Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “algebraic methods”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Electromagnetic Transient (EMT) Simulation Algorithms for Evaluation of Large-Scale Extreme Fast Charging Systems (T&D Models)

Simulation of high-fidelity models of extreme fast charging (XFC) systems and large-area power grids with many XFCs can be time consuming in traditional simulators. Traditional simulators use a single method of discretization for all the components that results in imposing a large computational burden of inverting a large matrix as well as increased computations related to single method of discretization (that is typically a trapezoidal method). To overcome the problem of simulating large-area power grids with many XFCs, in this paper, advanced numerical simulation algorithms are applied for the first time together to reduce the dimension of matrix inversion. Here, the algorithms include numerical stiffness-based segregation, time constant-based segregation, clustering and aggregation on differential algebraic equations (DAEs), and multi-order integration approaches. These algorithms apply multiple discretization algorithms rather than a single discretization algorithm that further reduces the computational burden. The approaches mentioned here have resulted in speed-up of up to 18x in the simulation of a single distribution system with 15 XFCs and of up to 271x in the simulation of a transmission-distribution system with 300 XFCs in multiple distribution feeders with respect to conventional simulators (like power systems computer aided design [PSCAD]).

42 ENGINEERING↗
DOE OSTI2023

RadSim: Math, Utility & RTK

This package includes three parts, (1) gov.llnl.math, (2)gov.llnl.utility and (3)gov.llnl.rtk, which are utilized in the development of Radiation Detector Simulator (RadSim) project. RadSim is being developed to provide the capability to: (1) simulate radiation source emissions, (2) interpolate results from radiation transport tools into a common format to prepare incident flux, and (3) model radiation detector response to rapidly produce synthetic radiation measurement templates. RadSim is targeted for open-source release, which will enable researchers and industry partners to model gamma-ray detectors response to simulated flux from the transport tool of their choice. The techniques and implementation will be entirely transparent, which will allow for improvements and boutique modifications by future researchers beyond the lifespan of this specific project. The first tool of the package, gov.llnl.math, includes classes and functions to define and perform basic math operations. Some of the example features available in the package include defining statistical distributions and performing algebra and matrix operations, all of which are already accessible on publicly available software packages such as MATLAB and ROOT. The second package gov.llnl.utility includes tools commonly used to enable optimization and readability of various data structures such as Java lists and external xml files. Lastly, the gov.llnl.rtk package includes classes and functions to implement methods commonly used in radiation physics, such as data structures to represent and characterize photon spectra and tools to apply well-defined and published methods to calibrate a given spectra.

Cheung, Hoi Sing↗
DOE OSTI2022

MAPPRAISER: A massively parallel map-making framework for multi-kilo pixel CMB experiments

Forthcoming cosmic microwave background (CMB) polarized anisotropy experiments have the potential to revolutionize our understanding of the Universe and fundamental physics. The sought-after, tale-telling signatures will be however distributed over voluminous data sets which these experiments will collect. These data sets will need to be efficiently processed and unwanted contributions due to astrophysical, environmental, and instrumental effects characterized and efficiently mitigated in order to uncover the signatures. This poses a significant challenge to data analysis methods, techniques, and software tools which will not only have to be able to cope with huge volumes of data but to do so with unprecedented precision driven by the demanding science goals posed for the new experiments. A keystone of efficient CMB data analysis is solvers of very large linear systems of equations. Such systems appear in very diverse contexts throughout CMB data analysis pipelines, however they typically display similar algebraic structures and can therefore be solved using similar numerical techniques. Linear systems arising in the so-called map-making problem are one of the most prominent and common ones. In this work we present a massively parallel, flexible and extensible framework, comprised of a numerical library, MIDAPACK, and a high level code, MAPPRAISER, which provide tools for solving efficiently such systems. Here, the framework implements iterative solvers based on conjugate gradient techniques: enlarged and preconditioned using different preconditioners. We demonstrate the framework on simulated examples reflecting basic characteristics of the forthcoming data sets issued by ground-based and satellite-borne instruments, executing it on as many as 16,384 compute cores. The software is developed as an open source project freely available to the community at: https://github.com/B3Dcmb/midapack.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Chiral spin liquid and quantum phase transition in the triangular-lattice Hofstadter-Hubbard model

Recent advances in moiré engineering motivate the study of lattice models of strongly correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular-lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120° antiferromagnetic phases. Here, we use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.

