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Results for “variational 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.

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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Investigation of mounting discrete chip components for hybrid microelectronic applications.

In the assembly of hybrid microcircuits, passive and active discrete chip components are attached by epoxy cements and by solders. This study was initiated to determine the integrity of such attachments. Alumina substrates were subjected to a group of thermal and mechanical test environments defined by test methods in MIL-STD-883. Lot samples of substrates with assembly variations were subjected to separately applied testing and to serial testing. These test methods were applied sequentially to the same lot of substrates. Epoxy cements were generally satisfactory with respect to separate tests, although sequential tests severely degraded epoxy bond strengths of all types. Bond strengths to unglazed substrates were slightly superior to those of the same components on glazed types. Solder joints were vulnerable to catastrophic failure in several environments, especially temperature cycling and thermal shock. Vibration and impact shock also produced solder joint failures.

Caruso, S. V.↗
NASA NTRS1993

Development of computational methods for heavy lift launch vehicles

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Yoon, Seokkwan↗
NASA NTRS1994

Development of advanced Navier-Stokes solver

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Yoon, Seokkwan↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A phase-field model for hydraulic fracture nucleation and propagation in porous media

Many geo-engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase-field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy-based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase-field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase-field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. In conclusion, the comparison of numerical results for two-dimensional test cases with existing analytical solutions demonstrates that the proposed phase-field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three-dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Gradient-Based Novelty Detection Boosted by Self-Supervised Binary Classification

Novelty detection aims to automatically identify out-of-distribution (OOD) data, without any prior knowledge of them. It is a critical step in data monitoring, behavior analysis and other applications, helping enable continual learning in the field. Conventional methods of OOD detection perform multi-variate analysis on an ensemble of data or features, and usually resort to the supervision with OOD data to improve the accuracy. In reality, such supervision is impractical as one cannot anticipate the anomalous data. In this paper, we propose a novel, self-supervised approach that does not rely on any pre-defined OOD data: (1) The new method evaluates the Mahalanobis distance of the gradients between the in-distribution and OOD data. (2) It is assisted by a self-supervised binary classifier to guide the label selection to generate the gradients, and maximize the Mahalanobis distance. In the evaluation with multiple datasets, such as CIFAR-10, CIFAR-100, SVHN and TinyImageNet, the proposed approach consistently outperforms state-of-the-art supervised and unsupervised methods in the area under the receiver operating characteristic (AUROC) and area under the precision-recall curve (AUPR) metrics. We further demonstrate that this detector is able to accurately learn one OOD class in continual learning.

Sun, Jingbo↗
DOE OSTI2024

Reweighting Monte Carlo predictions and automated fragmentation variations in Pythia 8

This work reports on a method for uncertainty estimation in simulated collider-event predictions. The method is based on a Monte Carlo-veto algorithm, and extends previous work on uncertainty estimates in parton showers by including uncertainty estimates for the Lund string-fragmentation model. This method is advantageous from the perspective of simulation costs: a single ensemble of generated events can be reinterpreted as though it was obtained using a different set of input parameters, where each event now is accompanied with a corresponding weight. This allows for a robust exploration of the uncertainties arising from the choice of input model parameters, without the need to rerun full simulation pipelines for each input parameter choice. Such explorations are important when determining the sensitivities of precision physics measurements. Accompanying code is available at https://gitlab.com/uchep/mlhad-weights-validation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1974

Useful extremum principle for the variational calculation of matrix elements

Variational principles are considered for the approximate evaluation of the diagonal matrix elements of an arbitrary known linear Hermitian operator. A method is derived that is immediately applicable to the variational determination of both the off-diagonal and diagonal matrix elements of normal and modified Green's functions.

Gerjuoy, E.↗
NASA NTRS1987

Variational approach to probabilistic finite elements

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗
NASA NTRS1991

Variational approach to probabilistic finite elements

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗
DOE OSTI2024

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

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

Chemical and Structural Alterations in the Amorphous Structure of Obsidian due to Nanolites

Obsidian is volcanic glass that results from the rapid cooling of silica-rich melt. Nanoscale crystallites precipitate out of the melt prior to solidification and remain embedded in the amorphous matrix. These crystallites provide information on the flow kinetics and composition of the melt. Due to the sparsity and size of nanolites, studies often focus on supramicron crystallites. This research takes advantage of the conchoidal fracture of obsidian by knapping samples with nanometer-thin edges for transmission electron microscopy characterization. Nanolites in the amorphous matrix are studied using energy-dispersive spectroscopy (EDS) and electron diffraction. Certain alkali and alkaline-earth cations exhibit patterns of depletion near Fe-oxide nanolites. EDS is used to identify nanolites and variations in the composition of the matrix. Parallel beam diffraction and radial distribution function analysis of nearest-neighbor distances determine average bond lengths in the matrix near nanolites, showing that nanolites influence the nearby short-range ordering and atomic character of the matrix. Analysis reveals decreased mean nearest-neighbor distances in the matrix adjacent to nanolites compared to the bulk. Our methods exhibit the required sensitivity to detect variations in the composition and structure near nanolites, and our findings indicate that obsidian nanolites contribute to quantifiable localized changes in the amorphous structure.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Small-scale experiments in STOVL ground effects

A series of tests was completed in which suckdown and fountain forces and pressures were measured on circular plates and twin-tandem-jet generic STOVL (short takeoff and vertical landing) configurations. The tests were conducted using a small-scale hover rig, for jet pressure ratios up to 6 and jet temperatures up to 700 F. The measured suckdown force on a circular plate with a central jet was greater than that found with a commonly used empirical prediction method. The present data showed better agreement with other sets of data. The tests of the generic STOVL configurations were conducted to provide force and pressure data with a parametric variation of parameters so that an empirical prediction method could be developed. The effects of jet pressure ratio and temperature were found to be small. Lift improvement devices were shown to substantially reduce the net suckdown forces.

