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At least 127 records · Page 7

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗

Performance of direct and iterative algorithms on an optical systolic processor

The frequency-multiplexed optical linear algebra processor (OLAP) is treated in detail with attention to its performance in the solution of systems of linear algebraic equations (LAEs). General guidelines suitable for most OLAPs, including digital-optical processors, are advanced concerning system and component error source models, guidelines for appropriate use of direct and iterative algorithms, the dominant error sources, and the effect of multiple simultaneous error sources. Specific results are advanced on the quantitative performance of both direct and iterative algorithms in the solution of systems of LAEs and in the solution of nonlinear matrix equations. Acoustic attenuation is found to dominate iterative algorithms and detector noise to dominate direct algorithms. The effect of multiple spatial errors is found to be additive. A theoretical expression for the amount of acoustic attenuation allowed is advanced and verified. Simulations and experimental data are included.

Ghosh, A. K.↗

Designing reduced-order linear multivariable controllers using experimentally derived plant data

An iterative numerical algorithm for simultaneously improving multiple performance and stability robustness criteria for multivariable feedback systems is developed. The unsatisfied design criteria are improved by updating the free parameters of an initial, stabilizing controller's state-space matrices. Analytical expressions for the gradients of the design criteria are employed to determine a parameter correction that improves all of the feasible, unsatisfied design criteria at each iteration. A controller design is performed using the algorithm with experimentally derived data from a large space structure test facility. Experimental results of the controller's performance at the facility are presented.

Frazier, W. G.↗

Subcritical Multiplication with a Fixed Source

In a subcritical, multiplying medium, the system multiplication describes the expected total number of neutrons created by a single source neutron. Subcriticality plays a large role in criticality safety and thus it is vital for the subcritical multiplication factor be accurate, especially as a system approaches criticality. This work examines the accuracy of calculating the system multiplication using the MCNP6.2 ® k-eigenvalue power iteration (KCODE) method when a fixed-point source is present in a multiplying medium, for near critical systems. This work compares the standard approach for calculating system multiplication, using the fixed-source calculational approach, to a new, single k-eigenvalue power iteration approach that incorporates a fixed-source component and a fission-source component into a single calculation. For the remainder of this paper, some theoretical background and numerical results for an approximate k eigenvalue approach, an accurate fixed-source approach and a new and more accurate k-eigenvalue approach to computing system multiplication are provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Adaptive Multi-Sensor Localization Information Fusion for Autonomous Urban Air Mobility Operations

An adaptive method is developed to iteratively fuse the information provided by multiple sensors to enable autonomous urban air mobility type operations. First, noisy and bias corrupted IMU readings are processed as soon as they arrive using kinematic equations represented in the vehicle's body frame. To correct the systems drift resulting from the integration, an information content measure is introduced to decide on the environment. For the cluttered environment the information provided by environmental sensors is counted as reliable and the drift correction as accurate. For the open space, the GPS data is counted as reliable, and the drift correction is done based on the GPS readings. The measurement noise effects are minimize using Iterated Extended Kalman Filter framework. The algorithm is implemented in the in-house developed FlightDeckz simulation environment using an IMU model, simulated video recorded from a camera mounted on the vehicle (for the purpose of this study, outside scenery was generated with XPlane), which flies in an urban environment, and GPS data generated from the environment's digital map.

Onboard Perception↗

The interaction of the ITER first wall with magnetic perturbations

Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures is subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is introduced because electrically separated tiles can act as a conducting surface for magnetic perturbations that have a normal component to the surface. A practical method for including this determinate subtlety into plasma simulations is developed. The shorter the timescales and the greater the localization, particularly in the toroidal direction, the more important the magnetic effects of the tiles become.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fox Trails

