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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Quantum Branch-and-Bound Algorithm and its Application to the Travelling Salesman Problem

We propose a quantum branch-and-bound algorithm based on the general scheme of the branch-and-bound method and the quantum nested searching algorithm and examine its computational efficiency. We also compare this algorithm with a similar classical algorithm on the example of the travelling salesman problem. We show that in the vast majority of problems, the classical algorithm is quicker than the quantum algorithm due to greater adaptability. However, the operation time of the quantum algorithm is constant for all problem, whereas the classical algorithm runs very slowly for certain problems. In the worst case, the quantum branch-and-bound algorithm is proved to be several times more efficient than the classical algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A fast algorithm for sparse matrix computations related to inversion

We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G{sup r} and G{sup <} for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round-off errors stay at a reasonable level.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

New Effective Multithreaded Matching Algorithms

Matching is an important combinatorial problem with a number of applications in areas such as community detection, sparse linear algebra, and network alignment. Since computing optimal matchings can be very time consuming, several fast approximation algorithms, both sequential and parallel, have been suggested. Common to the algorithms giving the best solutions is that they tend to be sequential by nature, while algorithms more suitable for parallel computation give solutions of less quality. We present a new simple 1 2 -approximation algorithm for the weighted matching problem. This algorithm is both faster than any other suggested sequential 1 2 -approximation algorithm on almost all inputs and also scales better than previous multithreaded algorithms. We further extend this to a general scalable multithreaded algorithm that computes matchings of weight comparable with the best sequential algorithms. The performance of the suggested algorithms is documented through extensive experiments on different multithreaded architectures.

matching, parallel algorithms↗
DOE OSTI2014

SU-E-J-218: Evaluation of CT Images Created Using a New Metal Artifact Reduction Reconstruction Algorithm for Radiation Therapy Treatment Planning

Purpose: Metal in patients creates streak artifacts in CT images. When used for radiation treatment planning, these artifacts make it difficult to identify internal structures and affects radiation dose calculations, which depend on HU numbers for inhomogeneity correction. This work quantitatively evaluates a new metal artifact reduction (MAR) CT image reconstruction algorithm (GE Healthcare CT-0521-04.13-EN-US DOC1381483) when metal is present. Methods: A Gammex Model 467 Tissue Characterization phantom was used. CT images were taken of this phantom on a GE Optima580RT CT scanner with and without steel and titanium plugs using both the standard and MAR reconstruction algorithms. HU values were compared pixel by pixel to determine if the MAR algorithm altered the HUs of normal tissues when no metal is present, and to evaluate the effect of using the MAR algorithm when metal is present. Also, CT images of patients with internal metal objects using standard and MAR reconstruction algorithms were compared. Results: Comparing the standard and MAR reconstructed images of the phantom without metal, 95.0% of pixels were within ±35 HU and 98.0% of pixels were within ±85 HU. Also, the MAR reconstruction algorithm showed significant improvement in maintaining HUs of non-metallic regions in the images taken of the phantom with metal. HU Gamma analysis (2%, 2mm) of metal vs. non-metal phantom imaging using standard reconstruction resulted in an 84.8% pass rate compared to 96.6% for the MAR reconstructed images. CT images of patients with metal show significant artifact reduction when reconstructed with the MAR algorithm. Conclusion: CT imaging using the MAR reconstruction algorithm provides improved visualization of internal anatomy and more accurate HUs when metal is present compared to the standard reconstruction algorithm. MAR reconstructed CT images provide qualitative and quantitative improvements over current reconstruction algorithms, thus improving radiation treatment planning accuracy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Sensitivity study of voxel-based PET image comparison to image registration algorithms

