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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

The Anatomy of Mr. Scan: A Dissection of Performance of an Extreme Scale GPU-Based Clustering Algorithm, In: 2014 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems

The emergence of leadership class systems with GPU-equipped nodes has the potential to vastly increase the performance of existing distributed applications. However, the inclusion of GPU computation into existing extreme scale distributed applications can reveal scalability issues that were absent in the CPU version. The issues exposed in scaling by a GPU can become limiting factors to overall application performance. We developed an extreme scale GPU-based application to perform data clustering on multi-billion point datasets. In this application, called Mr. Scan, we ran into several of these performance limiting issues. Through the use of complete end-to-end benchmarking of Mr. Scan (measuring time from reading and distribution to final output), we were able to identify three major sources of real world performance issues: data distribution, GPU load balancing, and system specific issues such as start-up time. These issues comprised a vast majority of the run time of Mr. Scan. Data distribution alone accounted for 68% of the total run time of Mr. Scan when processing 6.5 billion points on Cray Titan at 8192 nodes. With improvements in these areas, we have been able able to cut total run time of Mr. Scan from 17.5 minutes to 8.3 minutes when clustering 6.5 billion points.

Computer Science↗
DOE OSTI2016

Modified Closures in Monte Carlo Algorithms for Diffusive Binary Stochastic Media Transport Problems

In a stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media (BSM) is to use the atomic mix approximation in which the transport problem is solved using homogenized (volume-averaged) material properties. A common deterministic model developed for solving BSM particle transport problems is the Levermore-Pomraning (LP) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the LP equations and another Monte Carlo algorithm (Algorithm B) that locally preserves the sampled material realization; we refer to these Monte Carlo algorithms as the LP and LPLRP (LP local realization preserving) algorithms, respectively. One-dimensional (1D) planar geometry benchmark studies have shown that the LPLRP algorithm is often significantly more accurate than the LP algorithm for problems with an incident angular flux as well as for problems with an interior source. The LPLRP algorithm implementation in these benchmark comparisons made explicit use of the one-dimensional nature of the problem. The LP model is derived by assuming an 'upwind' closure in the coupling term relating the two materials in a binary stochastic medium. Su and Pomraning developed a modified form of this closure by considering the small correlation length limit and requiring the modified closure to produce the correct exponential decay for a source-free half-line albedo problem in rod geometry. They concluded that the modified closure is generally not inferior to the LP closure and in some cases is significantly better. Brantley investigated the use of the Su-Pomraning (SP) closure in the Monte Carlo LP algorithm (LP-SP) for the suite of benchmark problems and concluded that 1) the LP-SP algorithm was somewhat more accurate overall than the LP algorithm and somewhat less accurate overall than the LPLRP algorithm for an incident angular flux benchmark suite, and 2) the LP-SP algorithm was generally the least accurate of the algorithms for an interior source benchmark suite. Larsen et al. performed an asymptotic analysis of the transport equation in 1D planar geometry for the situation in which the physical system is 1) a random binary stochastic medium with material macroscopic total cross sections and mean slab width values of O(1) or smaller and 2) optically thick with weak absorption and sources at each spatial point and therefore globally diffusive. The asymptotic analysis demonstrates that, under these assumptions, the transport equation limits to the conventional diffusion equation with atomically-mixed (volume-averaged) material properties. Larsen et al. also demonstrate that, under these same assumptions, the LP equations asymptotically limit to an atomically-mixed diffusion equation with a diffusion coefficient that is too large, leading to an unphysical flattening of the ensemble-averaged scalar flux distribution. Vasques and Yadav recently performed an asymptotic analysis of an adjusted Levermore-Pomraning closure in which the Markovian transition functions are rescaled such that the equations asymptotically limit to the correct atomically-mixed diffusion equation; we refer to this model as LP-VY. In this paper, we demonstrate that the adjusted LP closure proposed by Vasques and Yadav is a special case of the SP closure obtained by assuming that the absorption cross sections in the two materials are equal. We further demonstrate that the Su-Pomraning closure has the correct asymptotic limit for the diffusive physical system and is therefore an appropriate closure for these problems. We also describe how to incorporate these various closures into the Monte Carlo LP and LPLRP particle transport algorithms, and we present numerical results comparing the accuracy of the Monte Carlo LP, LP-VY, LP-SP, LPLRP, and LPLRP-SP algorithms for the set of diffusive benchmark problems. We demonstrated that the SP closure has the correct asymptotic limit for the diffusive physical system under investigation in this paper and that the VY closure is a special case of the SP closure obtained by assuming equal absorption in the two materials. Both of these closures are readily implemented in the Monte Carlo LP and LPLRP algorithms for particle transport in BSM. Through numerical comparisons to a diffusive benchmark suite, we confirmed that 1) the LP and LPLRP algorithms do not limit to the appropriate diffusion solution and 2) the LP-VY, LP-SP, and LPLRP-SP algorithms limit to the appropriate diffusion solution and are of comparable accuracy. The LPLRP algorithm has been shown to be generally more accurate than the LP algorithm for non-diffusive problems. However, the numerical results in this paper indicate that the LPLRP algorithm does not limit to the correct diffusion equation for the asymptotic limit under consideration. The work in this paper demonstrates that the SP algorithm does limit to the correct diffusion equation for the asymptotic limit considered. Future work will investigate the possibility of whether the LPLRP-SP algorithm is accurate for both diffusive and non-diffusive problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Validation of deformable image registration algorithms on CT images of ex vivo porcine bladders with fiducial markers

