SEARCH · Engineering Papers

Results for “Computers”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,171 records · Page 65

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Computational approaches to model X-ray photon correlation spectroscopy from molecular dynamics

X-ray photon correlation spectroscopy (XPCS) allows for the resolution of dynamic processes within a material across a wide range of length and time scales. X-ray speckle visibility spectroscopy (XSVS) is a related method that uses a single diffraction pattern to probe ultrafast dynamics. Interpretation of the XPCS and XSVS data in terms of underlying physical processes is necessary to establish the connection between the macroscopic responses and the microstructural dynamics. To aid the interpretation of the XPCS and XSVS data, we present a computational framework to model these experiments by computing the X-ray scattering intensity directly from the atomic positions obtained from molecular dynamics simulations. We compare the efficiency and accuracy of two alternative computational methods: the direct method computing the intensity at each diffraction vector separately, and a method based on fast Fourier transform that computes the intensities at all diffraction vectors at once. Furthermore, the computed X-ray speckle patterns capture the density fluctuations over a range of length and time scales and are shown to reproduce the known properties and relations of experimental XPCS and XSVS for liquids.

36 MATERIALS SCIENCE↗

DOE OSTI2018

A case study evaluating the portability of an executable computable phenotype algorithm across multiple institutions and electronic health record environments

Abstract Electronic health record (EHR) algorithms for defining patient cohorts are commonly shared as free-text descriptions that require human intervention both to interpret and implement. We developed the Phenotype Execution and Modeling Architecture (PhEMA, http://projectphema.org) to author and execute standardized computable phenotype algorithms. With PhEMA, we converted an algorithm for benign prostatic hyperplasia, developed for the electronic Medical Records and Genomics network (eMERGE), into a standards-based computable format. Eight sites (7 within eMERGE) received the computable algorithm, and 6 successfully executed it against local data warehouses and/or i2b2 instances. Blinded random chart review of cases selected by the computable algorithm shows PPV ≥90%, and 3 out of 5 sites had >90% overlap of selected cases when comparing the computable algorithm to their original eMERGE implementation. This case study demonstrates potential use of PhEMA computable representations to automate phenotyping across different EHR systems, but also highlights some ongoing challenges.

Pacheco, Jennifer A.↗

DOE OSTI2019

Quantum-classical hybrid algorithm using an error-mitigating N -representability condition to compute the Mott metal-insulator transition

Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence, connectivity, and gate errors required for their experimental realization. Here we propose a class of quantumclassical hybrid algorithms that computes the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $N$-representability conditions, constraints for representing an $N$-electron wave function, which mitigate noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H 3 into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of “chemical accuracy,” even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Group theoretical approach to computing phonons and their interactions

Phonons and their interactions are necessary for determining a wide range of materials properties. In this paper, we present four independent advances which facilitate the computation of phonons and their interactions from first principles. First, we implement a group-theoretical approach to construct the order $\mathcal {N}$ Taylor series of a d-dimensional crystal purely in terms of space group irreducible derivatives (ID), which guarantees symmetry by construction and allows for a practical means of communicating and storing phonons and their interactions. Second, we prove that the smallest possible supercell which accommodates $\mathcal {N}$ given wave vectors in a d-dimensional crystal is determined using the Smith normal form of the matrix formed from the corresponding wave vectors; resulting in negligible computational cost to find said supercell, in addition to providing the maximum required multiplicity for uniform supercells at arbitrary $\mathcal {N}$ and d. Third, we develop a series of finite displacement methodologies to compute phonons and their interactions which exploit the first two developments: lone and bundled irreducible derivative (LID and BID) approaches. LID computes a single ID, or as few as possible, at a time in the smallest supercell possible, while BID exploits perturbative derivatives for some order less than $\mathcal {N}$ (e.g., Hellman-Feynman forces) in order to extract all ID in the smallest possible supercells using the fewest possible computations. Finally, we derive an equation for the order N volume derivatives of the phonons in terms of the order $\mathcal {N}$ = N + 2 ID. Given that the former are easily computed, they can be used as a stringent, infinite ranged test of the ID. Our general framework is illustrated on graphene, yielding irreducible phonon interactions to fifth order. Additionally, we provide a cost analysis for the rocksalt structure at $\mathcal {N}$ = 3, demonstrating a massive speedup compared to popular finite displacement methods in the literature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Accurate optimization of amino acid form factors for computing small-angle X-ray scattering intensity of atomistic protein structures

