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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 OSTI2017

Gauging Variational Inference

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where meanfield (MF) and belief propagation (BP) are arguably the most popular and successful approaches of a variational type. In this paper, we propose two new variational schemes, coined Gauged-MF (G-MF) and Gauged-BP (G-BP), improving MF and BP, respectively. Both provide lower bounds for the partition function by utilizing the so-called gauge transformation which modifies factors of GM while keeping the partition function invariant. Moreover, we prove that both G-MF and G-BP are exact for GMs with a single loop of a special structure, even though the bare MF and BP perform badly in this case. Our extensive experiments, on complete GMs of relatively small size and on large GM (up-to 300 variables) confirm that the newly proposed algorithms outperform and generalize MF and BP.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Numerical solution of the Stratonovich- and Ito–Euler equations: Application to the stochastic piston problem

We consider a piston with a velocity perturbed by Brownian motion moving into a straight tube filled with a perfect gas at rest. The shock generated ahead of the piston can be located by solving the one-dimensional Euler equations driven by white noise using the Stratonovich or Ito formulations. We approximate the Brownian motion with its spectral truncation and subsequently apply stochastic collocation using either sparse grid or the quasi-Monte Carlo (QMC) method. In particular, we first transform the Euler equations with an unsteady stochastic boundary into stochastic Euler equations over a fixed domain with a time-dependent stochastic source term. We then solve the transformed equations by splitting them up into two parts, i.e., a ‘deterministic part’ and a ‘stochastic part’. Numerical results verify the Stratonovich–Euler and Ito–Euler models against stochastic perturbation results, and demonstrate the efficiency of sparse grid and QMC for small and large random piston motions, respectively. The variance of shock location of the piston grows cubically in the case of white noise in contrast to colored noise reported in [1], where the variance of shock location grows quadratically with time for short times and linearly for longer times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Hubbard physics in the PAW GW approximation

It is demonstrated that the signatures of the Hubbard Model in the strongly interacting regime can be simulated by modifying the screening in the limit of zero wavevector in Projector-Augmented Wave GW calculations for systems without significant nesting. This modification, when applied to the Mott insulator CuO, results in the opening of the Mott gap by the splitting of states at the Fermi level into upper and lower Hubbard bands, and exhibits a giant transfer of spectral weight upon electron doping. The method is also employed to clearly illustrate that the M{sub 1} and M{sub 2} forms of vanadium dioxide are fundamentally different types of insulator. Standard GW calculations are sufficient to open a gap in M{sub 1} VO{sub 2}, which arise from the Peierls pairing filling the valence band, creating homopolar bonds. The valence band wavefunctions are stabilized with respect to the conduction band, reducing polarizability and pushing the conduction band eigenvalues to higher energy. The M{sub 2} structure, however, opens a gap from strong on-site interactions; it is a Mott insulator.

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

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Biased diffusion in tubes of alternating diameter: Numerical study over a wide range of biasing force

This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients—mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

On effective temperature in network models of collective behavior

Collective behavior of self-propelled units is studied analytically within the Vectorial Network Model (VNM), a mean-field approximation of the well-known Vicsek model. We propose a dynamical systems framework to study the stochastic dynamics of the VNM in the presence of general additive noise. We establish that a single parameter, which is a linear function of the circular mean of the noise, controls the macroscopic phase of the system—ordered or disordered. By establishing a fluctuation–dissipation relation, we posit that this parameter can be regarded as an effective temperature of collective behavior. The exact critical temperature is obtained analytically for systems with small connectivity, equivalent to low-density ensembles of self-propelled units. Numerical simulations are conducted to demonstrate the applicability of this new notion of effective temperature to the Vicsek model. The identification of an effective temperature of collective behavior is an important step toward understanding order–disorder phase transitions, informing consistent coarse-graining techniques and explaining the physics underlying the emergence of collective phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Multifidelity Approach to Sensitivity Estimation in Large-Eddy Simulation

A novel approach to compute affordable approximate sensitivities in a large-eddy simulation (LES) is proposed and assessed. The approach is based on solving a Reynolds-averaged Navier–Stokes (RANS) problem that has been linearized around the mean LES solution, with closure modeling required for the linearized changes in turbulent Reynolds stresses. In the present study, the closure modeling is based on a linearized algebraic turbulence model. The method is assessed for the flow over a NACA0012 airfoil at a fixed angle of attack, with the Reynolds number as the variable parameter. The results show that, provided an accurate linearized closure model, the method predicts the correct sensitivity of the skin friction coefficient and the mean velocity field at the cost of a linearized RANS, which provides an important proof-of-concept for this approach. Here, the linearized algebraic turbulence model with standard model coefficients produces a reasonably accurate sensitivity, but the results also suggest that accuracy could be gained from recalibrating the model coefficients for this new use of the model.