Divic, Stefan [University of Pennsylvania, Philade↗
DOE OSTI2020

Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

Summary We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear‐quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.

Barker, Andrew T.↗
DOE OSTI2020

A phase transition model and temporal logic specifications for smart energy systems - revisited

In this paper, we revisit the method of a phase transition model for representing hybrid systems and temporal logic specifications (TLSs) for specifying desired behaviors of systems, and discuss their usefulness for smart energy systems. On the one hand, the phase transition model incorporates the continuous model of the relay device action with a particular structural form that allows for the construction of a single, global differential-algebraic equation for hybrid systems (thus smoothed hybrid systems). On the other hand, the TLS allows sophisticated descriptions of control specifications addressing both magnitude and time simultaneously, which has recently been applied to the control strategy of several types of continuous and hybrid systems. We provide high-level descriptions of each of the two techniques and present simulation results in the context of smart energy systems.

Park, Byungkwon↗
DOE OSTI2025

Universal time scalings of sensitivity in Markovian quantum metrology

Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings. We find that via simple algebraic conditions (in terms of the Hamiltonian, the jump operators as well as their parameter derivatives), one can characterize the four classes of metrological models that represent: quadratic-linear, quadratic-quadratic, linear-linear, and linear-quadratic time scalings. We also investigate the relevant time scales on which the transition between the two regimes appears. Additionally, we provide universal numerical methods to obtain quantitative bounds on sensitivity that are the tightest that exist in the literature. Simplicity and universality of our results make it suitable for diverse applications in quantum metrology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Surface Analysis Insight Note: Observations relating to photoemission peak shapes, oxidation state, and chemistry of titanium oxide films

It is common practice to describe the coordination of metal atoms in a binding configuration with their nearest neighbors in terms of oxidation state, a measure by which the number of electrons redistributed between atoms forming chemical bonds. In XPS terms, change to an oxidation state is commonly inferred by correlating photoemission signal with binding energy. The assumption, when classifying photoemission signals into distinct spectral shapes, is that a distribution of intensities shifted to lower binding energy is evidence of a reduction in oxidation state. In this Insight note, we raise the prospect that changes in photoemission peak shape may occur without obvious changes, determined by XPS in stoichiometry for a material. It is well known that TiO 2 measured by XPS yields reproducible Ti 2p photoemission peaks. However, on exposing TiO 2 to ion beams, Ti 2p photoemission evolves to complex distributions in intensity, which are particularly difficult to analyze by traditional fitting of bell-shaped curves to these data. For these reasons, in this Insight note, a thin film of TiO 2 deposited on a silicon substrate is chosen for analysis by XPS and linear algebraic techniques. Alterations in spectral shapes created from modified TiO 2 , which might be interpreted as the change in oxidation state, are assessed in terms of relative proportions of titanium to oxygen. It is found through detailed analysis of spectra that quantification by XPS, using procedures routinely used in practice, is not in accord with the typical interpretations of photoemission shapes. The data processing methods used and results presented in this work are of particular relevance to elucidating fundamental phenomena governing the surface evolution of materials-enabled energy processes where cyclic/non-steady usage changes the nature of bonding, especially in the presence of contaminants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗
DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗
DOE OSTI2022

Dynamics retrieval from stochastically weighted incomplete data by low-pass spectral analysis