Corsiglia, Victor R.↗
NASA NTRS1990

Small-scale experiments in STOVL ground effects

A series of tests has been completed in which suckdown and fountain forces and pressures were measured on circular plates and twin-tandem-jet generic STOVL (short takeoff and vertical landing) configurations. The tests were conducted using a small-scale hover rig, for jet pressure ratios up to 6 and jet temperatures up to 700 F. The measured suckdown force on a circular plate with a central jet was greater than that found with a commonly used empirical prediction method. The present data showed better agreement with other sets of data. The tests of the generic STOVL configurations were conducted to provide force and pressure data with a parametric variation of parameters so that an empirical prediction method cold be developed. The effects of jet pressure ratio and temperature were found to be small. Lift improvement devices were shown to substantially reduce the net suckdown forces.

Corsiglia, Victor R.↗
NASA NTRS1985

Geophysical interpretation of the magnetic anomalies of the Earth derived from MAGSAT data

The ambiguities about geophysical implications based on the correlation of scalar magnetic anomalies and geological features were investigated. A method was developed to convert scalar magnetic anomalies into a map of the lateral variations of magnetic susceptibility of the lithosphere. This map is directly correlated with the causative sources. The method is based on spherical harmonic analysis of lateral variations seen on the scalar magnetic anomaly map and those of the lithospheric magnetic susceptibility. The harmonic coefficients are related through the fundamental causality relationship governing a magnetized body and its associated scalar magnetic anomaly. The main features of the resulting magnetic susceptibility anomalies are outlined.

Arkani-Hamed, J.↗
DOE OSTI2020

Correlation approach for quality assurance of additive manufactured parts based on optical metrology

Surface topography and surface finish are two significant factors for evaluating the quality of products in additive manufacturing (AM). AM parts are fabricated layer by layer, which is quite different from traditional formative or subtractive methods. Despite rapid progress in additive manufacturing and associated optical metrology for quality control and in-situ monitoring, limited research has been conducted to investigate the reliability of 3D surface measurement data. The surface topologies scanned by multiple optical systems demonstrated significant differences due to varying sampling mechanisms, resolutions, system noises, etc. The 3D datasets should be trustworthy in order to extract parameters for quality assurance or feedback control from 3D surface measurements. In this paper, we set up new standards to evaluate the reliability of 3D surface measurement data and analyze the variation in the topographical profile. In this study, two non-contact optical methods based on Focus Variation Microscopy (FVM) and Structured Light System (SLS) were adopted to measure the surface topography of the target components. The two optical metrology systems generated two entirely different point cloud datasets. Statistical methods were applied to test the difference between the data obtained from the two systems. By using a data analytics approach for comparison, it was found that the surface roughness estimated from the point cloud data sets of FVM and SLS has no significant difference, though the point cloud data sets were completely different. This paper provides standard validation approach to evaluate the plausibility of metrology data from in-situ real-time surface analysis for process planning of AM.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Autonomous design of new chemical reactions using a variational autoencoder

Artificial intelligence based chemistry models are a promising method of exploring chemical reaction design spaces. However, training datasets based on experimental synthesis are typically reported only for the optimal synthesis reactions. This leads to an inherited bias in the model predictions. Therefore, robust datasets that span the entirety of the solution space are necessary to remove inherited bias and permit complete training of the space. In this study, an artificial intelligence model based on a Variational AutoEncoder (VAE) has been developed and investigated to synthetically generate continuous datasets. The approach involves sampling the latent space to generate new chemical reactions. This developed technique is demonstrated by generating over 7,000,000 new reactions from a training dataset containing only 7,000 reactions. The generated reactions include molecular species that are larger and more diverse than the training set.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

(abstract) Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

Low thrust propulsion systems typically have their greatest benefit for high energy missions or missions with large post-launch maneuver requirements. Missions which have been examined include main belt asteroid rendezvous, comet rendezvous, outer planet and Mercury orbiters, Pluto flyby, and solar probe missions. Low thrust mission design software used to determine these trajectories is based on two distinct formulations of the optimal control problem: the indirect and direct methods. The traditional approach (indirect) is to use the calculus of variations to obtain first order necessary conditions on the states and costates. In contrast, direct methods are conceptually different in that no explicit integration takes place. A direct method based on differential inclusion concepts has been developed and successfully used to compute low thrust trajectories. This new approach removes explicit control dependence from the problem thereby reducing the dimension of the parameter space for the nonlinear programming problem. Also when compared to other direct methods, fewer nonlinear constraints are required to represent the dynamics of the problem.

low↗