42 ENGINEERING↗
DOE OSTI2013

Homogenization method based on the inverse problem

We present a method for deriving homogeneous multi-group cross sections to replace a heterogeneous region's multi-group cross sections; providing that the fluxes and the currents on the external boundary, and the region averaged fluxes are preserved. The method is developed using diffusion approximation to the neutron transport equation in a symmetrical slab geometry. Assuming that the boundary fluxes are given, two response matrices (RMs) can be defined. The first derives the boundary current from the boundary flux, the second derives the flux integral over the region from the boundary flux. Assuming that these RMs are known, we present a formula which reconstructs the multi-group cross-section matrix and the diffusion coefficients from the RMs of a homogeneous slab. Applying this formula to the RMs of a slab with multiple homogeneous regions yields a homogenization method; which produce such homogenized multi-group cross sections and homogenized diffusion coefficients, that the fluxes and the currents on the external boundary, and the region averaged fluxes are preserved. The method is based on the determination of the eigenvalues and the eigenvectors of the RMs. We reproduce the four-group cross section matrix and the diffusion constants from the RMs in numerical examples. We give conditions for replacing a heterogeneous region by a homogeneous one so that the boundary current and the region-averaged flux are preserved for a given boundary flux. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Direct probe of dark energy through gravitational lensing effect

We show that gravitational lensing can provide a direct method to probe the nature of dark energy at astrophysical scales. For lensing system as an isolated astrophysical object, we derive the dark energy contribution to gravitational potential as a repulsive power-law term, containing a generic equation of state parameter w . We find that it generates w -dependent and position-dependent modification to the conventional light orbital equation of w =−1. With post-Newtonian approximation, we compute its direct effect for an isolated lensing system at astrophysical scales and find that the dark energy force can deflect the path of incident light rays. We demonstrate that the dark-energy-induced deflection angle Δα{sub DE}∝ M {sup (1+1/3} {sup w} {sup )} (with 1+1/3 w > 0), which increases with the lensing mass M and consistently approaches zero in the limit M → 0. This effect is distinctive because dark energy tends to diffuse the rays and generates concave lensing effect . This is in contrast to the conventional convex lensing effect caused by both visible and dark matter. Measuring such concave lensing effect can directly probe the existence and nature of dark energy. We estimate this effect and show that the current gravitational lensing experiments are sensitive to the direct probe of dark energy at astrophysical scales. For the special case w =−1, our independent study favors the previous works that the cosmological constant can affect light bending, but our prediction qualitatively and quantitatively differ from the literature, including our consistent realization of Δα{sub DE} → 0 (under 0 M → ) at the leading order.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Approximate models for the study of exponential changed quantities: Application on the plasma waves growth rate or damping

Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.

36 MATERIALS SCIENCE↗
DOE OSTI2015

H{sub 4}: A challenging system for natural orbital functional approximations

The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D{sub 2h} to D{sub 4h} symmetry in H{sub 4} molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H{sub 4} D{sub 4h}/D{sub 2h} potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D{sub 2h}–D{sub 4h} transition of H{sub 4} has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H{sub 4} PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.

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

The redshift distribution of cosmological samples: a forward modeling approach

Determining the redshift distribution n ( z ) of galaxy samples is essential for several cosmological probes including weak lensing. For imaging surveys, this is usually done using photometric redshifts estimated on an object-by-object basis. We present a new approach for directly measuring the global n ( z ) of cosmological galaxy samples, including uncertainties, using forward modeling. Our method relies on image simulations produced using \textsc(UFig) (Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation) within the MCCL (Monte-Carlo Control Loops) framework. The galaxy population is modeled using parametric forms for the luminosity functions, spectral energy distributions, sizes and radial profiles of both blue and red galaxies. We apply exactly the same analysis to the real data and to the simulated images, which also include instrumental and observational effects. By adjusting the parameters of the simulations, we derive a set of acceptable models that are statistically consistent with the data. We then apply the same cuts to the simulations that were used to construct the target galaxy sample in the real data. The redshifts of the galaxies in the resulting simulated samples yield a set of n ( z ) distributions for the acceptable models. We demonstrate the method by determining n ( z ) for a cosmic shear like galaxy sample from the 4-band Subaru Suprime-Cam data in the COSMOS field. We also complement this imaging data with a spectroscopic calibration sample from the VVDS survey. We compare our resulting posterior n ( z ) distributions to the one derived from photometric redshifts estimated using 36 photometric bands in COSMOS and find good agreement. This offers good prospects for applying our approach to current and future large imaging surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A modified Monte Carlo 'local importance function transform' method