Structure modelling via small-angle X-ray scattering (SAXS) data generally requires intensive computations of scattering intensity from any given biomolecular structure, where the accurate evaluation of SAXS profiles using coarse-grained (CG) methods is vital to improve computational efficiency. To date, most CG SAXS computing methods have been based on a single-bead-per-residue approximation but have neglected structural correlations between amino acids. To improve the accuracy of scattering calculations, accurate CG form factors of amino acids are now derived using a rigorous optimization strategy, termed electron-density matching (EDM), to best fit electron-density distributions of protein structures. This EDM method is compared with and tested against other CG SAXS computing methods, and the resulting CG SAXS profiles from EDM agree better with all-atom theoretical SAXS data. By including the protein hydration shell represented by explicit CG water molecules and the correction of protein excluded volume, the developed CG form factors also reproduce the selected experimental SAXS profiles with very small deviations. Taken together, these EDM-derived CG form factors present an accurate and efficient computational approach for SAXS computing, especially when higher molecular details (represented by the q range of the SAXS data) become necessary for effective structure modelling.

Tong, Dudu↗

DOE OSTI2019

Biomimetic, Soft-Material Synapse for Neuromorphic Computing: from Device to Network

Neuromorphic computing refers to a variety of brain-inspired computers, devices, and models inspired by the interconnectivity, performance, and energy efficiency of the human brain. Unlike the ubiquitous von Neumann computer architectures with complex processor cores and sequential computation, biological neurons and synapses operate by storing and processing information simultaneously with the capacity of flexible adaptation resulting in massive computational capability with much less power consumption. The search for a synaptic material which can closely imitate bio-synapse has led to an alamethicin-doped, synthetic biomembrane which can emulate key synaptic functions due to generic memristive property enabling learning and computation. This two-terminal, biomolecular memristor, in contrast to its solid-state counterparts, features similar structure, switching mechanism, and ionic transport modality as biological synapses while consuming considerably lower power. In this paper, we outline a methodology for using this biomolecular synapse to build neural networks capable of solving real-world problems. The physical mechanism underlying its volatile memristance is explored followed by the development of a model of this device for circuit simulation. We outline a circuit design technique to integrate this synapse with solid-state neuron circuit for hardware implementation. Based on these results, we develop a high level simulation framework and use a training scheme called Evolutionary Optimization for Neuromorphic System (EONS) to generate networks for solving two problems, namely iris dataset classification and EEG classification task. The small network size and comparable to state-of-the-art accuracy of these preliminary networks show its potential to enhance synaptic functionality in next generation neuromorphic hardware.

Sakib hasan, Md↗

DOE OSTI2018

A High Performance Computational Framework for Dynamic Security Assessment under Uncertainty

Dynamic security assessment (DSA) is a critical function to evaluate power grids’ capability to survive the transition caused by a set of disturbances to an acceptable steady-state condition. Its computational burden is heavy. With the challenges brought by renewable energy and new smart grid technologies, DSA under uncertainty has to be considered to study the impact of forecast errors on DSA simulation, which further increases the computational burden. To address this challenge, this paper presents a high performance computational framework to support DSA simulation user uncertainty. The computational framework aims to provide a seamless workflow that links data from high performance computing, statistical analysis, to visualization so that a problem can be easily expressed in a way compatible with different functions. It also enables software compatibility such that application development can be more efficient. Case study results of the ESCA60 system and a western U.S. size system show the advantages and efficiency of the computational framework.

dynamic security assessment, high performance comp↗

DOE OSTI2023

Towards Redefining the Reproducibility in Quantum Computing: A Data Analysis Approach on NISQ Devices

Although the building of quantum computers has kept making rapid progress in recent years, noise is still the main challenge for any application to leverage the power of quantum computing. Existing works addressing noise in quantum devices proposed noise reduction when deploying a quantum algorithm to a specified quantum computer. The reproducibility issue of quantum algorithms has been raised since the noise levels vary on different quantum computers. Importantly, existing works largely ignore the fact that the noise of quantum devices varies as time goes by. Therefore, reproducing the results on the same hardware will even become a problem. We analyze the reproducibility of quantum machine learning (QML) algorithms based on daily model training and execution data collection. Our analysis shows a correlation between our QML models’ test accuracy and quantum computer hardware’s calibration features. We also demonstrate that noisy simulators for quantum computers are not a reliable tool for quantum machine learning applications.

