Results for “fast algorithm” — Page 84

NASA NTRS2006

Genetic Algorithm for Optimization: Preprocessing with n Dimensional Bisection and Error Estimation

A knowledge of the appropriate values of the parameters of a genetic algorithm (GA) such as the population size, the shrunk search space containing the solution, crossover and mutation probabilities is not available a priori for a general optimization problem. Recommended here is a polynomial-time preprocessing scheme that includes an n-dimensional bisection and that determines the foregoing parameters before deciding upon an appropriate GA for all problems of similar nature and type. Such a preprocessing is not only fast but also enables us to get the global optimal solution and its reasonably narrow error bounds with a high degree of confidence.

Sen, S. K.↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Block segmentation in feature space for realtime object detection in high granularity images

Computer vision has applications in object detection, image recognition and classification, and object tracking. One of the challenges of computer vision is the presence of useful information at multiple distance scales. Filtering techniques may sacrifice details at small scales in order to prioritize the analysis of large-scale features of the image. We present a strategy for coarse-graining multidimensional data while maintaining fine-grained detail for subsequent analysis. The algorithm is based on fixed-size block segmentation in the feature space. We apply this strategy to solve the long-standing challenge of detecting particle trajectories at the Large Hadron Collider in real time.

Computer vision↗

DOE OSTI2021

Fast Grain Mapping with Sub-Nanometer Resolution Using 4D-STEM with Grain Classification by Principal Component Analysis and Non-Negative Matrix Factorization

High-throughput grain mapping with sub-nanometer spatial resolution is demonstrated using scanning nanobeam electron diffraction (also known as 4D scanning transmission electron microscopy, or 4D-STEM) combined with high-speed direct-electron detection. An electron probe size down to 0.5 nm in diameter is used and the sample investigated is a gold–palladium nanoparticle catalyst. Computational analysis of the 4D-STEM data sets is performed using a disk registration algorithm to identify the diffraction peaks followed by feature learning to map the individual grains. Two unsupervised feature learning techniques are compared: principal component analysis (PCA) and non-negative matrix factorization (NNMF). The characteristics of the PCA versus NNMF output are compared and the potential of the 4D-STEM approach for statistical analysis of grain orientations at high spatial resolution is discussed.

47 OTHER INSTRUMENTATION↗

NASA NTRS2000

A Portable Ground-Based Atmospheric Monitoring System (PGAMS) for the Calibration and Validation of Atmospheric Correction Algorithms Applied to Aircraft and Satellite Images

Detecting changes in the Earth's environment using satellite images of ocean and land surfaces must take into account atmospheric effects. As a result, major programs are underway to develop algorithms for image retrieval of atmospheric aerosol properties and atmospheric correction. However, because of the temporal and spatial variability of atmospheric transmittance it is very difficult to model atmospheric effects and implement models in an operational mode. For this reason, simultaneous in situ ground measurements of atmospheric optical properties are vital to the development of accurate atmospheric correction techniques. Presented in this paper is a spectroradiometer system that provides an optimized set of surface measurements for the calibration and validation of atmospheric correction algorithms. The Portable Ground-based Atmospheric Monitoring System (PGAMS) obtains a comprehensive series of in situ irradiance, radiance, and reflectance measurements for the calibration of atmospheric correction algorithms applied to multispectral. and hyperspectral images. The observations include: total downwelling irradiance, diffuse sky irradiance, direct solar irradiance, path radiance in the direction of the north celestial pole, path radiance in the direction of the overflying satellite, almucantar scans of path radiance, full sky radiance maps, and surface reflectance. Each of these parameters are recorded over a wavelength range from 350 to 1050 nm in 512 channels. The system is fast, with the potential to acquire the complete set of observations in only 8 to 10 minutes depending on the selected spatial resolution of the sky path radiance measurements

Schiller, Stephen↗

NASA NTRS2001

Measurement of Microscopic Growth Rates in Float-Zone Silicon Crystals

Time dependent convective flows during crystal growth of doped semiconductors lead to fluctuations of the composition, so called dopant striations. In general, it is difficult to decide which is the main mechanism for the generation of these striations, it might be either the fluctuation of the concentration field in the melt and the extent of the solute boundary layer ahead of the solid-liquid interface or a variation of the growth velocity. Direct access to the concentration field is rather complicated to achieve, especially considering the high process temperature and the chemical activity of liquid silicon. The contribution of growth rate fluctuations to the formation of compositional fluctuations can be determined by measuring microscopic growth rates. The classical method of current pulses requires electrical feed-throughs and good electrical contacts, both are critical issues for the growth of high purity silicon crystals. Using a radiation based heating system, the heating power can be modulated very fast and effectively. We added to the normal heater power a sinusoidal off-set in the frequency range of 1 to 10 Hz, generating a narrow spaced weak rippling in the grown crystals which are superposed to the dopant striations caused by natural and by thermocapillary convection. The pulling speed was varied between 1 and 4mm/min. The microscope images of etched crystals slices have been analyzed by peak-search algorithms (measuring the spacing between each artificially induced marker) and by FFT. Performing growth experiments under a time-dependent flow regime, fluctuations of the microscopic growth velocity of Delta(v)/v(sub average) up to 50% have been measured. Damping the time-dependent convection by the use of an axial, static magnetic field of 500mT, the microscopic growth rate became constant within the resolution limit of this method. The results will be discussed using analytical methods for the calculation of microscopic growth velocity and by comparing them with measurements of temperature fluctuations in the melt during growth experiments itself.

