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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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DOE OSTI2015

Adaptive error covariances estimation methods for ensemble Kalman filters

This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for using information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Model averaging approaches to data subset selection

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models across different subsets of the data. Two different criteria have been proposed in the literature for how the data subsets should be weighted. We compare the two criteria closely in a unified treatment based on the Kullback-Leibler divergence and conclude that one of them is subtly flawed and will tend to yield larger uncertainties due to loss of information. Here, analytical and numerical examples are provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Systematic validation of non-equilibrium thermochemical models using Bayesian inference

The validation process proposed by Babuška et al. [1] is applied to thermochemical models describing post-shock flow conditions. In this validation approach, experimental data is involved only in the calibration of the models, and the decision process is based on quantities of interest (QoIs) predicted on scenarios that are not necessarily amenable experimentally. Moreover, uncertainties present in the experimental data, as well as those resulting from an incomplete physical model description, are propagated to the QoIs. We investigate four commonly used thermochemical models: a one-temperature model (which assumes thermal equilibrium among all inner modes), and two-temperature models developed by Macheret et al. [2], Marrone and Treanor [3], and Park [4]. Up to 16 uncertain parameters are estimated using Bayesian updating based on the latest absolute volumetric radiance data collected at the Electric Arc Shock Tube (EAST) installed inside the NASA Ames Research Center. Following the solution of the inverse problems, the forward problems are solved in order to predict the radiative heat flux, QoI, and examine the validity of these models. Our results show that all four models are invalid, but for different reasons: the one-temperature model simply fails to reproduce the data while the two-temperature models exhibit unacceptably large uncertainties in the QoI predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Universality Classes of Interaction Structures for NK Fitness Landscapes

Kauffman’s NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of k≤L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Reservoir Modeling by Data Integration via Intermediate Spaces and Artificial Intelligence Tools in MPS Simulation Frameworks

Conditioning stochastic simulations are very important in many geostatistical applications that call for the introduction of nonlinear and multiple-point data in reservoir modeling. Here, a new methodology is proposed for the incorporation of different data types into multiple-point statistics (MPS) simulation frameworks. Unlike the previous techniques that call for an approximate forward model (filter) for integration of secondary data into geologically constructed models, the proposed approach develops an intermediate space where all the primary and secondary data are easily mapped onto. Definition of the intermediate space, as may be achieved via application of artificial intelligence tools like neural networks and fuzzy inference systems, eliminates the need for using filters as in previous techniques. The applicability of the proposed approach in conditioning MPS simulations to static and geologic data is verified by modeling a real example of discrete fracture networks using conventional well-log data. The training patterns are well reproduced in the realizations, while the model is also consistent with the map of secondary data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Numerical strategies for filtering partially observed stiff stochastic differential equations

In this paper, we present a fast numerical strategy for filtering stochastic differential equations with multiscale features. This method is designed such that it does not violate the practical linear observability condition and, more importantly, it does not require the computationally expensive cross correlation statistics between multiscale variables that are typically needed in standard filtering approach. The proposed filtering algorithm comprises of a 'macro-filter' that borrows ideas from the Heterogeneous Multiscale Methods and a 'micro-filter' that reinitializes the fast microscopic variables to statistically reflect the unbiased slow macroscopic estimate obtained from the macro-filter and macroscopic observations at asynchronous times. We will show that the proposed micro-filter is equivalent to solving an inverse problem for parameterizing differential equations. Numerically, we will show that this microscopic reinitialization is an important novel feature for accurate filtered solutions, especially when the microscopic dynamics is not mixing at all.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems

This paper deals with the formulation of a semi-intrusive (SI) method allowing the computation of statistics of linear and non linear PDEs solutions. This method shows to be very efficient to deal with probability density function of whatsoever form, long-term integration and discontinuities in stochastic space. Given a stochastic PDE where randomness is defined on Ω, starting from (i) a description of the solution in term of a space variables, (ii) a numerical scheme defined for any event ω∈Ω and (iii) a (family) of random variables that may be correlated, the solution is numerically described by its conditional expectancies of point values or cell averages and its evaluation constructed from the deterministic scheme. One of the tools is a tessellation of the random space as in finite volume methods for the space variables. Then, using these conditional expectancies and the geometrical description of the tessellation, a piecewise polynomial approximation in the random variables is computed using a reconstruction method that is standard for high order finite volume space, except that the measure is no longer the standard Lebesgue measure but the probability measure. This reconstruction is then used to formulate a scheme on the numerical approximation of the solution from the deterministic scheme. This new approach is said semi-intrusive because it requires only a limited amount of modification in a deterministic solver to quantify uncertainty on the state when the solver includes uncertain variables. The effectiveness of this method is illustrated for a modified version of Kraichnan–Orszag three-mode problem where a discontinuous pdf is associated to the stochastic variable, and for a nozzle flow with shocks. The results have been analyzed in terms of accuracy and probability measure flexibility. Finally, the importance of the probabilistic reconstruction in the stochastic space is shown up on an example where the exact solution is computable, the viscous Burgers equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Subcell resolution in simplex stochastic collocation for spatial discontinuities

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC–SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers’ equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC–SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Adaptive approximation of higher order posterior statistics

Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Ensemble Kalman filters for dynamical systems with unresolved turbulence

Ensemble Kalman filters are developed for turbulent dynamical systems where the forecast model does not resolve all the active scales of motion. Coarse-resolution models are intended to predict the large-scale part of the true dynamics, but observations invariably include contributions from both the resolved large scales and the unresolved small scales. The error due to the contribution of unresolved scales to the observations, called ‘representation’ or ‘representativeness’ error, is often included as part of the observation error, in addition to the raw measurement error, when estimating the large-scale part of the system. It is here shown how stochastic superparameterization (a multiscale method for subgridscale parameterization) can be used to provide estimates of the statistics of the unresolved scales. In addition, a new framework is developed wherein small-scale statistics can be used to estimate both the resolved and unresolved components of the solution. The one-dimensional test problem from dispersive wave turbulence used here is computationally tractable yet is particularly difficult for filtering because of the non-Gaussian extreme event statistics and substantial small scale turbulence: a shallow energy spectrum proportional to k{sup −5/6} (where k is the wavenumber) results in two-thirds of the climatological variance being carried by the unresolved small scales. Because the unresolved scales contain so much energy, filters that ignore the representation error fail utterly to provide meaningful estimates of the system state. Inclusion of a time-independent climatological estimate of the representation error in a standard framework leads to inaccurate estimates of the large-scale part of the signal; accurate estimates of the large scales are only achieved by using stochastic superparameterization to provide evolving, large-scale dependent predictions of the small-scale statistics. Again, because the unresolved scales contain so much energy, even an accurate estimate of the large-scale part of the system does not provide an accurate estimate of the true state. By providing simultaneous estimates of both the large- and small-scale parts of the solution, the new framework is able to provide accurate estimates of the true system state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Switching of bound vector solitons for the coupled nonlinear Schroedinger equations with nonhomogenously stochastic perturbations

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schroedinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere

We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

A dynamic model for the Lagrangian stochastic dispersion coefficient

A stochastic sub-grid model is often used to accurately represent particle dispersion in turbulent flows using large eddy simulations. Models of this type have a free parameter, the dispersion coefficient, which is not universal and is strongly grid-dependent. In the present paper, a dynamic model for the evaluation of the coefficient is proposed and validated in decaying homogeneous isotropic turbulence. The grid dependence of the static coefficient is investigated in a turbulent mixing layer and compared to the dynamic model. The dynamic model accurately predicts dispersion statistics and resolves the grid-dependence. Dispersion statistics of the dynamically calculated constant are more accurate than any static coefficient choice for a number of grid spacings. Furthermore, the dynamic model produces less numerical artefacts than a static model and exhibits smaller sensitivity in the results predicted for different particle relaxation times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Low-temperature random matrix theory at the soft edge

“Low temperature” random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the “soft edge,” which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A stochastic extension of the explicit algebraic subgrid-scale models

The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