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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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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SU-F-BRF-13: Investigating the Feasibility of Accurate Dose Measurement in a Deforming Radiochromic Dosimeter

Purpose: Presage-Def, a deformable radiochromic 3D dosimeter, has been previously shown to have potential for validating deformable image registration algorithms. This work extends this effort to investigate the feasibility of using Presage-Def to validate dose-accumulation algorithms in deforming structures. Methods: Two cylindrical Presage-Def dosimeters (8cm diameter, 4.5cm length) were irradiated in a water-bath with a simple 4-field box treatment. Isocentric dose was 20Gy. One dosimeter served as control (no deformation) while the other was laterally compressed during irradiation by 21%. Both dosimeters were imaged before and after irradiation with a fast (∼10 minutes for 1mm isotropic resolution), broad beam, high resolution optical-CT scanner. Measured dose distributions were compared to corresponding distributions calculated by a commissioned Eclipse planning system. Accuracy in the control was evaluated with 3D gamma (3%/3mm). The dose distribution calculated for the compressed dosimeter in the irradiation geometry cannot be directly compared via profiles or 3D gamma to the measured distribution, which deforms with release from compression. Thus, accuracy under deformation was determined by comparing integral dose within the high dose region of the deformed dosimeter distribution versus calculated dose. Dose profiles were used to study temporal stability of measured dose distributions. Results: Good dose agreement was demonstrated in the control with a 3D gamma passing rate of 96.6%. For the dosimeter irradiated under compression, the measured integral dose in the high dose region (518.0Gy*cm3) was within 6% of the Eclipse-calculated integral dose (549.4Gy*cm3). Elevated signal was noted on the dosimeter edge in the direction of compression. Change in dosimeter signal over 1.5 hours was ≤2.7%, and the relative dose distribution remained stable over this period of time. Conclusion: Presage-Def is promising as a 3D dosimeter capable of accurately measuring dose in a deforming structure, and warrants further study to quantify comprehensive accuracy at different levels of deformation. This work was supported by NIH R01CA100835. John Adamovics is the president of Heuris Inc., which commercializes PRESAGE.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals

We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work (Daubechies et al., Pure Appl. Math. 57(11), 1413–1457, 2004), where the single vector signal can be infinite-dimensional, and (Fornasier and Rauhut, SIAM J. Numer. Anal. 46(2), 577613, 2008), which extends the aforementioned work to the joint sparse recovery of finite number of infinite-dimensional vectors. In our case, to take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty ℓ 2,1 . This paper discusses the computation of the solutions of linear inverse problems with such relaxation by a forward-backward splitting algorithm. However, since the solution matrix possesses infinitely many columns, the arguments of Daubechies et al. (Pure Appl. Math. 57(11), 1413–1457, 2004) no longer apply. As such, we establish new strong convergence results for the algorithm, in particular when the set of jointly sparse vectors is infinite.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Advanced Shuttle Strategies for Parallel QCCD Architectures

Trapped ions (TIs) are at the forefront of quantum computing implementation, offering unparalleled coherence, fidelity, and connectivity. However, the scalability of TI systems is hampered by the limited capacity of individual ion traps, necessitating intricate ion shuttling for advanced computational tasks. The quantum charge-coupled device (QCCD) framework has emerged as a promising solution, facilitating ion mobility for universal quantum computation. Current QCCD architectures predominantly feature a linear topology, which is increasingly recognized as inefficient for complex quantum operations. Anticipating the shift toward more efficacious designs, this article introduces an innovative quantum scheduling strategy optimized for parallel QCCD topologies. Our strategy proposes a probabilistic formula for ion movement, alongside ingenious methods for local layer generation and layer compression, yielding a significant reduction in ion shuttle times. Through simulations, we demonstrate that our strategy not only substantially outstrips the linear model but also exhibits better performance over other parallel strategies that employ greedy algorithms. This is achieved through our nuanced resolution of complexities, such as traffic blocks and trap capacity limitations. The consequent reduction in shuttle operations leads to lower energy consumption and an enhancement in the quantum computer's fidelity, ultimately accelerating program execution times.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Exploitation of Defects in High Entropy Ceramic Barrier Materials

A critical mission need exists to develop new materials that can withstand extreme environments and multiple sequential threats. High entropy materials, those containing 5 or more metals, exhibit many exciting properties which would potentially be useful in such situations. However, a particularly hard challenge in developing new high entropy materials is determining a priori which compositions will form the desired single phase material. The project outlined here combined several modeling and experimental techniques to explore several structure-property-relationships of high entropy ceramics in an effort to better understand the connection between their compositional components, their observed properties, and stability. We have developed novel machine learning algorithms which rapidly predict stable high entropy ceramic compositions, identified the stability interplay between configurational entropy and cation defects, and tested the mechanical stability of high entropy oxides using the unique capabilities at the Dynamic Compression Sector facility and the Saturn accelerator.

