Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “projected gradient method”

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.

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

At least 109 records · Page 6

Comparative Performance Analysis of Coarse Solvers for Algebraic Multigrid on Multicore and Manycore Architectures

In this paper, we study the performance of a two-level algebraic-multigrid algorithm, with a focus on the impact of the coarse-grid solver on performance. We consider two algorithms for solving the coarse-space systems: the preconditioned conjugate gradient method and a new robust HSS-embedded low-rank sparse-factorization algorithm. Our test data comes from the SPE Comparative Solution Project for oil-reservoir simulations. We contrast the performance of our code on one 12-core socket of a Cray XC30 machine with performance on a 60-core Intel Xeon Phi coprocessor. To obtain top performance, we optimized the code to take full advantage of fine-grained parallelism and made it thread-friendly for high thread count. We also developed a bounds-and-bottlenecks performance model of the solver which we used to guide us through the optimization effort, and also carried out performance tuning in the solver’s large parameter space. Finally, as a result, significant speedups were obtained on both machines.

97 MATHEMATICS AND COMPUTING↗

Conjugate gradient based projection - A new explicit methodology for frictional contact

With special attention towards the applicability to parallel computation or vectorization, a new and effective explicit approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focussed towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non-negative constraint condition; this direction is then applied to the Fletcher-Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction.

Tamma, Kumar K.↗

On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.

$\ell_0$-Constrained↗

Final Report for contract DE-SC0010151, "A Cost-Effective Oxygen Separation System Based on Open Gradient Magnetic Field by Polymer Beads"

At present much of the oxygen enrichment market is based primarily on cryogenic systems, ion transport membranes made of ceramics, or polymer membranes technologies. All these methods have some positive and some negative attributes, but remain too expensive for the cost effective production of pure oxygen needed for clean renewable energy conversion projects. In a very successful Phase I period, the ITN-TAMU team accomplished the completion of most of the sub-tasks on oxygen separation based on our proposed magnetic field gradients. Theoretical and computer simulation data under different conditions of flow rates, magnetic flux, magnetic beads packing density, pressure and temperature have resulted very valuable observations. Chitosan based polymer magnetic beads showed the best results for uniformity and column packing. Due to limited magnetic force of 1 Tesla, we were restricted to use only single small column of magnetic beads and limited air pressure with controlled flow rate. We also fabricated smaller sized beads column with metal and clear plastic frames to be used for more concentrated packed capacity. Beads made with rare earth Neodymium were not uniform and were quite brittle. Different surfactants have minimized the effect of the de-aggregation of polymer magnetic beads. This Phase I development work also included overcoming key packaging hurdles such as high packing capacity of magnetic polymer beads and formation of consistent batch of magnetic beads. Market and commercialization studies were also initiated to show that there is a growing market for the proposed cost-effective oxygen separation system for energy conversion projects.

20 FOSSIL-FUELED POWER PLANTS↗

Improved energies and local energies with weighted variational Monte Carlo

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Nachtsheim, Philip R.↗

Higher climatological temperature sensitivity of soil carbon in cold than warm climates

The projected loss of soil carbon to the atmosphere resulting from climate change is a potentially large but highly uncertain feedback to warming. The magnitude of this feedback is poorly constrained by observations and theory, and is disparately represented in Earth system models (ESMs). In this study, to assess the climatological temperature sensitivity of soil carbon, we calculate apparent soil carbon turnover times that reflect long-term and broad-scale rates of decomposition. We show that the climatological temperature control on carbon turnover in the top metre of global soils is more sensitive in cold climates than in warm climates and argue that it is critical to capture this emergent ecosystem property in global-scale models. We present a simplified model that explains the observed high cold-climate sensitivity using only the physical scaling of soil freeze-thaw state across climate gradients. Current ESMs fail to capture this pattern, except in an ESM that explicitly resolves vertical gradients in soil climate and carbon turnover. An observed weak tropical temperature sensitivity emerges in a different model that explicitly resolves mineralogical control on decomposition. Lastly, these results support projections of strong carbon-climate feedbacks from northern soils and demonstrate a method for ESMs to capture this emergent behaviour.