Purpose: Accurate deformable registration is essential for voxel-based comparison of sequential positron emission tomography (PET) images for proper adaptation of treatment plan and treatment response assessment. The comparison may be sensitive to the method of deformable registration as the optimal algorithm is unknown. This study investigated the impact of registration algorithm choice on therapy response evaluation. Methods: Sixteen patients with 20 lung tumors underwent a pre- and post-treatment computed tomography (CT) and 4D FDG-PET scans before and after chemoradiotherapy. All CT images were coregistered using a rigid and ten deformable registration algorithms. The resulting transformations were then applied to the respective PET images. Moreover, the tumor region defined by a physician on the registered PET images was classified into progressor, stable-disease, and responder subvolumes. Particularly, voxels with standardized uptake value (SUV) decreases >30% were classified as responder, while voxels with SUV increases >30% were progressor. All other voxels were considered stable-disease. The agreement of the subvolumes resulting from difference registration algorithms was assessed by Dice similarity index (DSI). Coefficient of variation (CV) was computed to assess variability of DSI between individual tumors. Root mean square difference (RMS{sub rigid}) of the rigidly registered CT images was used to measure the degree of tumor deformation. RMS{sub rigid} and DSI were correlated by Spearman correlation coefficient (R) to investigate the effect of tumor deformation on DSI. Results: Median DSI{sub rigid} was found to be 72%, 66%, and 80%, for progressor, stable-disease, and responder, respectively. Median DSI{sub deformable} was 63%–84%, 65%–81%, and 82%–89%. Variability of DSI was substantial and similar for both rigid and deformable algorithms with CV > 10% for all subvolumes. Tumor deformation had moderate to significant impact on DSI for progressor subvolume with R{sub rigid} = − 0.60 (p = 0.01) and R{sub deformable} = − 0.46 (p = 0.01–0.20) averaging over all deformable algorithms. For stable-disease subvolumes, the correlations were significant (p < 0.001) for all registration algorithms with R{sub rigid} = − 0.71 and R{sub deformable} = − 0.72. Progressor and stable-disease subvolumes resulting from rigid registration were in excellent agreement (DSI > 70%) for RMS{sub rigid} < 150 HU. However, tumor deformation was observed to have negligible effect on DSI for responder subvolumes with insignificant |R| < 0.26, p > 0.27. Conclusions: This study demonstrated that deformable algorithms cannot be arbitrarily chosen; different deformable algorithms can result in large differences of voxel-based PET image comparison. For low tumor deformation (RMS{sub rigid} < 150 HU), rigid and deformable algorithms yield similar results, suggesting deformable registration is not required for these cases.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-SPS-02: Accuracy of the Small Field Dosimetry Using the Monte Carlo and Sequential Dose Calculation Algorithms of Multiplan Treatment Planning System Within and Beyond Heterogeneous Media for Cyberknife M6 Unit

Purpose: In small field geometries, the electronic equilibrium can be lost, making it challenging for the dose-calculation algorithm to accurately predict the dose, especially in the presence of tissue heterogeneities. In this study, dosimetric accuracy of Monte Carlo (MC) advanced dose calculation and sequential algorithms of Multiplan treatment planning system were investigated for small radiation fields incident on homogeneous and heterogeneous geometries. Methods: Small open fields of fixed cones of Cyberknife M6 unit 100 to 500 mm2 were used for this study. The fields were incident on in house phantom containing lung, air, and bone inhomogeneities and also homogeneous phantom. Using the same film batch, the net OD to dose calibration curve was obtained using CK with the 60 mm fixed cone by delivering 0- 800 cGy. Films were scanned 48 hours after irradiation using an Epson 1000XL flatbed scanner. The dosimetric accuracy of MC and sequential algorithms in the presence of the inhomogeneities was compared against EBT3 film dosimetry Results: Open field tests in a homogeneous phantom showed good agreement between two algorithms and film measurement For MC algorithm, the minimum gamma analysis passing rates between measured and calculated dose distributions were 99.7% and 98.3% for homogeneous and inhomogeneous fields in the case of lung and bone respectively. For sequential algorithm, the minimum gamma analysis passing rates were 98.9% and 92.5% for for homogeneous and inhomogeneous fields respectively for used all cone sizes. In the case of the air heterogeneity, the differences were larger for both calculation algorithms. Overall, when compared to measurement, the MC had better agreement than sequential algorithm. Conclusion: The Monte Carlo calculation algorithm in the Multiplan treatment planning system is an improvement over the existing sequential algorithm. Dose discrepancies were observed for in the presence of air inhomogeneities.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-J-76: Evaluation of the Performance of Different Deformable Image Registration Algorithms in Helical, Axial and Cone-Beam CT Images of a Mobile Phantom