Purpose: The spatial accuracy of deformable image registration (DIR) is important in the implementation of image guided adaptive radiotherapy techniques for cancer in the pelvic region. Validation of algorithms is best performed on phantoms with fiducial markers undergoing controlled large deformations. Excised porcine bladders, exhibiting similar filling and voiding behavior as human bladders, provide such an environment. The aim of this study was to determine the spatial accuracy of different DIR algorithms on CT images ofex vivo porcine bladders with radiopaque fiducial markers applied to the outer surface, for a range of bladder volumes, using various accuracy metrics. Methods: Five excised porcine bladders with a grid of 30–40 radiopaque fiducial markers attached to the outer wall were suspended inside a water-filled phantom. The bladder was filled with a controlled amount of water with added contrast medium for a range of filling volumes (100–400 ml in steps of 50 ml) using a luer lock syringe, and CT scans were acquired at each filling volume. DIR was performed for each data set, with the 100 ml bladder as the reference image. Six intensity-based algorithms (optical flow or demons-based) implemented in theMATLAB platform DIRART, a b-spline algorithm implemented in the commercial software package VelocityAI, and a structure-based algorithm (Symmetric Thin Plate Spline Robust Point Matching) were validated, using adequate parameter settings according to values previously published. The resulting deformation vector field from each registration was applied to the contoured bladder structures and to the marker coordinates for spatial error calculation. The quality of the algorithms was assessed by comparing the different error metrics across the different algorithms, and by comparing the effect of deformation magnitude (bladder volume difference) per algorithm, using the Independent Samples Kruskal-Wallis test. Results: The authors found good structure accuracy without dependency on bladder volume difference for all but one algorithm, and with the best result for the structure-based algorithm. Spatial accuracy as assessed from marker errors was disappointing for all algorithms, especially for large volume differences, implying that the deformations described by the registration did not represent anatomically correct deformations. The structure-based algorithm performed the best in terms of marker error for the large volume difference (100–400 ml). In general, for the small volume difference (100–150 ml) the algorithms performed relatively similarly. The structure-based algorithm exhibited the best balance in performance between small and large volume differences, and among the intensity-based algorithms, the algorithm implemented in VelocityAI exhibited the best balance. Conclusions: Validation of multiple DIR algorithms on a novel physiological bladder phantom revealed that the structure accuracy was good for most algorithms, but that the spatial accuracy as assessed from markers was low for all algorithms, especially for large deformations. Hence, many of the available algorithms exhibit sufficient accuracy for contour propagation purposes, but possibly not for accurate dose accumulation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-91: Accuracy of Dose Calculation Algorithms for Patients Undergoing Stereotactic Ablative Radiotherapy