36 MATERIALS SCIENCE↗
DOE OSTI2023

High Speed Data Acquisition for Real Time Feedback in a Light Duty Engine Combustion-Mode Switching Application

The paper describes the integration of a high-speed data acquisition and diagnostics controller used in an advanced engine platform. The controller enables ultra-low emissions and new benchmarks of engine efficiency while running a Gasoline Compression Ignition (GCI) cycle on a 2.2L, 4-cylinder engine. The system enables real-time combustion feedback and vibration analysis in engines. The paper focuses on: (1) the development of an interpolative sampling algorithm for transposition of time acquired data to the crank angle domain using a production crank sensor (60-2 tooth wheel); (2) the control unit, high-speed data acquisition, communication rates between the dedicated data acquisition and base controller to ensure cycle-to-cycle feedback; and, (3) validation exercises using cylinder pressure measurements. Here, the study shows how the algorithm resolves cylinder pressure information over an engine cycle, validating its robustness across acquisition rates of 50 and 200 kHz, with crank angle resolutions of 0.5° and 0.1°. Results show that the 50 kHz, 0.5° hardware yield combustion phasing and torque estimates within 0.1° and 1% torque of those attained with the 200 kHz, 0.1° hardware. Finally, study shows the dedicated controller and communication speeds allow for next-cycle fuel injection correction for speeds above 5000 rpm.

42 ENGINEERING↗
DOE OSTI2025

SymbolNet: neural symbolic regression with adaptive dynamic pruning for compression

Abstract Compact symbolic expressions have been shown to be more efficient than neural network (NN) models in terms of resource consumption and inference speed when implemented on custom hardware such as field-programmable gate arrays (FPGAs), while maintaining comparable accuracy (Tsoi et al 2024 EPJ Web Conf. 295 09036). These capabilities are highly valuable in environments with stringent computational resource constraints, such as high-energy physics experiments at the CERN Large Hadron Collider. However, finding compact expressions for high-dimensional datasets remains challenging due to the inherent limitations of genetic programming (GP), the search algorithm of most symbolic regression (SR) methods. Contrary to GP, the NN approach to SR offers scalability to high-dimensional inputs and leverages gradient methods for faster equation searching. Common ways of constraining expression complexity often involve multistage pruning with fine-tuning, which can result in significant performance loss. In this work, we propose S y m b o l N e t , a NN approach to SR specifically designed as a model compression technique, aimed at enabling low-latency inference for high-dimensional inputs on custom hardware such as FPGAs. This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process, where both training loss and expression complexity are optimized simultaneously. We introduce a sparsity regularization term for each pruning type, which can adaptively adjust its strength, leading to convergence at a target sparsity ratio. Unlike most existing SR methods that struggle with datasets containing more than O ( 10 ) inputs, we demonstrate the effectiveness of our model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN (3072 inputs).

Tsoi, Ho Fung (ORCID:0000000225502184)↗
DOE OSTI2026

Lyapunov controlled counterdiabatic quantum optimization

We introduce a quantum algorithm that integrates counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to address combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces dependence on extensive higher-order CD terms and on classical optimization techniques, making it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

TU-F-17A-07: Real-Time Personalized Margins

Purpose: To maximize normal tissue sparing for treatments requiring motion encompassing margins. Motion mitigation techniques including DMLC or couch tracking can freeze tumor motion within the treatment aperture potentially allowing for smaller treatment margins and thus better sparing of normal tissue. To enable for a safe application of this concept in the clinic we propose adapting margins dynamically in real-time during radiotherapy delivery based on personalized tumor localization confidence. To demonstrate technical feasibility we present a phantom study. Methods: We utilize a realistic anthropomorphic dynamic thorax phantom with a lung tumor model embedded close to the spine. The tumor, a 3D-printout of a patient's GTV, is moved 15mm peak-to-peak by diaphragm compression and monitored by continuous EPID imaging in real-time. Two treatment apertures are created for each beam, one representing ITV -based and the other GTV-based margin expansion. A soft tissue localization (STiL) algorithm utilizing the continuous EPID images is employed to freeze tumor motion within the treatment aperture by means of DMLC tracking. Depending on a tracking confidence measure (TCM), the treatment aperture is adjusted between the ITV and the GTV leaf. Results: We successfully demonstrate real-time personalized margin adjustment in a phantom study. We measured a system latency of about 250 ms which we compensated by utilizing a respiratory motion prediction algorithm (ridge regression). With prediction in place we observe tracking accuracies better than 1mm. For TCM=0 (as during startup) an ITV-based treatment aperture is chosen, for TCM=1 a GTV-based aperture and for 0<TCM<1 a linear interpolation between the two apertures is chosen. Conclusions: We have proposed and demonstrated a concept to safely shrink treatment margins during radiotherapy and adapt to tracking confidence in real-time. Normal tissue sparing is maximized. The worst case scenario results in delivering a plan with standard margins used in the clinic today.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

