Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic 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 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Stochastic Vector Techniques in Ground-State Electronic Structure

Herein we review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The application of complex network time series analysis in turbulent heated jets

In the present study, we applied the methodology of the complex network-based time series analysis to experimental temperature time series from a vertical turbulent heated jet. More specifically, we approach the hydrodynamic problem of discriminating time series corresponding to various regions relative to the jet axis, i.e., time series corresponding to regions that are close to the jet axis from time series originating at regions with a different dynamical regime based on the constructed network properties. Applying the transformation phase space method (k nearest neighbors) and also the visibility algorithm, we transformed time series into networks and evaluated the topological properties of the networks such as degree distribution, average path length, diameter, modularity, and clustering coefficient. The results show that the complex network approach allows distinguishing, identifying, and exploring in detail various dynamical regions of the jet flow, and associate it to the corresponding physical behavior. In addition, in order to reject the hypothesis that the studied networks originate from a stochastic process, we generated random network and we compared their statistical properties with that originating from the experimental data. As far as the efficiency of the two methods for network construction is concerned, we conclude that both methodologies lead to network properties that present almost the same qualitative behavior and allow us to reveal the underlying system dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

An Improved Stochastic Unit Commitment Formulation to Accommodate Wind Uncertainty

The United States targets to supply 20% of its electricity generation using wind energy by 2030. The expansion of renewable resources, especially weather-based resources such as wind, creates more uncertainty and variability in the operation of the power grid. New methods and approaches in electricity market operations are needed to efficiently manage the continuing increase in variability and uncertainty caused by expanding intermittent wind. This paper proposes an improved stochastic programming approach for incorporating wind uncertainty into energy markets. The proposed formulation improves the two-stage stochastic unit commitment problem by introducing a dynamic decision making approach similar to a multi-stage formulation in the presence of wind power scenarios which are not well represented by a scenario tree. The numerical results present up to 1%-2% decrease in operational costs compared to the two-stage stochastic unit commitment formulation.

Electricity markets↗
DOE OSTI2014

ADAPTIVE ANNEALED IMPORTANCE SAMPLING FOR MULTIMODAL POSTERIOR EXPLORATION AND MODEL SELECTION WITH APPLICATION TO EXTRASOLAR PLANET DETECTION

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior. To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Post-hoc reweighting of hadron production in the Lund string model

We present a method for reweighting flavor selection in the Lund string fragmentation model. This is the process of calculating and applying event weights enabling fast and exact variation of hadronization parameters on pre-generated event samples. The procedure is post hoc, requiring only a small amount of additional information stored per event, and allowing for efficient estimation of hadronization uncertainties without repeated simulation. Weight expressions are derived from the hadronization algorithm itself, and validated against direct simulation for a wide range of observables and parameter shifts. The hadronization algorithm can be viewed as a hierarchical Markov process with stochastic rejections, a structure common to many complex simulations outside of high-energy physics. This perspective makes the method modular, extensible, and potentially transferable to other domains. We demonstrate the approach in Pythia, including both coverage considerations and timing benefits. For the purpose of this paper, our goal is to develop and demonstrate the the formalism, and we therefore exclude several model variations for baryon production (popcorn model, junction production) needed for proton collisions. These will be the topic of a future paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRSDate not supplied

Robust Trajectory Optimization Techniques Using a Sweeping Gradient Method and Linear Covariance Analysis

We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.

Benjamin W L Margolis↗
DOE OSTI2015

Multivariate moment closure techniques for stochastic kinetic models

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Size-dependent stochastic tensile properties in additively manufactured 316L stainless steel

Recent work in metal additive manufacturing (AM) suggests that mechanical properties may vary with feature size; however, these studies do not provide a statistically robust description of this phenomenon, nor do they provide a clear causal mechanism. Because of the huge design freedom afforded by 3D printing, AM parts typically contain a range of feature sizes, with particular interest in smaller features, so the size effect must be well understood in order to make informed design decisions. This work investigates the effect of feature size on the stochastic mechanical performance of laser powder bed fusion tensile specimens. A high-throughput tensile testing method was used to characterize the effect of specimen size on strength, elastic modulus and elongation in a statistically meaningful way. The effective yield strength, ultimate tensile strength and modulus decreased strongly with decreasing specimen size: all three properties were reduced by nearly a factor of two as feature dimensions were scaled down from 6.25 mm to 0.4 mm. Hardness and microstructural observations indicate that this size dependence was not due to an intrinsic change in material properties, but instead the effects of surface roughness on the geometry of the specimens. Finite element analysis using explicit representations of surface topography shows the critical role surface features play in creating stress concentrations that trigger deformation and subsequent fracture. The experimental and finite element results provide the tools needed to make corrections in the design process to more accurately predict the performance of AM components.