Purpose: The purpose of this study was to investigate and quantify the variation in dose distributions in small field lung cancer radiotherapy using seven different dose calculation algorithms. Methods: The study was performed in 21 lung cancer patients who underwent Stereotactic Ablative Body Radiotherapy (SABR). Two different methods (i) Same dose coverage to the target volume (named as same dose method) (ii) Same monitor units in all algorithms (named as same monitor units) were used for studying the performance of seven different dose calculation algorithms in XiO and Eclipse treatment planning systems. The seven dose calculation algorithms include Superposition, Fast superposition, Fast Fourier Transform ( FFT) Convolution, Clarkson, Anisotropic Analytic Algorithm (AAA), Acurous XB and pencil beam (PB) algorithms. Prior to this, a phantom study was performed to assess the accuracy of these algorithms. Superposition algorithm was used as a reference algorithm in this study. The treatment plans were compared using different dosimetric parameters including conformity, heterogeneity and dose fall off index. In addition to this, the dose to critical structures like lungs, heart, oesophagus and spinal cord were also studied. Statistical analysis was performed using Prism software. Results: The mean±stdev with conformity index for Superposition, Fast superposition, Clarkson and FFT convolution algorithms were 1.29±0.13, 1.31±0.16, 2.2±0.7 and 2.17±0.59 respectively whereas for AAA, pencil beam and Acurous XB were 1.4±0.27, 1.66±0.27 and 1.35±0.24 respectively. Conclusion: Our study showed significant variations among the seven different algorithms. Superposition and AcurosXB algorithms showed similar values for most of the dosimetric parameters. Clarkson, FFT convolution and pencil beam algorithms showed large differences as compared to superposition algorithms. Based on our study, we recommend Superposition and AcurosXB algorithms as the first choice of algorithms in lung cancer radiotherapy involving small fields. However, further investigation by Monte Carlo simulation is required to confirm our results.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

A matrix-algebraic formulation of distributed-memory maximal cardinality matching algorithms in bipartite graphs

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributed-memory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal matching algorithms with minimal changes. The newly developed algorithms have two benefits over existing graph-based algorithms. First, unlike existing parallel algorithms, cardinality of matching obtained by the new algorithms stays constant with increasing processor counts, which is important for predictable and reproducible performance. Second, relying on bulk-synchronous matrix operations, these algorithms expose a higher degree of parallelism on distributed-memory platforms than existing graph-based algorithms. We report high-performance implementations of three maximal matching algorithms using hybrid OpenMP-MPI and evaluate the performance of these algorithm using more than 35 real and randomly generated graphs. On real instances, our algorithms achieve up to 200 × speedup on 2048 cores of a Cray XC30 supercomputer. Even higher speedups are obtained on larger synthetically generated graphs where our algorithms show good scaling on up to 16,384 cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Performance of 12 DIR algorithms in low-contrast regions for mass and density conserving deformation