Dold, P.↗

NASA NTRS2015

Evaluating Surface Flux Results from CERES-FLASHFlux

The Fast Longwave and Shortwave Radiative Flux (FLASHFlux) data product was developed to provide a rapid release version of the Clouds and Earth's Radiant Energy System (CERES) results, which could be made available to the research and applications communities within one week of the satellite observations by exchanging some accuracy for speed of processing. Unlike standard CERES products, FLASHFlux does not maintain a long-term consistent record. Therefore the latest algorithm changes and input data can be incorporated into processing. FLASHFlux released Version3A (January 2013) and Version 3B (August 2014) which include the latest meteorological product from Global Modeling and Assimilation Office (GMAO), GEOS FP-IT (5.9.1), the latest spectral response functions and gains for the CERES instruments, and aerosol climatology based on the latest MATCH data. Version 3B included a slightly updated calibration and some changes to the surface albedo over snow/ice. Typically FLASHFlux does not reprocess earlier versions when a new version is released. The combined record of Time Interpolated Space Averaged (TISA) surface flux results from Versions3A and 3B for July 2012 to October 2015 have been compared to the ground-based measurements. The FLASHFlux results are also compared to two other CERES gridded products, SYN1deg and EBAF surface fluxes.

Wilber, Anne C.↗

DOE OSTI2020

Deep-Learning-Enabled Fast Optical Identification and Characterization of 2D Materials

Not provided.

Chemistry↗

DOE OSTI2023

Fast Parallel Tensor Times Same Vector for Hypergraphs

Hypergraphs are a popular paradigm to rep- resent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper- graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) oper- ation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVC computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph H-eigenvector centrality.

Shivakumar, Shruti↗

NASA NTRS1985

Microwave holography of large reflector antennas - Simulation algorithms

The performance of large reflector antennas can be improved by identifying the location and amount of their surface distortions and correcting them. To determine the accuracy of the constructed surface profiles, simulation studies are used to incorporate both the effects of systematic and random distortions, particularly the effects of the displaced surface panels. In this paper, different simulation models are investigated, emphasizing a model based on the vector diffraction analysis of a curved reflector with displaced panels. The simulated far-field patterns are then used to reconstruct the location and amount of displacement of the surface panels by employing a fast Fourier transform/iterative procedure. The sensitivity of the microwave holography technique based on the number of far-field sampled points, level of distortions, polarizations, illumination tapers, etc., is also examined.

Rahmat-Samii, Y.↗

NASA NTRS1992

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗

NASA NTRS1995

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗

DOE OSTI2023

Impact Report: Quantum Systems Accelerator

The Quantum Systems Accelerator (QSA) is a U.S. National Quantum Information Science Research Center established in August 2020 and funded by the Department of Energy (DOE) Office of Science. QSA is composed of 15 partner institutions— universities and national laboratories—bringing together pioneers of many of today’s unique quantum information science (QIS) and engineering capabilities. Led by Lawrence Berkeley National Laboratory (Berkeley Lab), with Sandia National Laboratories (Sandia Labs) as the lead partner, 250+ QSA researchers are catalyzing U.S. leadership in a fast-growing field that seeks solutions to the Nation’s and the world’s most pressing problems by harnessing the laws of quantum mechanics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates, which rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. Here, we present our theory in a unified framework, comparing everal implementations of ensemble Kalman updates that use perturbed observations, square root filtering and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Mathematics↗

NASA NTRS2017

The Generic Resolution Advisor and Conflict Evaluator (GRACE) for Detect-And-Avoid (DAA) Systems

The paper describes the Generic Resolution Advisor and Conflict Evaluator (GRACE), a novel alerting and guidance algorithm that combines flexibility, robustness, and computational efficiency. GRACE is "generic" in that it makes no assumptions regarding temporal or spatial scales, aircraft performance, or its sensor and communication systems. Accordingly, GRACE is well suited to research applications where alerting and guidance is a central feature and requirements are fluid involving a wide range of aviation technologies. GRACE has been used at NASA in a number of real-time and fast-time experiments supporting evolving requirements of DAA research, including parametric studies, NAS-wide simulations, human-in-the-loop experiments, and live flight tests.

Unmanned Aircraft↗

NASA NTRS2018

Fast Linearized Coronagraph Optimizer (FALCO) I: A Software Toolbox for Rapid Coronagraphic Design and Wavefront Correction

The Fast Linearized Coronagraph Optimizer (FALCO) is an open-source toolbox of routines for coronagraphic focal plane wavefront correction. The goal of FALCO is to provide a free, modular framework for the simulation or testbed operation of several common types of coronagraphs. FALCO includes routines for pair-wise probing estimation of the complex electric ﬁeld and Electric Field Conjugation (EFC) control, and we ask the community to contribute other wavefront correction algorithms. FALCO utilizes and builds upon PROPER, an established optical propagation library. The key innovation in FALCO is the rapid computation of the linearized response matrix for each deformable mirror (DM), which facilitates re-linearization after each control step for faster DM-integrated coronagraph design and wavefront correction experiments. FALCO is freely available as source code in MATLAB at github.com/ajeldorado/falco-matlab and will be available later this year in Python 3 at github.com/ajeldorado/falco-python.

Shaklan, Stuart B.↗