54 ENVIRONMENTAL SCIENCES↗

A More La Niña–Like Response to Radiative Forcing after Flux Adjustment in CESM2

Abstract In response to greenhouse gas forcing, most coupled global climate models project the tropical Pacific SST trend toward an “El Niño–like” state, with a reduced zonal SST gradient and a weakened Walker circulation. However, observations over the last five decades reveal a trend toward a more “La Niña–like” state with a strengthening zonal SST gradient. Recent research indicates that the identified trend differences are unlikely to be entirely due to internal variability and probably result, at least in part, from systematic model biases. In this study, Community Earth System Model, version 2 (CESM2), is used to explore how mean-state biases within the model may influence its forced response to radiative forcing in the tropical Pacific. The results show that using flux adjustment to reduce the mean-state bias in CESM2 over the tropical regions results in a more La Niña–like trend pattern in the tropical Pacific, with a strengthening of the tropical Pacific zonal SST gradient and a relatively enhanced Walker circulation, as hypothesized to occur if the ocean thermostat mechanism is stronger than the atmospheric mechanisms which by themselves would weaken the Walker circulation. We also find that the historical strengthening of the tropical Pacific zonal gradient is transient but persists into the near term in a high-emissions future warming scenario. These results suggest the potential of flux adjustment as a method for developing alternative projections that represent a wider range of possible future tropical Pacific warming scenarios, especially for a better understanding of regional patterns of climate risk in the near term.

Zhuo, Jing-Yi [Lamont-Doherty Earth Observatory, C↗

Towards a Third-Order Accurate, Second-Derivative-Free, Shock-Capturing Finite-Volume Method for Hypersonic Flows on Tetrahedral Grids

In this paper, we report progress in the development of a third-order accurate, second-derivative-free, shock-capturing finite-volume solver for three-dimensional unstructured grids. The method is economical in the sense that the computation and storage of second derivatives are not required for third-order accuracy. It is based on point-valued numerical solutions stored at cells, gradients computed and stored at nodes, and an efficient projected-derivative formula that eliminates the need for second derivatives in a quadratic solution interpolation. The projected-derivative formula is also used to eliminate second derivatives from a high-order flux quadrature formula, so that it can be implemented conveniently in the form of a numerical flux at a face center plus a correction term. Similarly, a high-order source quadrature formula can also be implemented in the form of a cell-center point evaluation plus a similar correction term. These features make it relatively straightforward to extend an existing second-order finite-volume code to third-order. This paper reports progress of implementing the method in the NASA VULCAN-CFD code and discusses the implementation of a high-order accurate limiter for shock capturing.

Weighted Least-Squares↗

Leveraging gradient weighted class activation mapping to improve classification effectiveness: Case study in transportation infrastructure characterization

Roadway “corners†are common for pedestrian use, whether designated with markings or not. Different types of markings have been deployed, ranging from simple parallel lines to more complex designs. Understanding the impact of different types of crosswalks is important for public safety. In this work we explore methods to improve the logging of marked crosswalk types. We used the Roadway Information Database from the Second Strategic Highway Research Project and used active learning methods with transfer learning to identify the crosswalk types (marked or unmarked). Upon completion we found our classifiers were unable to perform above roughly 94% correct classifications. To improve their efficacy, we separated the crosswalks into their “fine grained†types and used Gradient-Weighted Class Activation Mapping to isolate and study the features that classified the crosswalks. We compared this with sampled manually marked crosswalks and present findings. We believe this use case can represent a process to improve the active learning method for some visual machine learning applications.

Karnowski, Thomas↗

Large-Scale Optimization for Bayesian Inference in Complex Systems

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT₋Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas₋Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.

97 MATHEMATICS AND COMPUTING↗

Advanced Data Science Model for Detecting Intelligent Malware

This study focused on developing a robust artificial intelligence (AI) model capable of detecting and characterizing advanced malware in Internet of Things (IoT) devices using network data. By analyzing network traffic with various machine learning (ML) models, our AI model can identify and characterize malicious activities to significantly improve malware detection accuracy and reliability as compared to traditional methods. The developed AI/ML model was trained using network data from IoT devices, leveraging classifiers such as Random Forest, Gradient Boosting, AdaBoost, and others to optimize detection performance. This project demonstrates a scalable framework for real-time malware detection and characterization in IoT networks, capable of identifying infected devices and facilitating the necessary steps to remove or isolate them, thereby preventing further infections. Although digital twin (DT) integration is not yet implemented in the current model, it represents a promising future enhancement. By creating a virtual replica of physical IoT devices, DT technology would allow for real-time monitoring and analysis without directly accessing operational technology, thus reducing the risk of compromising or reducing the performance of actual devices. This integration would further enhance the security of IoT ecosystems, combining AI technology to better flag and detect indications of malware-infected devices within a nuclear system environment.