Purpose: To investigate quantitatively the performance of different deformable-image-registration algorithms (DIR) with helical (HCT), axial (ACT) and cone-beam CT (CBCT) by evaluating the variations in the CT-numbers and lengths of targets moving with controlled motion-patterns. Methods: Four DIR-algorithms including demons, fast-demons, Horn-Schunk and Locas-Kanade from the DIRART-software are used to register CT-images of a mobile-phantom. A mobile-phantom is scanned with different imaging techniques that include helical, axial and cone-beam CT. The phantom includes three targets with different lengths that are made from water-equivalent material and inserted in low-density-foam which is moved with adjustable motion-amplitudes and frequencies. Results: Most of the DIR-algorithms are able to produce the lengths of the stationary-targets, however, they do not produce the CT-number values in CBCT. The image-artifacts induced by motion are more regular in CBCT imaging where the mobile-target elongation increases linearly with motion-amplitude. In ACT and HCT, the motion-artifacts are irregular where some mobile -targets are elongated or shrunk depending on the motion-phase during imaging. The DIR-algorithms are successful in deforming the images of the mobile-targets to the images of the stationary-targets producing the CT-number values and length of the target for motion-amplitudes < 20 mm. Similarly in ACT, all DIR-algorithms produced the actual CT-number and length of the stationary-targets for motion-amplitudes < 15 mm. As stronger motion-artifacts are induced in HCT and ACT, DIR-algorithms fail to produce CT-values and shape of the stationary-targets and fast-demons-algorithm has worst performance. Conclusion: Most of DIR-algorithms produce the CT-number values and lengths of the stationary-targets in HCT and ACT images that has motion-artifacts induced by small motion-amplitudes. As motion-amplitudes increase, the DIR-algorithms fail to deform mobile-target images to the stationary-images in HCT and ACT. In CBCT, DIR-algorithms are successful in producing length and shape of the stationary-targets, however, they fail to produce the accurate CT-number level.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-G-JeP1-12: Head-To-Head Performance Characterization of Two Multileaf Collimator Tracking Algorithms for Radiotherapy