Purpose: Deformable image registration (DIR) has become a key tool for adaptive radiotherapy to account for inter- and intrafraction organ deformation. Of contemporary interest, the application to deformable dose accumulation requires accurate deformation even in low contrast regions where dose gradients may exist within near-uniform tissues. One expects high-contrast features to generally be deformed more accurately by DIR algorithms. The authors systematically assess the accuracy of 12 DIR algorithms and quantitatively examine, in particular, low-contrast regions, where accuracy has not previously been established.Methods: This work investigates DIR algorithms in three dimensions using deformable gel (DEFGEL) [U. J. Yeo, M. L. Taylor, L. Dunn, R. L. Smith, T. Kron, and R. D. Franich, “A novel methodology for 3D deformable dosimetry,” Med. Phys. 39, 2203–2213 (2012)], for application to mass- and density-conserving deformations. CT images of DEFGEL phantoms with 16 fiducial markers (FMs) implanted were acquired in deformed and undeformed states for three different representative deformation geometries. Nonrigid image registration was performed using 12 common algorithms in the public domain. The optimum parameter setup was identified for each algorithm and each was tested for deformation accuracy in three scenarios: (I) original images of the DEFGEL with 16 FMs; (II) images with eight of the FMs mathematically erased; and (III) images with all FMs mathematically erased. The deformation vector fields obtained for scenarios II and III were then applied to the original images containing all 16 FMs. The locations of the FMs estimated by the algorithms were compared to actual locations determined by CT imaging. The accuracy of the algorithms was assessed by evaluation of three-dimensional vectors between true marker locations and predicted marker locations.Results: The mean magnitude of 16 error vectors per sample ranged from 0.3 to 3.7, 1.0 to 6.3, and 1.3 to 7.5 mm across algorithms for scenarios I to III, respectively. The greatest accuracy was exhibited by the original Horn and Schunck optical flow algorithm. In this case, for scenario III (erased FMs not contributing to driving the DIR calculation), the mean error was half that of the modified demons algorithm (which exhibited the greatest error), across all deformations. Some algorithms failed to reproduce the geometry at all, while others accurately deformed high contrast features but not low-contrast regions—indicating poor interpolation between landmarks.Conclusions: The accuracy of DIR algorithms was quantitatively evaluated using a tissue equivalent, mass, and density conserving DEFGEL phantom. For the model studied, optical flow algorithms performed better than demons algorithms, with the original Horn and Schunck performing best. The degree of error is influenced more by the magnitude of displacement than the geometric complexity of the deformation. As might be expected, deformation is estimated less accurately for low-contrast regions than for high-contrast features, and the method presented here allows quantitative analysis of the differences. The evaluation of registration accuracy through observation of the same high contrast features that drive the DIR calculation is shown to be circular and hence misleading.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Maximum likelihood positioning algorithm for high-resolution PET scanners

Purpose: In high-resolution positron emission tomography (PET), lightsharing elements are incorporated into typical detector stacks to read out scintillator arrays in which one scintillator element (crystal) is smaller than the size of the readout channel. In order to identify the hit crystal by means of the measured light distribution, a positioning algorithm is required. One commonly applied positioning algorithm uses the center of gravity (COG) of the measured light distribution. The COG algorithm is limited in spatial resolution by noise and intercrystal Compton scatter. The purpose of this work is to develop a positioning algorithm which overcomes this limitation. Methods: The authors present a maximum likelihood (ML) algorithm which compares a set of expected light distributions given by probability density functions (PDFs) with the measured light distribution. Instead of modeling the PDFs by using an analytical model, the PDFs of the proposed ML algorithm are generated assuming a single-gamma-interaction model from measured data. The algorithm was evaluated with a hot-rod phantom measurement acquired with the preclinical HYPERION II {sup D} PET scanner. In order to assess the performance with respect to sensitivity, energy resolution, and image quality, the ML algorithm was compared to a COG algorithm which calculates the COG from a restricted set of channels. The authors studied the energy resolution of the ML and the COG algorithm regarding incomplete light distributions (missing channel information caused by detector dead time). Furthermore, the authors investigated the effects of using a filter based on the likelihood values on sensitivity, energy resolution, and image quality. Results: A sensitivity gain of up to 19% was demonstrated in comparison to the COG algorithm for the selected operation parameters. Energy resolution and image quality were on a similar level for both algorithms. Additionally, the authors demonstrated that the performance of the ML algorithm is less prone to missing channel information. A likelihood filter visually improved the image quality, i.e., the peak-to-valley increased up to a factor of 3 for 2-mm-diameter phantom rods by rejecting 87% of the coincidences. A relative improvement of the energy resolution of up to 12.8% was also measured rejecting 91% of the coincidences. Conclusions: The developed ML algorithm increases the sensitivity by correctly handling missing channel information without influencing energy resolution or image quality. Furthermore, the authors showed that energy resolution and image quality can be improved substantially by rejecting events that do not comply well with the single-gamma-interaction model, such as Compton-scattered events.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗
DOE OSTI2017