Time-resolved serial femtosecond crystallography (TR-SFX) provides access to protein dynamics on sub-picosecond timescales, and with atomic resolution. Due to the nature of the experiment, these datasets are often highly incomplete and the measured diffracted intensities are affected by partiality. To tackle these issues, one established procedure is that of splitting the data into time bins, and averaging the multiple measurements of equivalent reflections within each bin. This binning and averaging often involve a loss of information. Here, we propose an alternative approach, which we call low-pass spectral analysis (LPSA). In this method, the data are projected onto the subspace defined by a set of trigonometric functions, with frequencies up to a certain cutoff. This approach attenuates undesirable high-frequency features and facilitates retrieving the underlying dynamics. A time-lagged embedding step can be included prior to subspace projection to improve the stability of the results with respect to the parameters involved. Subsequent modal decomposition allows to produce a low-rank description of the system's evolution. Using a synthetic time-evolving model with incomplete and partial observations, we analyze the LPSA results in terms of quality of the retrieved signal, as a function of the parameters involved. We compare the performance of LPSA to that of a range of other sophisticated data analysis techniques. We show that LPSA allows to achieve excellent dynamics reconstruction at modest computational cost. Finally, we demonstrate the superiority of dynamics retrieval by LPSA compared to time binning and merging, which is, to date, the most commonly used method to extract dynamical information from TR-SFX data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Orders of vanishing and U(1) charges in F-theory

Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Holographic entanglement from the UV to the IR

In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Segregated Approach for Modeling the Electrochemistry in the 3-D Microstructure of Li-Ion Batteries and Its Acceleration Using Block Preconditioners

Abstract Battery performance is strongly correlated with electrode microstructure. Electrode materials for lithium-ion batteries have complex microstructure geometries that require millions of degrees of freedom to solve the electrochemical system at the microstructure scale. A fast-iterative solver with an appropriate preconditioner is then required to simulate large representative volume in a reasonable time. In this work, a finite element electrochemical model is developed to resolve the concentration and potential within the electrode active materials and the electrolyte domains at the microstructure scale, with an emphasis on numerical stability and scaling performances. The block Gauss-Seidel (BGS) numerical method is implemented because the system of equations within the electrodes is coupled only through the nonlinear Butler–Volmer equation, which governs the electrochemical reaction at the interface between the domains. The best solution strategy found in this work consists of splitting the system into two blocks—one for the concentration and one for the potential field—and then performing block generalized minimal residual preconditioned with algebraic multigrid, using the FEniCS and the Portable, Extensible Toolkit for Scientific Computation libraries. Significant improvements in terms of time to solution (six times faster) and memory usage (halving) are achieved compared with the MUltifrontal Massively Parallel sparse direct Solver. Additionally, BGS experiences decent strong parallel scaling within the electrode domains. Last, the system of equations is modified to specifically address numerical instability induced by electrolyte depletion, which is particularly valuable for simulating fast-charge scenarios relevant for automotive application.

25 ENERGY STORAGE↗
DOE OSTI2021

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Machine-Learning Assisted Identification of Battery Life Models

Predictive battery life models are commonly utilized to extrapolate degradation trends observed during accelerated aging tests for simulation of degradation in real-world applications. Thus, fitting accelerated aging data as accurately as possible and with low uncertainty is crucial for making believable projections of battery lifetime, but it is challenging to identify algebraic expressions that accurately fit multivariate degradation trends. A review of models published in literature reveal some common expressions for fitting calendar aging data, which is only dependent on temperature and state-of-charge, but no consistency across many models for fitting cycle aging data, indicating the need for a statistically rigorous data driven approach for developing empirical models. This talk will describe a machine-learning assisted method for identification of predictive battery life models utilizing bilevel optimization and symbolic regression. Bilevel optimization with cross-validation is used to statistically determine cell- and stress-dependent model parameters, while symbolic regression identifies both linear and multiplicative candidate expressions to predict stress-dependent degradation rates by selecting low-order subsets of features from a generated feature library. Because model expressions are identified empirically, it is crucial to ensure resulting models behave according to physical expectations, so the stability of models for interpolation or extrapolation is interrogated qualitatively through simulation and quantitatively through cross-validation and uncertainty quantification via bootstrap resampling. This model identification approach substantially improves upon models identified purely using expert judgement in terms of both accuracy and uncertainty. Model simulation and validation is then conducted by deriving a state-equation form of the predictive model, enabling simulation of battery aging under dynamic stresses. This enables validation of the predictive battery model on lab-based tests with varying conditions or on drive-cycle or application-cycle testing protocols. Parameter uncertainty can be carried forward into model simulation, giving lifetime estimates and confidence windows for cell- or system-level lifetime. The financial impact of battery model uncertainty can be estimated by incorporating uncertainty into a technoeconomic model.

battery↗