Purpose: Multi-leaf collimator (MLC) tracking is being clinically pioneered to continuously compensate for thoracic and abdominal motion during radiotherapy. The purpose of this work is to characterize the performance of two MLC tracking algorithms for cancer radiotherapy, based on a direct optimization and a piecewise leaf fitting approach respectively. Methods: To test the algorithms, both physical and in silico experiments were performed. Previously published high and low modulation VMAT plans for lung and prostate cancer cases were used along with eight patient-measured organ-specific trajectories. For both MLC tracking algorithm, the plans were run with their corresponding patient trajectories. The physical experiments were performed on a Trilogy Varian linac and a programmable phantom (HexaMotion platform). For each MLC tracking algorithm, plan and patient trajectory, the tracking accuracy was quantified as the difference in aperture area between ideal and fitted MLC. To compare algorithms, the average cumulative tracking error area for each experiment was calculated. The two-sample Kolmogorov-Smirnov (KS) test was used to evaluate the cumulative tracking errors between algorithms. Results: Comparison of tracking errors for the physical and in silico experiments showed minor differences between the two algorithms. The KS D-statistics for the physical experiments were below 0.05 denoting no significant differences between the two distributions pattern and the average error area (direct optimization/piecewise leaf-fitting) were comparable (66.64 cm2/65.65 cm2). For the in silico experiments, the KS D-statistics were below 0.05 and the average errors area were also equivalent (49.38 cm2/48.98 cm2). Conclusion: The comparison between the two leaf fittings algorithms demonstrated no significant differences in tracking errors, neither in a clinically realistic environment nor in silico. The similarities in the two independent algorithms give confidence in the use of either algorithm for clinical implementation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (≈20pJ/word on-die to ≈10,000 pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use many-core processors on each compute nodes that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignment constraints and avoids gather/scat;ter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of ×2 to ×2.5 speed-up in double precision for particle shape factor of orders 1–3. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles). Program summary Program Title: vec_deposition Program Files doi:http://dx.doi.org/10.17632/nh77fv9k8c.1 Licensing provisions: BSD 3-Clause Programming language: Fortran 90 External routines/libraries: OpenMP > 4.0 Nature of problem: Exascale architectures will have many-core processors per node with long vector data registers capable of performing one single instruction on multiple data during one clock cycle. Data register lengths are expected to double every four years and this pushes for new portable solutions for efficiently vectorizing Particle-In-Cell codes on these future many-core architectures. One of the main hotspot routines of the PIC algorithm is the current/charge deposition for which there is no efficient and portable vector algorithm. Solution method: Here we provide an efficient and portable vector algorithm of current/charge deposition routines that uses a new data structure, which significantly reduces gather/scatter operations. Vectorization is controlled using OpenMP 4.0 compiler directives for vectorization which ensures portability across different architectures. Restrictions: Here we do not provide the full PIC algorithm with an executable but only vector routines for current/charge deposition. These scalar/vector routines can be used as library routines in your 3D Particle-In-Cell code. However, to get the best performances out of vector routines you have to satisfy the two following requirements: (1) Your code should implement particle tiling (as explained in the manuscript) to allow for maximized cache reuse and reduce memory accesses that can hinder vector performances. The routines can be used directly on each particle tile. (2) You should compile your code with a Fortran 90 compiler (e.g Intel, gnu or cray) and provide proper alignment flags and compiler alignment directives (more details in README file).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Parallel algorithms for finding connected components using linear algebra

Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a class of parallel connected-component algorithms designed using linear-algebraic primitives. These algorithms are based on a PRAM algorithm by Shiloach and Vishkin and can be designed using standard GraphBLAS operations. Here, we demonstrate two algorithms of this class, one named LACC for Linear Algebraic Connected Components, and the other named FastSV which can be regarded as LACC’s simplification. With the support of the highly-scalable Combinatorial BLAS library, LACC and FastSV outperform the previous state-of-the-art algorithm by a factor of up to 12x for small to medium scale graphs. For large graphs with more than 50B edges, LACC and FastSV scale to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperform previous algorithms by a significant margin. This remarkable performance is accomplished by (1) exploiting sparsity that was not present in the original PRAM algorithm formulation, (2) using high-performance primitives of Combinatorial BLAS, and (3) identifying hot spots and optimizing them away by exploiting algorithmic insights.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Annealed Importance Sampling Reversible Jump MCMC algorithms

It will soon be 20 years since reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithms have been proposed. They have significantly extended the scope of Markov chain Monte Carlo simulation methods, offering the promise to be able to routinely tackle transdimensional sampling problems, as encountered in Bayesian model selection problems for example, in a principled and flexible fashion. Their practical efficient implementation, however, still remains a challenge. A particular difficulty encountered in practice is in the choice of the dimension matching variables (both their nature and their distribution) and the reversible transformations which allow one to define the one-to-one mappings underpinning the design of these algorithms. Indeed, even seemingly sensible choices can lead to algorithms with very poor performance. The focus of this paper is the development and performance evaluation of a method, annealed importance sampling RJ-MCMC (aisRJ), which addresses this problem by mitigating the sensitivity of RJ-MCMC algorithms to the aforementioned poor design. As we shall see the algorithm can be understood as being an “exact approximation” of an idealized MCMC algorithm that would sample from the model probabilities directly in a model selection set-up. Such an idealized algorithm may have good theoretical convergence properties, but typically cannot be implemented, and our algorithms can approximate the performance of such idealized algorithms to an arbitrary degree while not introducing any bias for any degree of approximation. Our approach combines the dimension matching ideas of RJ-MCMC with annealed importance sampling and its Markov chain Monte Carlo implementation. We illustrate the performance of the algorithm with numerical simulations which indicate that, although the approach may at first appear computationally involved, it is in fact competitive.

annealed importance sampling↗
DOE OSTI2020

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Final Report: Sampling-Based Algorithms for Estimating Structure in Big Data.

