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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Adaptive hybrid simulations for multiscale stochastic reaction networks

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Variance reduction for Fokker–Planck based particle Monte Carlo schemes

Recently, Fokker–Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1–3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker–Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker–Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1995

A simulation to study the feasibility of improving the temporal resolution of LAGEOS geodynamic solutions by using a sequential process noise filter

A key drawback to estimating geodetic and geodynamic parameters over time based on satellite laser ranging (SLR) observations is the inability to accurately model all the forces acting on the satellite. Errors associated with the observations and the measurement model can detract from the estimates as well. These 'model errors' corrupt the solutions obtained from the satellite orbit determination process. Dynamical models for satellite motion utilize known geophysical parameters to mathematically detail the forces acting on the satellite. However, these parameters, while estimated as constants, vary over time. These temporal variations must be accounted for in some fashion to maintain meaningful solutions. The primary goal of this study is to analyze the feasibility of using a sequential process noise filter for estimating geodynamic parameters over time from the Laser Geodynamics Satellite (LAGEOS) SLR data. This evaluation is achieved by first simulating a sequence of realistic LAGEOS laser ranging observations. These observations are generated using models with known temporal variations in several geodynamic parameters (along track drag and the J(sub 2), J(sub 3), J(sub 4), and J(sub 5) geopotential coefficients). A standard (non-stochastic) filter and a stochastic process noise filter are then utilized to estimate the model parameters from the simulated observations. The standard non-stochastic filter estimates these parameters as constants over consecutive fixed time intervals. Thus, the resulting solutions contain constant estimates of parameters that vary in time which limits the temporal resolution and accuracy of the solution. The stochastic process noise filter estimates these parameters as correlated process noise variables. As a result, the stochastic process noise filter has the potential to estimate the temporal variations more accurately since the constraint of estimating the parameters as constants is eliminated. A comparison of the temporal resolution of solutions obtained from standard sequential filtering methods and process noise sequential filtering methods shows that the accuracy is significantly improved using process noise. The results show that the positional accuracy of the orbit is improved as well. The temporal resolution of the resulting solutions are detailed, and conclusions drawn about the results. Benefits and drawbacks of using process noise filtering in this type of scenario are also identified.

Hartman, Brian Davis↗
DOE OSTI2015

Theoretical consideration of the energy resolution in planar HPGe detectors for low energy X-rays

In this work, theoretical consideration of the processes in planar High Purity Ge (HPGe) detectors for low energy X-rays using the random stochastic processes formalism was carried out. Using the random stochastic processes formalism, the generating function of the processes of X-rays registration in a planar HPGe detector was derived. The power serial expansions of the detector amplitude and the variance in terms of the inverse bias voltage were derived. The coefficients of these expansions allow determining the Fano factor, electron mobility lifetime product, nonuniformity of the trap density, and other characteristics of the semiconductor material. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Experimental Evidence that Stochasticity Contributes to Bacterial Composition and Functioning in a Decomposer Community

ABSTRACT Stochasticity emerging from random differences in replication, death, mutation, and dispersal is thought to alter the composition of ecological communities. However, the importance of stochastic effects remains somewhat speculative because stochasticity is not directly measured but is instead inferred from unexplained variations in beta-diversity. Here, we performed a field experiment to more directly disentangle the role of stochastic processes, environmental selection, and dispersal in the composition and functioning of a natural bacterial decomposer community in the field. To increase our ability to detect these effects, we reduced initial biological and environmental heterogeneity using replicate nylon litterbags in the field. We then applied two treatments: ambient/added precipitation and bacterial and fungal dispersal using “open” litterbags (made from 18.0-μm-pore-size mesh) (“open bacterial dispersal”) versus bacterial and fungal dispersal using “closed” litterbags (made from 22.0-μm-pore-size mesh) (“closed bacterial dispersal”). After 5 months, we assayed composition and functioning by the use of three subsamples from each litterbag to disentangle stochastic effects from residual variation. Our results indicate that stochasticity via ecological drift can contribute to beta-diversity in bacterial communities. However, residual variation, which had previously been included in stochasticity estimates, accounted for more than four times as much variability. At the same time, stochastic effects on beta-diversity were not attenuated at the functional level, as measured by genetic functional potential and extracellular enzyme activity. Finally, dispersal was found to interact with precipitation availability to influence the degree to which stochasticity contributed to functional variation. Together, our results demonstrate that the ability to quantify stochastic processes is key to understanding microbial diversity and its role in ecosystem functioning. IMPORTANCE Randomness can alter the diversity and composition of ecological communities. Such stochasticity may therefore obscure the relationship between the environment and community composition and hinder our ability to predict the relationship between biodiversity and ecosystem functioning. This study investigated the role of stochastic processes, environmental selection, and dispersal in microbial composition and its functioning on an intact field community. To do this, we used a controlled and replicated experiment that was similar to that used to study population genetics in the laboratory. Our study showed that, while the stochastic effects on taxonomic composition are smaller than expected, the degree to which stochasticity contributes to variability in ecosystem processes may be much higher than previously assumed.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-“coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