42 ENGINEERING↗

Summary Proceedings of a Wind Shear Workshop

A number of recent program results and current issues were addressed: the data collection phase of the highly successful Joint Airport Weather Study (JAWS) Project and the NASA-B5f7B Gust Gradient Program, the use of these data for flight crew training through educational programs (e.g., films) and with manned flight training simulators, methods for post-accident determination of wind conditions from flight data recorders, the microburst wind shear phenomenon which was positively measured and described the ring vortex as a possible generating mechanism, the optimum flight procedure for use during an unexpected wind shear encounter, evaluation of the low-level wind shear alert system (LLWSAS), and assessment of the demonstrated and viable application of Doppler radar as an operational wind shear warning and detection system.

Enders, J. H.↗

Moire deflectometry with deferred analysis

A simplified version of moire deflectometry for flow visualization is presented. The modification comprises replacement of the second grating, the ground glass screen, and the camera with a plate film holder to obtain a shadow picture. Postanalysis proceeds by placing a grid transparency of the same periodicity of the remaining glass grating on the negative for projection viewing. The rotational angle between the grating and the plate alters the moire fringe periodicity. Use of the method in studying flows is predicted to reveal weak density gradient areas and shocks.

Rhodes, D. B.↗

Refining a Novel Process Monitoring Method to Safeguard Continuously Cycling Designs Using Isotopic Ratios

In advanced reactor (AR) designs, a common feature is continuous chemical processing and circulation of the nuclear material. This work bridges a significant measurement gap in safeguarding reactors with circulating fuel or continuous refueling by leveraging and building on the isotope ratio method first developed by our team under an FY21 Advanced Reactors International Safeguards Engagement (ARISE) project (Uribe et al. 2021). In circulating fuel designs, the radioisotope inventory changes from traditional effects (e.g., radioactive decay, fission) but also includes material transport due to pressure and temperature gradients. Such designs may also require regular or continuous additions or removals during operation, which significantly increases the rate of inventory change compared to traditional pressurized water reactor (PWR)s. Thus, directly tracking the nuclear inventory is ineffective since the isotopes are continuously added and removed. The isotope ratio method instead focuses on detecting changes to the input and output flows of radioisotopes. Previous work showed that for well-chosen pairs of isotopes, the isotopic ratio provides a sensitive and lasting indicator of deviation from normal conditions (e.g., startup, shutdown, diversion). The isotope ratio method is a process monitoring method with potential for application in for forward-looking approaches to International Atomic Energy Agency (IAEA) safeguards. The original process monitoring method was developed for a specific case—the decay tank of a thorium-fueled molten salt breeder reactor. In this expanded work, we explored other types of reactors and processes with nonstationary (e.g., flowing) nuclear material, which are difficult to safeguard with traditional methods because of the transient nature of the systems. The goal of the present work is to generalize the isotope ratio method for use in processes with continuously flowing nuclear material. All continuous processes have an average time for isotopes to be replaced in the system. The isotope ratio method works by choosing radioisotopes with half-lives both above and below the processing time. The present work seeks to explore which isotopes are suitable for the method by simulating the nuclear inventory, radioisotope emissions, and detector responses for several classes of advanced reactors. While the method can in principle be applied to other processes (e.g., enrichment or reprocessing facilities), the present work limits scope to ARs with continuously flowing fuel. Section 2 details the mathematics supporting the isotope ratio method, and Section 3 introduces the representative ARs selected for this work. Section 4 discusses how each reactor was analyzed, and Section 5 showcases the results for each representative reactor. Finally, Section 6 provides concluding remarks and suggests pathways for further analysis.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Risk of Skin Cancer from Space Radiation

We review the methods for estimating the probability of increased incidence of skin cancers from space radiation exposure, and describe some of the individual factors that may contribute to risk projection models, including skin pigment, and synergistic effects of combined ionizing and UV exposure. The steep dose gradients from trapped electrons, protons, and heavy ions radiation during EVA and limitations in EVA dosimetry are important factors for projecting skin cancer risk of astronauts. We estimate that the probability of increased skin cancer risk varies more than 10-fold for individual astronauts and that the risk of skin cancer could exceed 1 % for future lunar base operations for astronauts with light skin color and hair. Limitations in physical dosimetry in estimating the distribution of dose at the skin suggest that new biodosimetry methods be developed for responding to accidental overexposure of the skin during future space missions.

Cucinotta, Francis A.↗

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