The purpose of this project was to develop sampling-based algorithms to discover hidden struc- ture in massive data sets. Inferring structure in large data sets is an increasingly common task in many critical national security applications. These data sets come from myriad sources, such as network traffic, sensor data, and data generated by large-scale simulations. They are often so large that traditional data mining techniques are time consuming or even infeasible. To address this problem, we focus on a class of algorithms that do not compute an exact answer, but instead use sampling to compute an approximate answer using fewer resources. The particular class of algorithms that we focus on are streaming algorithms , so called because they are designed to handle high-throughput streams of data. Streaming algorithms have only a small amount of working storage - much less than the size of the full data stream - so they must necessarily use sampling to approximate the correct answer. We present two results: * A streaming algorithm called HyperHeadTail , that estimates the degree distribution of a graph (i.e., the distribution of the number of connections for each node in a network). The degree distribution is a fundamental graph property, but prior work on estimating the degree distribution in a streaming setting was impractical for many real-world application. We improve upon prior work by developing an algorithm that can handle streams with repeated edges, and graph structures that evolve over time. * An algorithm for the task of maintaining a weighted subsample of items in a stream, when the items must be sampled according to their weight, and the weights are dynamically changing. To our knowledge, this is the first such algorithm designed for dynamically evolving weights. We expect it may be useful as a building block for other streaming algorithms on dynamic data sets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Quantum Optimization and Approximation Algorithms

Shor's groundbreaking quantum algorithm for integer factoring provides an exponential speedup over the best-known classical algorithms. In the 20 years since Shor's algorithm was conceived, only a handful of fundamental quantum algorithmic kernels, generally providing modest polynomial speedups over classical algorithms, have been invented. To better understand the potential advantage quantum resources provide over their classical counterparts, one may consider other resources than execution time of algorithms. Quantum Approximation Algorithms direct the power of quantum computing towards optimization problems where quantum resources provide higher-quality solutions instead of faster execution times. We provide a new rigorous analysis of the recent Quantum Approximate Optimization Algorithm, demonstrating that it provably outperforms the best known classical approximation algorithm for special hard cases of the fundamental Maximum Cut graph-partitioning problem. We also develop new types of classical approximation algorithms for finding near-optimal low-energy states of physical systems arising in condensed matter by extending seminal discrete optimization techniques. Our interdisciplinary work seeks to unearth new connections between discrete optimization and quantum information science.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Preliminary IHLW Formulation Algorithm Description