1. This software utilizes python pandas to pull data from P6 databases or XER files. The software transforms the datasets into multiple main tables by joining, filtering, iteratively flattening hierarchical structured data, and pivoting datasets to give simple flat output tables. The activity table includes all of the information related to an activity including activity codes, global, EPS, and project codes, UDFs, and WBS information as separate columns. This includes the code id, code value and sequence number for all levels in hierarchical codes. The resource table is similar to the activity table and includes all of the information related to resources on activities including UPFs and resource codes. The resource time phased table takes the resource information and time phases it for the budget, forecast, late, and actual dates/units/costs that closely matches P6's user interface's values as it implements the resource curve and calendars. The wbs table contains the WBS structure broken out by levels and includes UDFs, codes, and notebook topics. The final P6 data table is the relationships table which simply contains the relationships. 2. When a user updates the tool with data (via giving it P6 project names with database username/password information or XER files) the system creates the data in #1, then creates a networkx graph with the activity data imbedded in the node data and the relationships added as edges. Each edge also has it's float calculated (working time distance between the predecessor and successor) and attached to the edge. Activities are also tagged as a potential start of a path based on their constraints, constraint dates, remaining start date, and activity status. When a user enters an activity ID into the UI, it runs a shortest path calculation on the network graph between each node tagged as potential start to the entered activity id based on the float tagged on the edge. Each path returned by the algorithm contains all of the nodes on the path in order, as well as the total float of the edges that make the path. This data is then collected and returned to the user in the form of a gantt chart with groupings for each path that includes the total float for each group. 3. Similar to 2, if the user passes through a reference dataset each activity set in the path is checked to see if it had a path in the reference dataset, if that path was the primary path between the start and end activities, and what has changed regarding logic and durations. These changes are color coded and summarized before sent to the user to be displayed by the UI for simple discovery. 4. Utilizing the data from #1, the user can submit desired grouping code(s) and filters to the system. The system will then pull the activities, resources, and relationships and create a gantt chart based on the groupings sent and filtered based on the filters sent. 5. The system will produce a gantt chart in a similar method to #4, but allows interactivity with the data. As the user interacts with the gantt chart, the software captures the changes and stores it with the user making the change so that project controls and implement those changes in P6.

Fox, Ben↗

A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

Carpenter, Mark H.↗

Modern Design of Resonant Edge-Slot Array Antennas

Resonant edge-slot (slotted-waveguide) array antennas can now be designed very accurately following a modern computational approach like that followed for some other microwave components. This modern approach makes it possible to design superior antennas at lower cost than was previously possible. Heretofore, the physical and engineering knowledge of resonant edge-slot array antennas had remained immature since they were introduced during World War II. This is because despite their mechanical simplicity, high reliability, and potential for operation with high efficiency, the electromagnetic behavior of resonant edge-slot antennas is very complex. Because engineering design formulas and curves for such antennas are not available in the open literature, designers have been forced to implement iterative processes of fabricating and testing multiple prototypes to derive design databases, each unique for a specific combination of operating frequency and set of waveguide tube dimensions. The expensive, time-consuming nature of these processes has inhibited the use of resonant edge-slot antennas. The present modern approach reduces costs by making it unnecessary to build and test multiple prototypes. As an additional benefit, this approach affords a capability to design an array of slots having different dimensions to taper the antenna illumination to reduce the amplitudes of unwanted side lobes. The heart of the modern approach is the use of the latest commercially available microwave-design software, which implements finite-element models of electromagnetic fields in and around waveguides, antenna elements, and similar components. Instead of building and testing prototypes, one builds a database and constructs design curves from the results of computational simulations for sets of design parameters. The figure shows a resonant edge-slot antenna designed following this approach. Intended for use as part of a radiometer operating at a frequency of 10.7 GHz, this antenna was fabricated from dimensions defined exclusively by results of computational simulations. The final design was found to be well optimized and to yield performance exceeding that initially required.

Gosselin, R. B.↗

Selection of Thermal Worst-Case Orbits via Modified Efficient Global Optimization

Efficient Global Optimization (EGO) was used to select orbits with worst-case hot and cold thermal environments for the Stratospheric Aerosol and Gas Experiment (SAGE) III. The SAGE III system thermal model changed substantially since the previous selection of worst-case orbits (which did not use the EGO method), so the selections were revised to ensure the worst cases are being captured. The EGO method consists of first conducting an initial set of parametric runs, generated with a space-filling Design of Experiments (DoE) method, then fitting a surrogate model to the data and searching for points of maximum Expected Improvement (EI) to conduct additional runs. The general EGO method was modified by using a multi-start optimizer to identify multiple new test points at each iteration. This modification facilitates parallel computing and decreases the burden of user interaction when the optimizer code is not integrated with the model. Thermal worst-case orbits for SAGE III were successfully identified and shown by direct comparison to be more severe than those identified in the previous selection. The EGO method is a useful tool for this application and can result in computational savings if the initial Design of Experiments (DoE) is selected appropriately.

Moeller, Timothy M.↗

NASA DEVELOP’s User-Centric Approach to Building Capacity to Use Earth Observations for Decision Making

The DEVELOP Program, part of NASA’s Applied Sciences, conducts 50-60 feasibility studies annually that center on user needs. Each project is tailored to its partner’s decision making processes with the goal of identifying and implementing opportunities for Earth observation data and information to be integrated into environmental decision making processes. These projects are conducted by a team of early career professionals through a 10-week term where the DEVELOP team rapidly iterates with partners culminating in a “recipe” for using NASA Earth observations. This presentation will introduce the DEVELOP model for user-centered design of projects, share the program's iterative approach to project execution, highlight multiple case studies, and lessons learned in the program’s model evolution.

