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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Model Order Reduction Algorithm for Estimating the Absorption Spectrum

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator’s eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.

IDREAM, K-Edge, theoretical, computational, electr↗
DOE OSTI2022

Performance Evaluation of an Advanced Distributed Energy Resource Management Algorithm

This paper presents performance evaluation of a new distributed energy resource management system (DERMS) algorithm via an advanced hardware-in-the-loop (HIL) platform. The HIL platform provides realistic testing in a laboratory environment, including the accurate modeling of sub-transmission and distribution networks, the DERMS software controller, and 84 power hardware solar photovoltaic (PV) inverters, standard communication protocols, and a capacitor bank controller. The DERMS algorithm is also called, Grid-Optimization of Solar (GO-Solar) platform which includes predictive state estimation (PSE) and online multiple objective optimization (OMOO) to dispatch the legacy devices and distributed energy resources (e.g., PV). The voltage regulation performance is evaluated under three scenarios, volt-var smart inverter (baseline), and DERMS control for 100% and 30% of PV. The results show that controlling 30% of PV systems with the GO-Solar platform may provide the best balance of control performance and implementation cost.

distributed energy resource management system (DER↗
DOE OSTI2016

Efficient Approximation Algorithms for Weighted $b$-Matching

We describe a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a speci ed number b(v) of edges in M are incident on each vertex v. Subject to this restriction we maximize the sum of the weights of the edges in M. We prove that the b-Suitor algorithm computes the same b-Matching as the one obtained by the greedy algorithm for the problem. We implement the algorithm on serial and shared-memory parallel processors, and compare its performance against a collection of approximation algorithms that have been proposed earlier. Our results show that the b-Suitor algorithm outperforms the Greedy and Locally Dominant edge algorithms by one to two orders of magnitude on a serial processor. The b-Suitor algorithm has a high degree of concurrency, and it scales well up to 240 threads on a shared memory multiprocessor. The b-Suitor algorithm outperforms the Locally Dominant edge algorithm by a factor of fourteen on 16 cores of an Intel Xeon multiprocessor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Computational Complexity of Neuromorphic Algorithms

Neuromorphic computing has several characteristics that make it an extremely compelling computing paradigm for post Moore computation. Some of these characteristics include intrinsic parallelism, inherent scalability, collocated processing and memory, and event-driven computation. While these characteristics impart energy efficiency to neuromorphic systems, they do come with their own set of challenges. One of the biggest challenges in neuromorphic computing is to establish the theoretical underpinnings of the computational complexity of neuromorphic algorithms. In this paper, we take the first steps towards defining the space and time complexity of neuromorphic algorithms. Specifically, we describe a model of neuromorphic computation and state the assumptions that govern the computational complexity of neuromorphic algorithms. Next, we present a theoretical framework to define the computational complexity of a neuromorphic algorithm. We explicitly define what space and time complexities mean in the context of neuromorphic algorithms based on our model of neuromorphic computation. Finally, we leverage our approach and define the computational complexities of six neuromorphic algorithms: constant function, successor function, predecessor function, projection function, neuromorphic sorting algorithm and neighborhood subgraph extraction algorithm.

Date, Prasanna↗
DOE OSTI2014

SU-E-T-481: Dosimetric Comparison of Acuros XB and Anisotropic Analytic Algorithm with Commercial Monte Carlo Based Dose Calculation Algorithm for Stereotactic Body Radiation Therapy of Lung Cancer

Purpose: To evaluate performance of three commercially available treatment planning systems for stereotactic body radiation therapy (SBRT) of lung cancer using the following algorithms: Boltzmann transport equation based algorithm (AcurosXB AXB), convolution based algorithm Anisotropic Analytic Algorithm (AAA); and Monte Carlo based algorithm (XVMC). Methods: A total of 10 patients with early stage non-small cell peripheral lung cancer were included. The initial clinical plans were generated using the XVMC based treatment planning system with a prescription of 54Gy in 3 fractions following RTOG0613 protocol. The plans were recalculated with the same beam parameters and monitor units using AAA and AXB algorithms. A calculation grid size of 2mm was used for all algorithms. The dose distribution, conformity, and dosimetric parameters for the targets and organs at risk (OAR) are compared between the algorithms. Results: The average PTV volume was 19.6mL (range 4.2–47.2mL). The volume of PTV covered by the prescribed dose (PTV-V100) were 93.97±2.00%, 95.07±2.07% and 95.10±2.97% for XVMC, AXB and AAA algorithms, respectively. There was no significant difference in high dose conformity index; however, XVMC predicted slightly higher values (p=0.04) for the ratio of 50% prescription isodose volume to PTV (R50%). The percentage volume of total lungs receiving dose >20Gy (LungV20Gy) were 4.03±2.26%, 3.86±2.22% and 3.85±2.21% for XVMC, AXB and AAA algorithms. Examination of dose volume histograms (DVH) revealed small differences in targets and OARs for most patients. However, the AAA algorithm was found to predict considerable higher PTV coverage compared with AXB and XVMC algorithms in two cases. The dose difference was found to be primarily located at the periphery region of the target. Conclusion: For clinical SBRT lung treatment planning, the dosimetric differences between three commercially available algorithms are generally small except at target periphery. XVMC and AXB algorithms are recommended for accurate dose estimation at tissue boundaries.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

An Algorithm of an X-ray Hit Allocation to a Single Pixel in a Cluster and Its Test-Circuit Implementation