Senapati, Priyabrata↗

DOE OSTI2016

Select Advances in Computational Accelerator Physics

Computational accelerator physics has changed and broadened over the last decade or so. Part of the change is due to the advent of multiple ways of parallel computing. Another part comes from algorithmic developments. The multiple ways of parallel computing include distributed memory parallelism and on-chip parallelism, with the latter coming from architectures (CPU and GPU) having multiple processing elements (cores or streaming multiprocessors) and wide vector (SIMD) instruction units. The basics of these new architectures and their application to computational accelerator physics are briefly reviewed. Algorithmic advances in the select areas of spin tracking, cavity calculations, plasma acceleration, and electron cooling are also reviewed. In some cases the algorithms provide increased fidelity improving the overall accuracy, while in other cases, such as controlled dispersion, the algorithms provide increased fidelity by better modeling the essential physical interaction. Finally, the use of computational frameworks, which provide the basic computational infrastructure, while allowing the capability developer to concentrate on the math and physics, is reviewed in the context of the Vorpal application, which has found use across accelerator physics and many other fields.

Engineering↗

DOE OSTI2024

Enhancing risk and crisis communication with computational methods: A systematic literature review

Abstract Recent developments in risk and crisis communication (RCC) research combine social science theory and data science tools to construct effective risk messages efficiently. However, current systematic literature reviews (SLRs) on RCC primarily focus on computationally assessing message efficacy as opposed to message efficiency. We conduct an SLR to highlight any current computational methods that improve message construction efficacy and efficiency. We found that most RCC research focuses on using theoretical frameworks and computational methods to analyze or classify message elements that improve efficacy. For improving message efficiency, computational and manual methods are only used in message classification. Specifying the computational methods used in message construction is sparse. We recommend that future RCC research apply computational methods toward improving efficacy and efficiency in message construction. By improving message construction efficacy and efficiency, RCC messaging would quickly warn and better inform affected communities impacted by current hazards. Such messaging has the potential to save as many lives as possible.

Mathematical Methods In Social Sciences↗

DOE OSTI2025

Comparison of a Full-Scale and a 1:10 Scale Low-Speed Two-Stroke Marine Engine Using Computational Fluid Dynamics

International marine shipping is a growing component of international trade; a vast majority of all the world’s goods are being transported on large ocean-going vessels. The International Maritime Organization (IMO) introduced the Energy Efficiency Design Index in 2013, a regulatory framework of associated metrics for reducing emissions of CO 2 per tonne-mile from shipping by approximately 10% each decade. Therefore, decarbonizing the maritime sector requires the development of new fuel sources. Because of the extremely large physical size of the internal combustion engines present in shipping vessels, experimental iterative development of the engine and fuel system is cost-prohibitive. Thus, the ability to perform combustion system development in a scaled platform that can be more easily operated and modeled computationally is of interest. To that end, scaling relationships are needed to translate the results from a smaller engine to a larger counterpart. Scaling studies to date have been restricted to low scaling ratios, four-stroke light-duty engines, and under-resolved computational fluid dynamic simulations that likely do not accurately capture the physics of scaling. In this work, computational models of a 1:10 scale and a full-scale two-stroke crosshead low-speed marine engine were created and validated against experiments obtained in a real 1:10 scale engine installed at Oak Ridge National Laboratory. Further, due to the large size of the full-scale engine, the model required large high-performance computing resources to be evaluated. The availability of high-performance computing resources at the Department of Energy’s Leadership Computing Facilities is an enabler of the current work. The results of the small- and large-scale engine simulations were compared to analyze the effectiveness of the appropriate scaling laws under these extreme scaling ratio conditions.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Assessing the stability of noisy quantum computation

Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum computation face technical challenges due to the noise and errors that arise from imperfect implementation of the technology. Here, we frame the concepts of computational accuracy, result reproducibility, device reliability and program stability in the context of quantum computation. We provide intuitive definitions for these concepts in the context of quantum computation that lead to operationally meaningful bounds on program output. Our assessment highlights the continuing need for statistical analyses of quantum computing program to increase our confidence in the burgeoning field of quantum information science.