Capacity Building↗

wa-hls4ml and lui-gnn: A benchmark and GNN-based surrogate model for hls4ml resource and latency estimation

As machine learning (ML) increasingly serves as a tool for addressing real-time challenges in scientific applications, the development of advanced tooling has significantly reduced the time required to iterate on various designs. These advancements have solved major obstacles, but also exposed new challenges. For example, processes that were not previously considered bottlenecks, such as model synthesis, are now becoming limiting factors in the rapid iteration of designs. To reduce these emerging constraints, multiple efforts are being launched toward designing an ML-based surrogate model that estimates resource usage of synthesized accelerator architectures. This model would reduce the design iteration time, especially when designing within a set of given hardware constraints. This approach shows considerable potential, but as it stands, the effort is early and would benefit from coordination and standardization to assist future work as it emerges. We introduce wa-hls4ml, a benchmark for ML accelerator resource and latency estimation, and its corresponding initial dataset of more than 100,000 fully connected neural networks, all synthesized using hls4ml and targeting Xilinx FPGAs. In addition to the resource utilization and latency data provided, the dataset includes generated artifacts and log files for many of the synthesized neural networks, in order to support future research in ML-based code generation. The benchmark evaluates the performance of resource and latency predictors against several common ML model architectures, primarily originating from scientific domains, as exemplar models, as well as the average performance across a subset of the dataset. We measure the performance of a given predictor model through multiple metrics, including $R^2$ score and SMAPE on regression tasks, as well as inference time to further characterize the estimator under test. Additionally, we introduce the latency/utilization inference graph neural network (lui-gnn), a surrogate model that uses a graph neural network to represent input architectures in the form of a directed graph. This graph representation allows for a diverse set of model architectures to all be effectively handled by a surrogate model. We present the architecture and performance of the model, as evaluated by the new proposed benchmark, including SMAPE, $R^2$ score, and inference times, and find that lui-gnn generally predicts latency and utilization for the 75\% quantile within several percent of the synthesized resources on the synthetic test dataset, indicating that this approach of estimating resource and latency via a surrogate models has promise and warrants further research.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit Ansätze

Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this paper, we introduce an algorithm called TETRIS-ADAPT-VQE (tiling efficient trial circuits with rotations implemented simultaneously adaptive derivative-assembled problem-tailored variational quantum eigensolver), which iteratively builds up variational a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm, in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of controlled- gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared with ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. Published by the American Physical Society 2024

Anastasiou, Panagiotis G. (ORCID:0000000256601791)↗

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗

Radiation pattern synthesis of planar antennas using the iterative sampling method

A synthesis method is presented for determining an excitation of an arbitrary (but fixed) planar source configuration. The desired radiation pattern is specified over all or part of the visible region. It may have multiple and/or shaped main beams with low sidelobes. The iterative sampling method is used to find an excitation of the source which yields a radiation pattern that approximates the desired pattern to within a specified tolerance. In this paper the method is used to calculate excitations for line sources, linear arrays (equally and unequally spaced), rectangular apertures, rectangular arrays (arbitrary spacing grid), and circular apertures. Examples using these sources to form patterns with shaped main beams, multiple main beams, shaped sidelobe levels, and combinations thereof are given.

Stutzman, W. L.↗

Optical implementation of inner product neural associative memory

An optical implementation of an inner-product neural associative memory is realized with a first spatial light modulator for entering an initial two-dimensional N-tuple vector and for entering a thresholded output vector image after each iteration until convergence is reached, and a second spatial light modulator for entering M weighted vectors of inner-product scalars multiplied with each of the M stored vectors, where the inner-product scalars are produced by multiplication of the initial input vector in the first iterative cycle (and thresholded vectors in subsequent iterative cycles) with each of the M stored vectors, and the weighted vectors are produced by multiplication of the scalars with corresponding ones of the stored vectors. A Hughes liquid crystal light valve is used for the dual function of summing the weighted vectors and thresholding the sum vector. The thresholded vector is then entered through the first spatial light modulator for reiteration of the process cycle until convergence is reached.

Liu, Hua-Kuang↗

Massively parallel computation of RCS with finite elements

One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary steps expected to result in a robust low i/o system for very large finite element problems.

Parker, Jay↗