An on-chip implementable algorithm for allocation of an X-ray photon imprint, called a hit, to a single pixel in the presence of charge sharing in a highly segmented pixel detector is described. Its proof-of-principle implementation is also given supported by the results of tests using a highly collimated X-ray photon beam from a synchrotron source. The algorithm handles asynchronous arrivals of X-ray photons. Activation of groups of pixels, comparisons of peak amplitudes of pulses within an active neighborhood and finally latching of the results of these comparisons constitute the three procedural steps of the algorithm. A grouping of pixels to one virtual pixel, that recovers composite signals and event driven strobes, to control comparisons of fractional signals between neighboring pixels are the actuators of the algorithm. The circuitry necessary to implement the algorithm requires an extensive inter-pixel connection grid of analog and digital signals, that are exchanged between pixels. A test-circuit implementation of the algorithm was achieved with a small array of 32 × 32 pixels and the device was exposed to an 8 keV highly collimated to a diameter of 3-μm X-ray beam. Furthermore, the results of these tests are given in this paper assessing physical implementation of the algorithm.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Multiscale high-order/low-order (HOLO) algorithms and applications

We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Comparison of new and existing algorithms for the analysis of 2D radioxenon beta gamma spectra

The aim of this paper is to compare radioxenon beta-gamma analysis algorithms using simulated spectra with experimentally measured background, where the ground truth of the signal is known. We believe that this is among the largest efforts to date in terms of the number of synthetic spectra generated and number of algorithms compared using identical spectra. We generate an estimate for the Minimum Detectable Counts (MDC) for each isotope using each algorithm. The paper also points out a conceptual model to put the various algorithms into a continuum. Our results show that existing algorithms can be improved and some newer algorithms can be better than the currently used ones.

actinides↗
DOE OSTI2015

Toward adaptive radiotherapy for head and neck patients: Uncertainties in dose warping due to the choice of deformable registration algorithm

Purpose: The aims of this work were to evaluate the performance of several deformable image registration (DIR) algorithms implemented in our in-house software (NiftyReg) and the uncertainties inherent to using different algorithms for dose warping. Methods: The authors describe a DIR based adaptive radiotherapy workflow, using CT and cone-beam CT (CBCT) imaging. The transformations that mapped the anatomy between the two time points were obtained using four different DIR approaches available in NiftyReg. These included a standard unidirectional algorithm and more sophisticated bidirectional ones that encourage or ensure inverse consistency. The forward (CT-to-CBCT) deformation vector fields (DVFs) were used to propagate the CT Hounsfield units and structures to the daily geometry for “dose of the day” calculations, while the backward (CBCT-to-CT) DVFs were used to remap the dose of the day onto the planning CT (pCT). Data from five head and neck patients were used to evaluate the performance of each implementation based on geometrical matching, physical properties of the DVFs, and similarity between warped dose distributions. Geometrical matching was verified in terms of dice similarity coefficient (DSC), distance transform, false positives, and false negatives. The physical properties of the DVFs were assessed calculating the harmonic energy, determinant of the Jacobian, and inverse consistency error of the transformations. Dose distributions were displayed on the pCT dose space and compared using dose difference (DD), distance to dose difference, and dose volume histograms. Results: All the DIR algorithms gave similar results in terms of geometrical matching, with an average DSC of 0.85 ± 0.08, but the underlying properties of the DVFs varied in terms of smoothness and inverse consistency. When comparing the doses warped by different algorithms, we found a root mean square DD of 1.9% ± 0.8% of the prescribed dose (pD) and that an average of 9% ± 4% of voxels within the treated volume failed a 2%pD DD-test (DD{sub 2%-pp}). Larger DD{sub 2%-pp} was found within the high dose gradient (21% ± 6%) and regions where the CBCT quality was poorer (28% ± 9%). The differences when estimating the mean and maximum dose delivered to organs-at-risk were up to 2.0%pD and 2.8%pD, respectively. Conclusions: The authors evaluated several DIR algorithms for CT-to-CBCT registrations. In spite of all methods resulting in comparable geometrical matching, the choice of DIR implementation leads to uncertainties in dose warped, particularly in regions of high gradient and/or poor imaging quality.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. Furthermore, the results demonstrate the advantage of the algorithm in finding high-precision solutions.

interior point method↗
DOE OSTI2021

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Precise ROCOF estimation algorithm for low inertia power grids

The precise estimation of Rate Of Change Of Frequencies (ROCOFs) in a generation trip event can be helpful on power system inertia estimation, fast system response, and accurate event capturing. However, the ROCOF estimations from the existing Synchronized Measurement Devices (SMDs) are usually simply calculated by the finite difference between two adjacent frequency measurement points. The ineluctable noises, disturbances, and spikes from real-world frequency measurements can bring large dynamics to the ROCOF estimation and thus can result in an inaccurate estimation of the initial ROCOF. This issue becomes more serious when the target power grid has low inertia, and a large amount of distributed energy sources are deployed. To address this issue, a precise ROCOF estimation algorithm is designed based on least square method with flexible window size. In addition, a median filter is also designed and applied on the frequency measurements before using the proposed algorithm. The window size and thresholds in the proposed algorithm are determined with historical event data analysis. The proposed algorithm is deployed in a low cost, flexible, and distribution level universal grid analyzer (UGA) platform. In conclusion, multiple experiments are conducted in both a laboratory and the Hawaiian Islands to verify the effectiveness of the proposed algorithm.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

A weighted state redistribution algorithm for embedded boundary grids

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions. Second, we discuss several algorithmic changes and improvements motivated by the more complicated cut cell geometries that can occur in higher dimensions. In particular, we introduce a weighted version with less dissipation in an easily generalizable framework. Third, we demonstrate that state redistribution can also stabilize a solution update that includes both advective and diffusive contributions. Notably, the stabilization algorithm is shown to be effective for incompressible as well as compressible reacting flows. Finally, we discuss the implementation of the algorithm for several exascale-ready simulation codes based on AMReX, demonstrating ease of use in combination with domain decomposition, hybrid parallelism and complex physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