of acoustic waves is examined for two- and three-dimensional model problems. A simple but general interpolation scheme at the patched boundary passes acoustic waves without distortion, provided that a sufficiently small time step is taken. A guideline is provided for the maximum permissible time step or zone speed that gives an acceptable error introduced by the sliding-zone interface.

Rumsey, Christopher L.↗

NASA NTRS1987

Numerical tests of a modified full implicit continuous Eulerian (FICE) scheme with projected normal characteristic boundary conditions for MHD flows

A numerical method has been developed based on a modified full implicit continuous Eulerian (FICE) scheme and projected normal characteristic boundary conditions for simulating MHD flows which undergo a long process of evolution. An astrophysical flow is chosen for illustration of this procedure, and numerical tests are made to verify the computational stability and physically realistic solution. Three computational tests have been accomplished; they are tests of solving methods, characteristic boundary condition, and time steps. The tests show that the program from the modified FICE scheme with proper boundary conditions and time steps can be made numerically stable for a time long enough to obtain physically plausible solutions.

Wu, S. T.↗