316L stainless steel↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2022

An indirect approach to optimize the reaction rates of thermal NO formation for diesel engines

With stringent emission regulations, it has become more important for modern diesel engine manufacturers to accurately predict engine-out nitrogen oxide (NO x ) emissions across a wide range of operating conditions. Thermal NO is the major source of engine-out NO x in modern diesel engines. For thermal NO formation, several earlier studies have recommended the forward and reverse reaction rate coefficients of the rate-limiting reaction (O + N 2 ⇌ NO + N). However, due to deficiencies in sub-models and inadequacies of reduced chemical mechanisms to represent diesel combustion, these recommended values more often than not need to be adjusted in reduced order combustion models to accurately predict engine-out NO x . Hence, in this work a systematic and computationally efficient approach has been proposed to streamline the process of determining the optimum reaction rate coefficients. Here, to develop the optimization approach, four different production diesel engines with different operating conditions in terms of speed, load, and exhaust-gas recirculation have been considered. Numerical simulations have been performed using a detailed zero-dimensional velocity-composition-frequency transported probability density function (0D-VCF-tPDF) model that uses hundreds of notional particles to capture in-cylinder stratification. Four different combinations of hydrocarbon and NO x chemical mechanisms were used to represent chemistry. It was found that for the rate-limiting reaction, the pre-exponent factors (A f1 , A r1 ) and activation energies (E A,f1 , E A,r1 ) of the forward and reverse reaction rates follow a linear band in A f1 - E A,f1 and A r1 - E A,r1 space where predicted engine-out NO x match the measured values closely. By encompassing such bands from different engines and considering constraints on activation energies, a reduced search domain of pre-exponent factors and activation energies was constructed that is expected to be applicable to any diesel engine. Eventually, computationally efficient three-line and one-line search approaches were proposed to determine the optimum values of the pre-exponent factors and activation energies that led to a minimum error between measured and predicted engine-out NO x . Finally, these three-line and one-line NO x optimization approaches were applied to a fifth production diesel engine for which the 0D-VCF-tPDF model showed a very good predictive performance in terms of predicting peak pressure, 50% burn rate, and engine-out NO x when compared to measured and 3D-CFD values.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2015

Sum over Histories Representation for Chemical Kinetics

A new representation for chemical kinetics is introduced that is based on a sum over histories formulation that employs chemical pathways defined at a molecular level. The time evolution of a chemically reactive system is described by enumerating the most important pathways followed by a chemical moiety. An explicit formula for the pathway probabilities is derived and takes the form of an integral over a time-ordered product. When evaluating long pathways, the time-ordered product has a simple Monte Carlo representation that is computationally efficient. A small numerical stochastic simulation was used to identify the most important paths to include in the representation. The method was applied to a realistic H-2/O-2 combustion problem and is shown to yield accurate results.

Bai, Shirong↗
DOE OSTI2011

Coupled-Channels Density-Matrix Approach to Low-Energy Nuclear Reaction Dynamics

Atomic nuclei are complex, quantum many-body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom. Collective modes (vibration and/or rotation) dominate at low energy (near the ground-state). The associated states are usually employed, within a truncated model space, as a basis in (coherent) coupled channels approaches to low-energy reaction dynamics. However, excluded states can be essential, and their effects on the open (nuclear) system dynamics are usually treated through complex potentials. Is this a complete description of open system dynamics? Does it include effects of quantum decoherence? Can decoherence be manifested in reaction observables? In this contribution, I discuss these issues and the main ideas of a coupled-channels density-matrix approach that makes it possible to quantify the role and importance of quantum decoherence in low-energy nuclear reaction dynamics. Topical applications, which refer to understanding the astrophysically important collision {sup 12}C+{sup 12}C and achieving a unified quantum dynamical description of relevant reaction processes of weakly-bound nuclei, are highlighted.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Demixing-stimulated lane formation in binary complex plasma