This report documents the initial algorithm that could be used by the Waste Treatment and Immobilization Plant (WTP) in batching high-level waste (HLW) and glass-forming chemicals (GFCs) in the HLW melter feed preparation vessel (MFPV) (HFP-VSL-00001 and -00005). Not all Hanford tank waste can be accommodated by the models developed for this report and significant expansion of the model boundaries could be achievable to reduce the WTP mission life and total canister production count. The immobilized HLW (IHLW) must meet a series of constraints to be acceptable for disposal in the Monitored Geologic Repository, which are contained in the Specification 1 of the Contract (DOE 2000), the Waste Acceptance Product Specifications (WAPS, DOE 1996), and the Waste Acceptance System Requirements Document (WASRD, DOE 2007). The IHLW Waste Form Compliance Plan (WCP, 24590-HLW-PL-RT-07-0001, Rev 3) specifies that the formulation algorithm will be developed and used to comply with the constraints associated with glass composition and properties. This report is not an engineering calculation, does not provide design input, and is not an engineering study. Algorithm inputs include the chemical analyses of the blended HLW in the HLW blend vessel (HBV) (HLP-VSL-00028, the volume and composition of the MFPV heel, the volume and composition of the MFPV after waste addition, the volume and composition of MFPV batch after GFC addition, the compositions of individual GFCs, and the mass of glass in each canister. In addition to these inputs, uncertainties in the HLW composition and processing parameters are included in the algorithm. Using the above inputs, the algorithm calculates the following outputs: 1) the volume of HLW to be transferred from the HBV to the MFPV, 2) the mass of each GFC for addition to the MFPV, 3) the composition of the glass that will be produced along with uncertainties, and 4) the predicted properties, with associated uncertainties, of the resulting IHLW. The algorithm uses the property-composition models to calculate properties with associated uncertainties and compares them with various constraints to ensure that a processable feed is formulated and a compliant IHLW is produced. The GFC additions are determined using an optimization approach to provide high confidence that the HLW glass will meet all product quality requirements and key processing constraints. For most HLW batches there are many possible glass compositions that meet all constraints. In these cases, the glass composition is optimized for a series of target component concentrations and target property values. The algorithm also incorporates process measurement and product quality uncertainties, based on the work of Piepel et al. (2005). Estimates of the various process and measurement uncertainties that affect glass compositions and predicted glass properties have been previously reported (Piepel et al. 2005, 2006) and the impacts of these estimated uncertainties on the IHLW composition envelope that meets product quality and processing-related properties with sufficient confidence were evaluated. The details of work performed to date to develop this initial GFC addition and batching algorithm are summarized in Sections 4 and 5. An example data set is used to illustrate the calculations of the algorithm summarized in Section 6. Finally, in Section 7, there is a statement of the required work to achieve a final operational IHLW formulation control algorithm. This report is not an engineering calculation, does not provide design input, and is not an engineering study.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗
DOE OSTI2016

A robust return-map algorithm for general multisurface plasticity

Three new contributions to the field of multisurface plasticity are presented for general situations with an arbitrary number of nonlinear yield surfaces with hardening or softening. A method for handling linearly dependent flow directions is described. A residual that can be used in a line search is defined. An algorithm that has been implemented and comprehensively tested is discussed in detail. Examples are presented to illustrate the computational cost of various components of the algorithm. The overall result is that a single Newton-Raphson iteration of the algorithm costs between 1.5 and 2 times that of an elastic calculation. Examples also illustrate the successful convergence of the algorithm in complicated situations. For example, without using the new contributions presented here, the algorithm fails to converge for approximately 50% of the trial stresses for a common geomechanical model of sedementary rocks, while the current algorithm results in complete success. Since it involves no approximations, the algorithm is used to quantify the accuracy of an efficient, pragmatic, but approximate, algorithm used for sedimentary-rock plasticity in a commercial software package. Furthermore, the main weakness of the algorithm is identified as the difficulty of correctly choosing the set of initially active constraints in the general setting.

15 GEOTHERMAL ENERGY↗
DOE OSTI2018

Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace

A computationally efficient integration algorithm for anisotropic plasticity is proposed, which is identified as a generalization of the radial-return mapping algorithm to anisotropy. The algorithm is based upon formulation within the eigenspace of a material anisotropy tensor associated with anisotropic quadratic von Mises (J 2 ) plasticity (also called Hill plasticity), for which it is shown to ensure that the flow rule remains associative, ie, the normality condition is satisfied. Extension of the algorithm to include anisotropic elasticity (anisotropic elastoplasticity) is further provided, made possible by the identification of a certain fourth-order material tensor dependent on both the elastic and plastic anisotropy. The derivation of the fully elastoplastically anisotropic algorithm involves further complexity, but the resulting algorithm is shown to closely resemble the purely plastically anisotropic one once the appropriate eigenspace is identified. The proposed generalized radial-return algorithm is compared to a classical closest-point projection algorithm, for which it is shown to provide considerable advantage in computational cost. In conclusion, the efficiency, accuracy, and robustness of the algorithm are demonstrated through various illustrative test cases and in the finite element simulation of Taylor impact tests on tantalum.

36 MATERIALS SCIENCE↗