42 ENGINEERING↗
DOE OSTI2023

Digital quantum simulation of NMR experiments

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

WE-G-207-03: Mask Guided Image Reconstruction (MGIR): A Novel Method for Ultra-Low-Dose 3D and Enhanced 4D Cone-Beam Computer-Tomography

Purpose: Recently, compressed sensing (CS) based iterative reconstruction (IR) method is receiving attentions to reconstruct high quality cone beam computed tomography (CBCT) images using sparsely sampled or noisy projections. The aim of this study is to develop a novel baseline algorithm called Mask Guided Image Reconstruction (MGIR), which can provide superior image quality for both low-dose 3DCBCT and 4DCBCT under single mathematical framework. Methods: In MGIR, the unknown CBCT volume was mathematically modeled as a combination of two regions where anatomical structures are 1) within the priori-defined mask and 2) outside the mask. Then we update each part of images alternatively thorough solving minimization problems based on CS type IR. For low-dose 3DCBCT, the former region is defined as the anatomically complex region where it is focused to preserve edge information while latter region is defined as contrast uniform, and hence aggressively updated to remove noise/artifact. In 4DCBCT, the regions are separated as the common static part and moving part. Then, static volume and moving volumes were updated with global and phase sorted projection respectively, to optimize the image quality of both moving and static part simultaneously. Results: Examination of MGIR algorithm showed that high quality of both low-dose 3DCBCT and 4DCBCT images can be reconstructed without compromising the image resolution and imaging dose or scanning time respectively. For low-dose 3DCBCT, a clinical viable and high resolution head-and-neck image can be obtained while cutting the dose by 83%. In 4DCBCT, excellent quality 4DCBCT images could be reconstructed while requiring no more projection data and imaging dose than a typical clinical 3DCBCT scan. Conclusion: The results shown that the image quality of MGIR was superior compared to other published CS based IR algorithms for both 4DCBCT and low-dose 3DCBCT. This makes our MGIR algorithm potentially useful in various on-line clinical applications. Provisional Patent: UF#15476; WGS Ref. No. U1198.70067US00.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Identifying Climate Patterns Using Clustering Autoencoder Techniques

Abstract The complexity of growing spatiotemporal resolution of climate simulations produces a variety of climate patterns under different projection scenarios. This paper proposes a new data-driven climate classification workflow via an unsupervised deep learning technique that can dimensionally reduce the vast volume of spatiotemporal numerical climate projection data into a compact representation. We aim to identify distinct zones that capture multiple climate variables as well as their future changes under different climate change scenarios. Our approach leverages convolutional autoencoders combined with k -means clustering (standard autoencoder) and online clustering based on the Sinkhorn–Knopp algorithm (clustering autoencoder) across the conterminous United States (CONUS) to capture unique climate patterns in a data-driven fashion from the Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G). The developed approach compresses 70 years of GFDL-ESM2G simulation at 0.125° spatial resolution across the CONUS under multiple warming scenarios to a lower-dimensional space by a factor of 660 000 and then tested on 150 years of GFDL-ESM2G simulation data. The results show that five climate clusters capture physically reasonable and spatially stable climatological patterns matched to known climate classes defined by human experts. Results also show that using a clustering autoencoder can reduce the computational time for clustering by up to 9.2 times when compared to using a standard autoencoder. Our five unique climate patterns resulting from the deep learning–based clustering of the lower-dimensional space thereby enable us to provide insights on hydrometeorology and its spatial heterogeneity across the conterminous United States immediately without downloading large climate datasets. Significance Statement This paper presents a data-driven climate classification approach using unsupervised deep learning to dimensionally reduce climate model outputs and to identify distinct climate regions for their future changes. Our approach compresses climate information for 70 years of Geophysical Fluid Dynamics Laboratory Earth System Model data across the conterminous United States (CONUS) at 0.125° spatial resolution. The results reveal that five climate clusters capture reasonable and stable climatological patterns matched to known climate patterns. The embedded clustering process in deep learning provides ×9.2 times faster execution than the k -means clustering technique. These results give us insight about climate spatial patterns and heterogeneity of hydrological patterns across the conterminous United States without downloading large climate datasets.