Dasgupta, Samudra↗

DOE OSTI2014

Experimental validation of a kilovoltage x-ray source model for computing imaging dose

Purpose: To introduce and validate a kilovoltage (kV) x-ray source model and characterization method to compute absorbed dose accrued from kV x-rays. Methods: The authors propose a simplified virtual point source model and characterization method for a kV x-ray source. The source is modeled by: (1) characterizing the spatial spectral and fluence distributions of the photons at a plane at the isocenter, and (2) creating a virtual point source from which photons are generated to yield the derived spatial spectral and fluence distribution at isocenter of an imaging system. The spatial photon distribution is determined by in-air relative dose measurements along the transverse (x) and radial (y) directions. The spectrum is characterized using transverse axis half-value layer measurements and the nominal peak potential (kVp). This source modeling approach is used to characterize a Varian{sup ®} on-board-imager (OBI{sup ®}) for four default cone-beam CT beam qualities: beams using a half bowtie filter (HBT) with 110 and 125 kVp, and a full bowtie filter (FBT) with 100 and 125 kVp. The source model and characterization method was validated by comparing dose computed by the authors’ inhouse software (kVDoseCalc) to relative dose measurements in a homogeneous and a heterogeneous block phantom comprised of tissue, bone, and lung-equivalent materials. Results: The characterized beam qualities and spatial photon distributions are comparable to reported values in the literature. Agreement between computed and measured percent depth-dose curves is ⩽2% in the homogeneous block phantom and ⩽2.5% in the heterogeneous block phantom. Transverse axis profiles taken at depths of 2 and 6 cm in the homogeneous block phantom show an agreement within 4%. All transverse axis dose profiles in water, in bone, and lung-equivalent materials for beams using a HBT, have an agreement within 5%. Measured profiles of FBT beams in bone and lung-equivalent materials were higher than their computed counterparts resulting in an agreement within 2.5%, 5%, and 8% within solid water, bone, and lung, respectively. Conclusions: The proposed virtual point source model and characterization method can be used to compute absorbed dose in both the homogeneous and heterogeneous block phantoms within of 2%–8% of measured values, depending on the phantom and the beam quality. The authors’ results also provide experimental validation for their kV dose computation software, kVDoseCalc.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2015

Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer. Conclusions: The simulation results showed that the deterministic method can be effectively used to estimate the absorbed dose in a CTDI phantom. The accuracy of the discrete ordinates method was close to that of a Monte Carlo simulation, and the primary benefit of the discrete ordinates method lies in its rapid computation speed. It is expected that further optimization of this method in routine clinical CT dose estimation will improve its accuracy and speed.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2015

WE-AB-303-09: Rapid Projection Computations for On-Board Digital Tomosynthesis in Radiation Therapy

Purpose: To facilitate fast and accurate iterative volumetric image reconstruction from limited-angle on-board projections. Methods: Intrafraction motion hinders the clinical applicability of modern radiotherapy techniques, such as lung stereotactic body radiation therapy (SBRT). The LIVE system may impact clinical practice by recovering volumetric information via Digital Tomosynthesis (DTS), thus entailing low time and radiation dose for image acquisition during treatment. The DTS is estimated as a deformation of prior CT via iterative registration with on-board images; this shifts the challenge to the computational domain, owing largely to repeated projection computations across iterations. We address this issue by composing efficient digital projection operators from their constituent parts. This allows us to separate the static (projection geometry) and dynamic (volume/image data) parts of projection operations by means of pre-computations, enabling fast on-board processing, while also relaxing constraints on underlying numerical models (e.g. regridding interpolation kernels). Further decoupling the projectors into simpler ones ensures the incurred memory overhead remains low, within the capacity of a single GPU. These operators depend only on the treatment plan and may be reused across iterations and patients. The dynamic processing load is kept to a minimum and maps well to the GPU computational model. Results: We have integrated efficient, pre-computable modules for volumetric ray-casting and FDK-based back-projection with the LIVE processing pipeline. Our results show a 60x acceleration of the DTS computations, compared to the previous version, using a single GPU; presently, reconstruction is attained within a couple of minutes. The present implementation allows for significant flexibility in terms of the numerical and operational projection model; we are investigating the benefit of further optimizations and accurate digital projection sub-kernels. Conclusion: Composable projection operators constitute a versatile research tool which can greatly accelerate iterative registration algorithms and may be conducive to the clinical applicability of LIVE. National Institutes of Health Grant No. R01-CA184173; GPU donation by NVIDIA Corporation.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-D-206-02: Evaluation of Partial Storage of the System Matrix for Cone Beam Computed Tomography Using a GPU Platform

