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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗
DOE OSTI2020

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually suitable for these purposes, but it can be much slower than the unpivoted QR algorithm. For large matrices, the difference in performance is due to increased communication between the processor and slow memory, which QRCP needs in order to choose pivots during decomposition. Our main algorithm, Randomized QR with Column Pivoting (RQRCP), uses randomized projection to make pivot decisions from a much smaller sample matrix, which we can construct to reside in a faster level of memory than the original matrix. This technique may be understood as trading vastly reduced communication for a controlled increase in uncertainty during the decision process. Furthermore, for rank-revealing purposes, the selection mechanism in RQRCP produces results that are the same quality as the standard algorithm, but with performance near that of unpivoted QR (often an order of magnitude faster for large matrices). Additionally, we also propose two formulas that facilitate further performance improvements. The first efficiently updates sample matrices to avoid computing new randomized projections. The second avoids large trailing updates during the decomposition in truncated low-rank approximations. Our truncated version of RQRCP also provides a key initial step in our truncated SVD approximation, TUXV. These advances open up a new performance domain for large matrix factorizations that will support efficient problem-solving techniques for challenging applications in science, engineering, and data analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Computationally Efficient Decompositions of Oblique Projection Matrices

Oblique projection matrices arise in problems in weighted least squares, signal processing, and optimization. While these matrices can be potentially very large, their low-rank structure can be exploited for efficient computation. Here, we propose fast and scalable algorithms for computing their eigendecomposition and singular value decomposition (SVD). Numerical experiments that compare our proposed approaches to existing methods, including randomized SVD, are presented. In addition, we test their accuracy on linear systems from equality constrained optimization problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Novel techniques for data decomposition and load balancing for parallel processing of vision systems: Implementation and evaluation using a motion estimation system

Computer vision systems employ a sequence of vision algorithms in which the output of an algorithm is the input of the next algorithm in the sequence. Algorithms that constitute such systems exhibit vastly different computational characteristics, and therefore, require different data decomposition techniques and efficient load balancing techniques for parallel implementation. However, since the input data for a task is produced as the output data of the previous task, this information can be exploited to perform knowledge based data decomposition and load balancing. Presented here are algorithms for a motion estimation system. The motion estimation is based on the point correspondence between the involved images which are a sequence of stereo image pairs. Researchers propose algorithms to obtain point correspondences by matching feature points among stereo image pairs at any two consecutive time instants. Furthermore, the proposed algorithms employ non-iterative procedures, which results in saving considerable amounts of computation time. The system consists of the following steps: (1) extraction of features; (2) stereo match of images in one time instant; (3) time match of images from consecutive time instants; (4) stereo match to compute final unambiguous points; and (5) computation of motion parameters.

Choudhary, Alok Nidhi↗
NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
DOE OSTI2020

Rendezvous algorithms for large-scale modeling and simulation

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor. Though they were originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide. We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Direct handling of equality constraints in multilevel optimization

In recent years there have been several hierarchic multilevel optimization algorithms proposed and implemented in design studies. Equality constraints are often imposed between levels in these multilevel optimizations to maintain system and subsystem variable continuity. Equality constraints of this nature will be referred to as coupling equality constraints. In many implementation studies these coupling equality constraints have been handled indirectly. This indirect handling has been accomplished using the coupling equality constraints' explicit functional relations to eliminate design variables (generally at the subsystem level), with the resulting optimization taking place in a reduced design space. In one multilevel optimization study where the coupling equality constraints were handled directly, the researchers encountered numerical difficulties which prevented their multilevel optimization from reaching the same minimum found in conventional single level solutions. The researchers did not explain the exact nature of the numerical difficulties other than to associate them with the direct handling of the coupling equality constraints. The coupling equality constraints are handled directly, by employing the Generalized Reduced Gradient (GRG) method as the optimizer within a multilevel linear decomposition scheme based on the Sobieski hierarchic algorithm. Two engineering design examples are solved using this approach. The results show that the direct handling of coupling equality constraints in a multilevel optimization does not introduce any problems when the GRG method is employed as the internal optimizer. The optimums achieved are comparable to those achieved in single level solutions and in multilevel studies where the equality constraints have been handled indirectly.

