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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems

We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Stochastic Spectral Descent for Discrete Graphical Models

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Radiation Transport in Random Media With Large Fluctuations

Strongly heterogeneous media arise in several applications that include radiation shields, nuclear fuel, BWR moderators, clouds, planetary and stellar atmospheres, turbulent gases and plasmas. Neutral and charged particle transport computations in such media have relied heavily on formulating transport equations with spatially random coefficients (physical data) and developing solution methods to deal with the additional stochastic dimensions. Attempts at developing approximate closures that yield only low order statistical information (e.g., mean and variance of the flux) have proved to be highly restrictive under real physics conditions or rely on techniques that require fluctuation amplitudes to be small for robustness. Recently, stochastic spectral methods such as polynomial chaos and stochastic collocation have been developed for aleatoric uncertainty quantification and sensitivity analysis, and successfully applied in radiation transport work. Advances in UQ techniques have tended to focus on efficiently handling large numbers of uncertain variables but the rigorous stochastic basis of the approach also promotes its use in situations where stochasticity is due to spatial heterogeneity and the associated uncertainty is large. Here we apply these techniques to radiation transport in media with spatially randomly varying cross sections without restriction on fluctuation amplitudes. Specifically, we represent the cross sections as a lognormal spatial random process with specified mean, variance and covariance function and use a Karhunen-Loeve (KL) decomposition to generate cross section realizations that are strictly positive. Woodcock Monte Carlo (WMC) is then used to simulate transport using random sampling of cross sections and deterministic sampling based on a stochastic collocation technique. Numerical results for the mean and variance in the scalar flux and leakage currents are obtained for weak and strong random variations. We focus in this work on demonstrating the approach and defer application to specific problems to a future investigation. We have demonstrated that a combination of stochastic spectral representation and Woodcock Monte Carlo simulation allows efficient computation of radiation transport in strongly random media. The use of a lognormal distribution to represent the fluctuations in medium properties facilitates enforcement of strict positivity of cross section realizations, a condition that has challenged standard approaches that assume Gaussian fluctuations. The fact that the lognormal random process is a memoryless nonlinear transformation of a Gaussian process further enables efficient and accurate reconstruction of the random cross section realizations using a Karhunen-Loeve representation of the cross section. Finally, the robustness of this model enables fluctuations of arbitrarily large amplitude to be studied, using both random sampling Monte Carlo and more efficient stochastic collocation techniques. The present work is being extended to allow reconstruction of probability density functions of output variables using polynomial chaos representation, and to accommodate general cross section covariance functions. Also, techniques are being explored to more judiciously select ceiling cross sections to enhance the efficiency of Woodcock Monte Carlo for transport in random media. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Stochastic generation of explicit pore structures by thresholding Gaussian random fields

We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone. -- Graphical abstract: -- Highlights: •An efficient method to stochastically generate realistic pore structures is provided. •Samples are generated by applying a level threshold to a Gaussian field realization. •Two user prescribed quantities determine the topology and geometry of the pore space. •Multiple pore structures and preferential flow directions can be produced. •A pore space based on Berea sandstone is generated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Galerkin finite element method for time-fractional stochastic diffusion equations

In this paper, Galerkin finite element method for solving the time-fractional stochastic diffusion equations with multiplicative noise is proposed and investigated. The pathwise regularity properties of solutions to the semidiscrete Galerkin approximations are demonstrated and the convergence of optimal rates are derived. And also we construct the fully discrete scheme which is based on the approximations of the Mittag–Leffler function and analyze the error estimates of convergence in L{sub 2}-norm space. Finally, numerical results are conducted to confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms

We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Advanced Computing is at the Forefront of a New “Moonshot” Revolutionizing the North American Power Grid

In the 50+ years since the first humans landed on the moon, computing has grown at breakneck speed. We are faced with another challenge that is just as daunting, and just as important to overcome-modernizing the North American electric power grid-and high-performance computing (HPC) systems with specialized software will be an important element in rising to this challenge. We describe at a high level how software developed in the ExaSGD project addresses this "moonshot" goal by utilizing exascale computing and a novel high performance solver software stack to support the mission of decarbonizing power grid operations in an environment of uncertain weather and climate. To reach the exascale benchmark the team has made a number of first-of-their-kind innovations, including novel method for stochastic optimization, fine grained parallel methods for modeling power systems, and GPU resident sparse numerical linear solvers.