Purpose: Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersections between the photons’ trajectories and the object, also called ray-tracing or system matrix computation. This work evaluates different ways to store the system matrix, aiming to reconstruct dense image grids in reasonable time. Methods: We propose an optimized implementation of the Siddon’s algorithm using graphics processing units (GPUs) with a novel data storage scheme. The algorithm computes a part of the system matrix on demand, typically, for one projection angle. The proposed method was enhanced with accelerating options: storage of larger subsets of the system matrix, systematic reuse of data via geometric symmetries, an arithmetic-rich parallel code and code configuration via machine learning. It was tested on geometries mimicking a cone beam CT acquisition of a human head. To realistically assess the execution time, the ray-tracing routines were integrated into a regularized Poisson-based reconstruction algorithm. The proposed scheme was also compared to a different approach, where the system matrix is fully pre-computed and loaded at reconstruction time. Results: Fast ray-tracing of realistic acquisition geometries, which often lack spatial symmetry properties, was enabled via the proposed method. Ray-tracing interleaved with projection and backprojection operations required significant additional time. In most cases, ray-tracing was shown to use about 66 % of the total reconstruction time. In absolute terms, tracing times varied from 3.6 s to 7.5 min, depending on the problem size. The presence of geometrical symmetries allowed for non-negligible ray-tracing and reconstruction time reduction. Arithmetic-rich parallel code and machine learning permitted a modest reconstruction time reduction, in the order of 1 %. Conclusion: Partial system matrix storage permitted the reconstruction of higher 3D image grid sizes and larger projection datasets at the cost of additional time, when compared to the fully pre-computed approach. This work was supported in part by the Fonds de recherche du Quebec - Nature et technologies (FRQ-NT). The authors acknowledge partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council of Canada (Grant No. 432290).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

WE-DE-202-00: Connecting Radiation Physics with Computational Biology

Radiation therapy for the treatment of cancer has been established as a highly precise and effective way to eradicate a localized region of diseased tissue. To achieve further significant gains in the therapeutic ratio, we need to move towards biologically optimized treatment planning. To achieve this goal, we need to understand how the radiation-type dependent patterns of induced energy depositions within the cell (physics) connect via molecular, cellular and tissue reactions to treatment outcome such as tumor control and undesirable effects on normal tissue. Several computational biology approaches have been developed connecting physics to biology. Monte Carlo simulations are the most accurate method to calculate physical dose distributions at the nanometer scale, however simulations at the DNA scale are slow and repair processes are generally not simulated. Alternative models that rely on the random formation of individual DNA lesions within one or two turns of the DNA have been shown to reproduce the clusters of DNA lesions, including single strand breaks (SSBs), double strand breaks (DSBs) without the need for detailed track structure simulations. Efficient computational simulations of initial DNA damage induction facilitate computational modeling of DNA repair and other molecular and cellular processes. Mechanistic, multiscale models provide a useful conceptual framework to test biological hypotheses and help connect fundamental information about track structure and dosimetry at the sub-cellular level to dose-response effects on larger scales. In this symposium we will learn about the current state of the art of computational approaches estimating radiation damage at the cellular and sub-cellular scale. How can understanding the physics interactions at the DNA level be used to predict biological outcome? We will discuss if and how such calculations are relevant to advance our understanding of radiation damage and its repair, or, if the underlying biological processes are too complex for a mechanistic approach. Can computer simulations be used to guide future biological research? We will debate the feasibility of explaining biology from a physicists’ perspective. Learning Objectives: Understand the potential applications and limitations of computational methods for dose-response modeling at the molecular, cellular and tissue levels Learn about mechanism of action underlying the induction, repair and biological processing of damage to DNA and other constituents Understand how effects and processes at one biological scale impact on biological processes and outcomes on other scales J. Schuemann, NCI/NIH grantsS. McMahon, Funding: European Commission FP7 (grant EC FP7 MC-IOF-623630)

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Edge Pushing is Equivalent to Vertex Elimination for Computing Hessians

We prove the equivalence of two different Hessian evaluation algorithms in AD. The first is the Edge Pushing algorithm of Gower and Mello, which may be viewed as a second order Reverse mode algorithm for computing the Hessian. In earlier work, we have derived the Edge Pushing algorithm by exploiting a Reverse mode invariant based on the concept of live variables in compiler theory. The second algorithm is based on eliminating vertices in a computational graph of the gradient, in which intermediate variables are successively eliminated from the graph, and the weights of the edges are updated suitably. We prove that if the vertices are eliminated in a reverse topological order while preserving symmetry in the computational graph of the gradient, then the Vertex Elimination algorithm and the Edge Pushing algorithm perform identical computations. In this sense, the two algorithms are equivalent. This insight that unifies two seemingly disparate approaches to Hessian computations could lead to improved algorithms and implementations for computing Hessians. Read More: http://epubs.siam.org/doi/10.1137/1.9781611974690.ch11

Wang, Mu↗