Kurihana, Takuya↗
DOE OSTI2017

Understanding the Hierarchy of Dense Subgraphs in Stationary and Temporally Varying Setting

Graphs are widely used to model relationships in a wide variety of domains such as sociology, bioinformatics, infrastructure, the WWW, to name a few. One of the key observations is that while real-world graphs are often globally sparse, they are locally dense. In other words, the average degree is often quite small (say at most 10 in a million vertex graph), but vertex neighborhoods are often dense. Finding dense subgraphs is a critical aspect of graph mining It has been used for finding communities and spam link farms in web graphs, graph visualization, real-time story identification, DNA motif detection in biological networks, finding correlated genes, epilepsy prediction, finding price value motifs in financial data, graph compression, distance query indexing, and increasing the throughput of social networking site servers. However, most standard formulations of this problem (like clique, quasi-clique, k-densest subgraph) are NP-hard. Furthermore, current dense subgraph finding algorithms usually optimize some objective, and only find a few such subgraphs without providing any structural relations, whereas the goal is rarely to find the "true optimum," but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine relationships among them. In this project, we first aim to devise algorithms and provide 3 implementations with nice visualizations to find the hierarchy between dense subgraphs, and then understand the structure of the hierarchy to gain more insight on the hidden patterns in real-world networks. Another important aspects in graph analysis is the temporal nature of networks. Networks evolve over time and in many applications data arrives at a high velocity, and thus it is important to design algorithms that can process data efficiently. We report three main results towards identifying dense structures in large evolving graphs. First, we will show how the hierarchical connectedness structure can be maintained efficiently, where connectedness is defined by increasing levels of connectivity strength. Next, we present dense structure can be identified in bipartite graphs without building projection graphs. And finally, we present a new method for peeling algorithms This new approach avoids sequential nature of peeling algorithms and is amenable to parallelization, which is crucial for processing high velocity data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Hierarchical ensemble Kalman methods with sparsity-promoting generalized gamma hyperpriors

This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods, generalizing the iterative alternating scheme to nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a hierarchical Bayesian model characterized by a conditionally Gaussian prior and generalized gamma hyperpriors. Suitable choices of hyperparameters yield sparsity-promoting regularization. We propose an iterative algorithm for MAP estimation, which alternates between updating the unknown with an ensemble Kalman method and updating the hyperparameters in the regularization to promote sparsity. Here, the effectiveness of our methodology is demonstrated in several computed examples, including compressed sensing and subsurface flow inverse problems.

Ensemble Kalman methods↗
DOE OSTI2018

SIRIUS: Enabling Progressive Data Exploration for Extreme-Scale Scientific Data

Scientific simulations on high performance computing (HPC) platforms generate large quantities of data. To bridge the widening gap between compute and I/O, and enable data to be more efficiently stored and analyzed, simulation outputs need to be refactored, reduced, and appropriately mapped to storage tiers. However, a systematic solution to support these steps has been lacking in the current HPC software ecosystem. To that end, this paper develops SIRIUS, a progressive JPEG-like data management scheme for storing and analyzing big scientific data. It co-designs data decimation, compression, and data storage, taking the hardware characteristics of each storage tier into considerations. With reasonably low overhead, our approach refactors simulation data, using either topological or uniform decimation, into a much smaller, reduced-accuracy base dataset, and a series of deltas that is used to augment the accuracy if needed. The base dataset and deltas are compressed and written to multiple storage tiers. Data saved on different tiers can then be selectively retrieved to restore the level of accuracy that satisfies data analytics. Thus, SIRIUS provides a paradigm shift towards elastic data analytics and enables end users to make trade-offs between analysis speed and accuracy on-the-fly. This paper further develops algorithms to preserve statistics for data decimation, a common requirement for reducing data. Here, we assess the impact of SIRIUS on unstructured triangular meshes, a pervasive data model used in scientific simulations. In particular, we evaluate two realistic use cases: the blob detection in fusion and high-pressure area extraction in computational fluid dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10 -5 , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Correction of the baseline fluctuations in the GEM-based ALICE TPC

To operate the ALICE Time Projection Chamber in continuous mode during the Run 3 and Run 4 data-taking periods of the Large Hadron Collider, the multi-wire proportional chamber-based readout was replaced with gas-electron multipliers. As expected, the detector performance is affected by the so-called common-mode effect, which leads to significant baseline fluctuations. A detailed study of the pulse shape with the new readout has revealed that it is also affected by ion tails. Since reconstruction and data compression are performed fully online, these effects must be corrected at the hardware level in the FPGA-based common readout units. The characteristics of the common-mode effect and of the ion tail, as well as the algorithms developed for their online correction, are described in this paper. The common-mode dependencies are studied using machine-learning techniques. Toy Monte Carlo simulations are performed to illustrate the importance of online corrections and to investigate the performance of the developed algorithms.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Summary Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well‐known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm.

Aliaga, José I.↗