Parallel Asynchronous Distributed-Memory Maximal Independent Set Algorithm with Work Ordering

The maximal independent set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of graph data suggests the use of distributed memory hardware as a cost-effective approach to providing necessary compute and memory resources. Existing distributed memory parallel MIS algorithms rely on synchronous communication and use techniques such as subgraph computations. In this paper, we present an asynchronous distributed-memory parallel graph algorithm that relies on a virtual directed acyclic graph (DAG) that is created during the algorithm execution. We introduce two additional algorithms that save computations by ordering generated work. The first algorithm applies ordering globally to reduce computations, and the second algorithm applies ordering locally at the level of threads to minimize the synchronization overhead. We use two different implementations of Luby’s algorithm variants as baseline to compare the performance of the presented algorithms: (1) vertex-centric Luby A and Luby B implementations, and (2) the CombBLAS linear-algebra Luby A implementation. Results show that proposed algorithms outperform both implementations of Luby algorithms, especially in distributed execution. Furthermore, we show that for low-diameter graphs the algorithm that applies global ordering scales better than other algorithms and for high diameter graphs the original asynchronous algorithm and thread-level ordering algorithm show better performance.

maximal independent set (MIS), distributed memory ↗
DOE OSTI2015

SU-E-T-793: Validation of COMPASS 3D Dosimetry as Pre Treatment Verification with Commercial TPS Algorithms

Purpose: The purpose of this study was to validate the advent of COMPASS 3D dosimetry as a routine pre treatment verification tool with commercially available CMS Monaco and Oncentra Masterplan planning system. Methods: Twenty esophagus patients were selected for this study. All these patients underwent radical VMAT treatment in Elekta Linac and plans were generated in Monaco v5.0 with MonteCarlo(MC) dose calculation algorithm. COMPASS 3D dosimetry comprises an advanced dose calculation algorithm of collapsed cone convolution(CCC). To validate CCC algorithm in COMPASS, The DICOM RT Plans generated using Monaco MC algorithm were transferred to Oncentra Masterplan v4.3 TPS. Only final dose calculations were performed using CCC algorithm with out optimization in Masterplan planning system. It is proven that MC algorithm is an accurate algorithm and obvious that there will be a difference with MC and CCC algorithms. Hence CCC in COMPASS should be validated with other commercially available CCC algorithm. To use the CCC as pretreatment verification tool with reference to MC generated treatment plans, CCC in OMP and CCC in COMPASS were validated using dose volume based indices such as D98, D95 for target volumes and OAR doses. Results: The point doses for open beams were observed <1% with reference to Monaco MC algorithms. Comparisons of CCC(OMP) Vs CCC(COMPASS) showed a mean difference of 1.82%±1.12SD and 1.65%±0.67SD for D98 and D95 respectively for Target coverage. Maximum point dose of −2.15%±0.60SD difference was observed in target volume. The mean lung dose of −2.68%±1.67SD was noticed between OMP and COMPASS. The maximum point doses for spinal cord were −1.82%±0.287SD. Conclusion: In this study, the accuracy of CCC algorithm in COMPASS 3D dosimetry was validated by compared with CCC algorithm in OMP TPS. Dose calculation in COMPASS is feasible within < 2% in comparison with commercially available TPS algorithms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

First-order convex feasibility algorithms for x-ray CT

Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144 Degree-Sign . The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