The Local Importance Function Transform (LIFT) method uses an approximation of the contribution transport problem to bias a forward Monte-Carlo (MC) source-detector simulation [1-3]. Local (cell-based) biasing parameters are calculated from an inexpensive deterministic adjoint solution and used to modify the physics of the forward transport simulation. In this research, we have developed a new expression for the LIFT biasing parameter, which depends on a cell-average adjoint current to scalar flux (J{sup *}/{phi}{sup *}) ratio. This biasing parameter differs significantly from the original expression, which uses adjoint cell-edge scalar fluxes to construct a finite difference estimate of the flux derivative; the resulting biasing parameters exhibit spikes in magnitude at material discontinuities, causing the original LIFT method to lose efficiency in problems with high spatial heterogeneity. The new J{sup *}/{phi}{sup *} expression, while more expensive to obtain, generates biasing parameters that vary smoothly across the spatial domain. The result is an improvement in simulation efficiency. A representative test problem has been developed and analyzed to demonstrate the advantage of the updated biasing parameter expression with regards to solution figure of merit (FOM). For reference, the two variants of the LIFT method are compared to a similar variance reduction method developed by Depinay [4, 5], as well as MC with deterministic adjoint weight windows (WW). (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Approximation of functions in variable-exponent Lebesgue and Sobolev spaces by finite Fourier-Haar series

The paper deals with the space L{sup p(x)} consisting of classes of real measurable functions f(x) on [0,1] with finite integral ∫{sub 0}{sup 1}|f(x)|{sup p(x)} dx. If 1≤p(x)≤ p-bar <∞, then the space L{sup p(x)} can be made into a Banach space with the norm ∥f∥{sub p(⋅)}=inf(α > 0:∫{sub 0}{sup 1}|f(x)/α|{sup p(x)} dx≤ 1). The inequality ∥f−Q{sub n}(f)∥{sub p(⋅)}≤c(p)Ω(f,1/n){sub p(⋅)}, which is an analogue of the first Jackson theorem, is shown to hold for the finite Fourier-Haar series Q{sub n}(f), provided that the variable exponent p(x) satisfies the condition |p(x)−p(y)|ln (1/|x−y|)≤ c. Here, Ω(f,δ){sub p(⋅)} is the modulus of continuity in L{sup p(x)} defined in terms of Steklov functions. If the function f(x) lies in the Sobolev space W{sub p(⋅)}{sup 1} with variable exponent p(x), it is shown that ∥f−Q{sub n}(f)∥{sub p(⋅)}≤c(p)/n∥f{sup ′}∥{sub p(⋅)}. Methods for estimating the deviation |f(x)−Q{sub n}(f,x)| for f(x)∈W{sub p(⋅)}{sup 1} at a given point x∈[0,1] are also examined. The value of sup{sub f∈W{sub p{sup 1}(1)}}|f(x)−Q{sub n}(f,x)| is calculated in the case when p(x)≡p= const, where W{sub p}{sup 1}(1)=(f∈W{sub p}{sup 1}:∥f{sup ′}∥{sub p(⋅)}≤1). Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On the Statistical Calibration of Physical Models

ABSTRACT We introduce a novel statistical calibration framework for physical models, relying on probabilistic embedding of model discrepancy error within the model. For clarity of illustration, we take the measurement errors out of consideration, calibrating a chemical model of interest with respect to a more detailed model, considered as “truth” for the present purpose. We employ Bayesian statistical methods for such model‐to‐model calibration and demonstrate their capabilities on simple synthetic models, leading to a well‐defined parameter estimation problem that employs approximate Bayesian computation. The method is then demonstrated on two case studies for calibration of kinetic rate parameters for methane air chemistry, where ignition time information from a detailed elementary‐step kinetic model is used to estimate rate coefficients of a simple chemical mechanism. We show that the calibrated model predictions fit the data and that uncertainty in these predictions is consistent in a mean‐square sense with the discrepancy from the detailed model data.

Sargsyan, K.↗
DOE OSTI2014

Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides

The technique that was used to build the EigCG algorithm for sparse symmetric linear systems is extended to the nonsymmetric case using the BiCG algorithm. We show that, similarly to the symmetric case, we can build an algorithm that is capable of computing a few smallest magnitude eigenvalues and their corresponding left and right eigenvectors of a nonsymmetric matrix using only a small window of the BiCG residuals while simultaneously solving a linear system with that matrix. For a system with multiple right-hand sides, we give an algorithm that computes incrementally more eigenvalues while solving the first few systems and then uses the computed eigenvectors to deflate BiCGStab for the remaining systems. Our experiments on various test problems, including Lattice QCD, show the remarkable ability of EigBiCG to compute spectral approximations with accuracy comparable to that of the unrestarted, nonsymmetric Lanczos. Furthermore, our incremental EigBiCG followed by appropriately restarted and deflated BiCGStab provides a competitive method for systems with multiple right-hand sides.

Abdel-Rehim, A M↗
DOE OSTI2021

A minimally invasive, efficient method for propagation of full-field uncertainty in solid dynamics

In this work, we present a minimally invasive method for forward propagation of material property uncertainty to full-field quantities of interest in solid dynamics. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi-one-dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.

42 ENGINEERING↗