17 WIND ENERGY↗
DOE OSTI2018

Fluctuating Hydrodynamic Methods for Fluid-Structure Interactions in Confined Channel Geometries

Computational methods are developed for the study of fluid-structure interactions subject to thermal fluctuations when conned within channels having slit-like geometry. The methods take into account the hydrodynamic coupling and diusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered nite volume discretization. We show that by imposing an exact fluctuation-dissipation condition to discretize the stochastic driving elds combined with using an exact projection method to enforce incompressibility is sucient to ensure results consistent with statistical mechanics. We demonstrate our methods by investigating how the proximity of ellipsoidal colloids to the channel wall eects their active hydrodynamic responses and passive diusivity. We also study the collective dynamics of a large number of particles by considering the intermediate scattering functions for the relaxation of density fluctuations. We expect our introduced stochastic computational methods to be applicable broadly to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations. uctuations.

Wang, Yaohong↗
NASA NTRS1972

On stochastic control system design methods for weakly coupled large scale linear systems.

This paper considers the problem of decentralized control of two weakly coupled linear stochastic systems, using quadratic performance indices. The basic idea is to have each controller control independently his own system, based upon noisy measurements of his own output. To compensate for the effects of weak coupling upon the resultant performance, fake white plant noise is introduced to each system. The appropriate intensity of the fake plant noise is obtained through the solution of an off-line deterministic matrix optimal control problem. The effects of this design method upon the overall coupled system performance are analyzed as a function of the degree of intersystem coupling.

Kwong, R.↗
DOE OSTI2023

Adaptive, Active Learning, and Multifidelity Monte Carlo Methods in the MOOSE Stochastic Tools Module

MOOSE is an open-source computational platform for constructing multi-physics models and executing them in a massively parallel fashion. It has a stochastic tools module (STM) for forward/inverse uncertainty quantification (UQ) and surrogate modeling. This presentation details some recent developments to the STM with respect to the implementation of adaptive, active learning, and multifidelity Monte Carlo methods for forward UQ of computational models. Specifically, the adaptive Monte Carlo methods include Markov Chain Monte Carlo (MCMC)-driven algorithms like adaptive importance sampling and parallelized subset simulation for statistical QoI estimation, rare events analysis, and stochastic gradient-free optimization. The active learning methods include Gaussian Process (GP) surrogates and their training via Adam optimization, design of acquisition functions, and integration with samplers like Monte Carlo, adaptive importance, and parallelized subset simulation. These active learning methods are also designed to work in a batch mode, wherein, the required calls to the full computational model are executed in parallel whenever a user-specified batch size is met. The multifidelity methods in STM are broadly divided into two categories: hierarchical, where a defined hierarchy exists among the low-fidelity models, and peer, where all the low-fidelity models are treated equally. A GP surrogate is used to learn the differences between the low- and high-fidelity models in both multifidelity categories, and acquisition functions from the active learning classes are used to decide whether to rely on a low-fidelity model or call the expensive high-fidelity model. Alongside the software description and usage, applications are also presented to nuclear engineering computational models including a TRISO nuclear fuel particle, a reactor pressure vessel, and a heat-pipe microreactor.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

Here, we consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of stochastic function evaluations within a common random number framework. We develop modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations and provide global convergence results to the neighborhood of a locally optimal solution. We present numerical experiments on simulation optimization problems to illustrate the performance of the proposed algorithm. When compared with classical zeroth-order stochastic gradient methods, we observe that our strategies of adapting the sample sizes significantly improve performance in terms of the number of stochastic function evaluations required.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

Within this work, we establish a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact method is provided to seek the stochastic contact variational integrators. Numerical experiments are performed to verify the validity of this approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Stochastic sensing through covalent interactions

A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthal resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

A New Stochastic Equivalent Linearization Implementation for Prediction of Geometrically Nonlinear Vibrations

In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.

Muravyov, Alexander A.↗
DOE OSTI2012

The principal component analysis method used with polynomial Chaos expansion to propagate uncertainties through critical transport problems

A critical neutron transport problem with random material properties is introduced. The total cross section and the average neutron multiplicity are assumed to be uncertain, characterized by the mean and variance with a log-normal distribution. The average neutron multiplicity and the total cross section are assumed to be uncorrected and the material properties for differing materials are also assumed to be uncorrected. The principal component analysis method is used to decompose the covariance matrix into eigenvalues and eigenvectors and then 'realizations' of the material properties can be computed. A simple Monte Carlo brute force sampling of the decomposed covariance matrix is employed to obtain a benchmark result for each test problem. In order to save computational time and to characterize the moments and probability density function of the multiplication factor the polynomial chaos expansion method is employed along with the stochastic collocation method. A Gauss-Hermite quadrature set is convolved into a multidimensional tensor product quadrature set and is successfully used to compute the polynomial chaos expansion coefficients of the multiplication factor. Finally, for a particular critical fuel pin assembly the appropriate number of random variables and polynomial expansion order are investigated. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

Stochastic-field cavitation model

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