Renaud, John E.↗
DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗
DOE OSTI2020

Model-Free Data Authentication for Cyber Security in Power Systems

With the development and wide deployment of measurement equipment, data can be automatically measured and visualized for situation awareness in power systems. However, the cyber security of power systems is also threated by data spoofing attacks. This letter proposed a measurement data source authentication (MDSA) algorithm based on feature extraction techniques including ensemble empirical mode decomposition (EEMD) and fast Fourier transform (FFT), and machine learning for real-time measurement data classification. Compared with previous work, the proposed algorithm can achieve higher accuracy of MDSA using a shorter window of data from closely located synchrophasor measurement sensors.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1993

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Storaasli, Olaf O.↗
DOE OSTI2022

Quantum state preparation and nonunitary evolution with diagonal operators

Realizing nonunitary transformations on unitary-gate-based quantum devices is critically important for simulating a variety of physical problems, including open quantum systems and subnormalized quantum states. Here, we present a dilation-based algorithm to simulate nonunitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal nonunitary operator, which we show can be implemented by a diagonal unitary operator in a one-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random subnormalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate nonunitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude-damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general nonunitary operations when the SVD can be readily computed, which is the case for most operators in the noisy intermediate-scale quantum computing era.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Data processing pipeline for Tianlai experiment

The Tianlai project is a 21cm intensity mapping experiment for detecting dark energy by measuring the baryon acoustic oscillation (BAO) features in the large scale structure power spectrum. This experiment provides an opportunity to test the data processing methods for cosmological 21cm signal extraction, which is still a great challenge in current radio astronomy research. The 21cm signal is much weaker than the foregrounds and easily aected by the imperfections in the instrumental responses. Furthermore, processing the large volumes of interferometer data poses a practical challenge. We have developed a data processing pipeline called tlpipe to process the drift scan survey data from the Tianlai experiment. It performs oine data processing tasks such as radio frequency interference (RFI) agging, array calibration, binning, and map-making, etc. It also includes utility functions needed for the data analysis, such as data selection, transformation, visualization and others. A number of new algorithms are implemented, for example the eigenvector decomposition method for array calibration and the Tikhnov regularization for m-mode analysis. In this paper we describe the design and implementation of the pipeline and illustrate its functions with some analysis of real data. Finally, we outline directions for future development of this publicly code.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Fermionic quantum processing with programmable neutral atom arrays

Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Artificial intelligence-empowered cellular morphometric risk score improves prognostic stratification of cutaneous squamous cell carcinoma

Abstract Background Risk stratification of cutaneous squamous cell carcinoma (cSCC) is essential for managing patients. Objectives To determine if artificial intelligence and machine learning might help to stratify patients with cSCC by risk using more than solely clinical and histopathological factors. Methods We retrieved a retrospective cohort of 104 patients whose cSCCs had been excised with clear margins. Clinical and histopathological risk factors were evaluated. Haematoxylin and eosin-stained slides were scanned and analysed by an algorithm based on the stacked predictive sparse decomposition technique. Cellular morphometric biomarkers (CMBs) were identified via machine learning and used to derive a cellular morphometric risk score (CMRS) that classified cSCCs into clusters of differential prognoses. Concordance analysis, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and accuracy were calculated and compared with results obtained with the Brigham and Women’s Hospital (BWH) staging system. The performance of the combination of the BWH staging system and the CMBs was also analysed. Results There were no differences among the CMRS groups in terms of clinical and histopathological risk factors and T-stage assignment, but there were significant differences in prognosis. Combining the CMRS with BWH staging systems increased distinctiveness and improved prognostic performance. C-indices were 0.91 local recurrence and 0.91 for nodal metastasis when combining the two approaches. The NPV was 94.41% and 96.00%, the PPV was 36.36% and 41.67%, and accuracy reached 86.75% and 89.16%, respectively, with the combined approach. Conclusions CMRS is helpful for cSCC risk stratification beyond classic clinical and histopathological risk features. Combining the information from the CMRS and the BWH staging system offers outstanding prognostic performance for patients with high-risk cSCC.

Pérez-Baena, Manuel J.↗
DOE OSTI2020

Extending the Frontier of Quantum Computers with Qutrits

Here, we advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log 2 (3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla - an exponential improvement over the best qubit-only equivalent. Our approach features a 70× improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-Time Bayesian Inference at Extreme Scale: A Digital Twin for Tsunami Early Warning Applied to the Cascadia Subduction Zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic–gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline–online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

97 MATHEMATICS AND COMPUTING↗