Recently lane formation and phase separation have been reported for experiments with binary complex plasmas in the PK3-Plus laboratory onboard the International Space Station (ISS). Positive non-additivity of particle interactions is known to stimulate phase separation (demixing), but its effect on lane formation is unknown. In this work, we used Langevin dynamics (LD) simulation to probe the role of non-additivity interactions on lane formation. The competition between laning and demixing leads to thicker lanes. Analysis based on anisotropic scaling indices reveals a crossover from normal laning mode to a demixing-stimulated laning mode. Extensive numerical simulations enabled us to identify a critical value of the non-additivity parameter {Delta} for the crossover.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Fluctuating hydrodynamics of multicomponent membranes with embedded proteins

A simulation method for the dynamics of inhomogeneous lipid bilayer membranes is presented. The membrane is treated using stochastic Saffman-Delbrück hydrodynamics, coupled to a phase-field description of lipid composition and discrete membrane proteins. Multiple applications are considered to validate and parameterize the model. The dynamics of membrane composition fluctuations above the critical point and phase separation dynamics below the critical point are studied in some detail, including the effects of adding proteins to the mixture.

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

Classical shadows for quantum process tomography on near-term quantum computers

Quantum process tomography is a powerful tool for understanding quantum channels and characterizing the properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [H.-Y. Huang, R. Kueng, and J. Preskill, .], we have developed ShadowQPT, a classical shadow method for quantum process tomography. We introduce two related formulations with and without ancilla qubits. ShadowQPT stochastically reconstructs the Choi matrix of the device allowing for an classical evaluation of the device on arbitrary inputs with respect to arbitrary outputs. Using shadows, we then show how to compute overlaps, generate all k -weight reduced processes, and perform reconstruction via Hamiltonian learning. These latter two tasks are efficient for large systems as the number of quantum measurements needed scales only logarithmically with the number of qubits. A number of additional approximations and improvements are developed, including the use of a pair-factorized Clifford shadow and a series of postprocessing techniques that significantly enhance the accuracy for recovering the quantum channel. We have implemented ShadowQPT using both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to n = 4 qubits, and we achieved good performance. Published by the American Physical Society 2024

Levy, Ryan (ORCID:0000000349527156)↗
DOE OSTI2025

Effect of pattern transfer process on roughness of block copolymer patterns from directed self-assembly

Block copolymer-directed self-assembly (DSA) remains promising for improving pattern quality and reducing the stochastic variations that challenge high numerical aperture extreme ultraviolet lithography. Equally critical is refining pattern transfer methods for accurately transferring the rectified DSA features to the underlying substrate. We compare two atomic layer deposition (ALD)-based techniques: sequential infiltration synthesis (SIS) and dry liftoff, applied to polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) DSA patterns. Both methods utilize aluminum oxide hard masks, with one synthesized through infiltration into the PMMA domains and the other through conformal ALD coating. High-resolution scanning electron micrographs were analyzed to measure line edge, width, and placement roughness for both the line (PMMA) and space (PS) features. Although both methods yielded similar overall 3σ rms roughness, they differed significantly in the frequency-dependent power spectral density (PSD) profiles. SIS reduced line placement roughness at length scales associated with the polymer pitch, but increased space width roughness at low frequencies, whereas dry liftoff mimicked the frequency content of the original guiding pattern. This study underscores the importance of PSD evaluation in selecting optimal pattern transfer strategies for specific applications.

Block copolymers↗
DOE OSTI2016

HackAttack: Game-Theoretic Analysis of Realistic Cyber Conflicts

Game theory is appropriate for studying cyber conflict because it allows for an intelligent and goal-driven adversary. Applications of game theory have led to a number of results regarding optimal attack and defense strategies. However, the overwhelming majority of applications explore overly simplistic games, often ones in which each participant s actions are visible to every other participant. These simplifications strip away the fundamental properties of real cyber conflicts: probabilistic alerting, hidden actions, unknown opponent capabilities. In this paper, we demonstrate that it is possible to analyze a more realistic game, one in which different resources have different weaknesses, players have different exploits, and moves occur in secrecy, but they can be detected. Certainly, more advanced and complex games are possible, but the game presented here is more realistic than any other game we know of in the scientific literature. While optimal strategies can be found for simpler games using calculus, case-by-case analysis, or, for stochastic games, Q-learning, our more complex game is more naturally analyzed using the same methods used to study other complex games, such as checkers and chess. We define a simple evaluation function and employ multi-step searches to create strategies. We show that such scenarios can be analyzed, and find that in cases of extreme uncertainty, it is often better to ignore one s opponent s possible moves. Furthermore, we show that a simple evaluation function in a complex game can lead to interesting and nuanced strategies.

botnets↗