Radiative transfer calculated from a Markov chain formalism

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Esposito, L. W.↗
DOE OSTI2016

Bayesian estimation of Karhunen–Loève expansions; A random subspace approach

One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition) on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stochastic nucleation processes and substrate abundance explain time-dependent freezing in supercooled droplets

Atmospheric immersion freezing (IF), a heterogeneous ice nucleation process where an ice nucleating particle (INP) is immersed in supercooled water, is a dominant ice formation pathway impacting the hydrological cycle and climate. Implementation of IF derived from field and laboratory data in cloud and climate models is difficult due to the high variability in spatio-temporal scales, INP composition, and morphological complexity. We demonstrate that IF can be consistently described by a stochastic nucleation process accounting for uncertainties in the INP surface area. This approach accounts for time-dependent freezing, a wide range of surface areas and challenges phenomenological descriptions typically used to interpret IF. The results have an immediate impact on the current description, interpretation, and experiments of IF and its implementation in models. The findings are in accord with nucleation theory, and thus should hold for any supercooled liquid material that nucleates in contact with a substrate.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models

Stochastic particle-resolved methods have proven useful for simulating multi-dimensional systems such as composition-resolved aerosol size distributions. While particle-resolved methods have substantial benefits for highly detailed simulations, these techniques suffer from high computational cost, motivating efforts to improve their algorithmic efficiency. Here we formulate an algorithm for accelerating particle removal processes by aggregating particles of similar size into bins. We present the Binned Algorithm for particle removal processes and analyze its performance with application to the atmospherically relevant process of aerosol dry deposition. We show that the Binned Algorithm can dramatically improve the efficiency of particle removals, particularly for low removal rates, and that computational cost is reduced without introducing additional error. In simulations of aerosol particle removal by dry deposition in atmospherically relevant conditions, we demonstrate about 50-times increase in algorithm efficiency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Efficient gradient estimation using finite differencing and likelihood ratios for kinetic Monte Carlo simulations

While many optimization and control methods for stochastic processes require gradient information from the process of interest, obtaining gradient information from experiments is prohibitively expensive and time-consuming. As a result, such information is often obtained from stochastic process simulations. Computing gradients efficiently and accurately from stochastic simulations is challenging, especially for simulations involving computationally expensive models with significant inherent noise. In this work, we analyze and characterize the applicability of two gradient estimation methods for kinetic Monte Carlo simulations: finite differencing and likelihood ratio. We developed a systematic method for choosing an optimal perturbation size for finite differencing and discuss, for both methods, important implementation issues such as scaling with respect to the number of elements in the gradient vector. Through a series of numerical experiments, the methods were compared across different time and size regimes to characterize the precision and accuracy associated with each method. We determined that the likelihood ratio method is appropriate for estimating gradients at short (transient) times or for systems with small population sizes, whereas finite differencing is better-suited for gradient estimation at long times (steady state) or for systems with large population sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

On the use of stochastic process-based methods for the analysis of hyperspectral data

Further development in remote sensing technology requires refinement of information system design aspects, i.e., the ability to specify precisely the data to collect and the means to extract increasing amounts of information from the increasingly rich and complex data stream created. One of the principal directions of advance is that data from much larger numbers of spectral bands can be collected, but with significantly increased signal-to-noise ratio. The theory of stochastic or random processes may be applied to the modeling of second-order variations. A multispectral data set with a large number of spectral bands is analyzed using standard pattern recognition techniques. The data were classified using first a single spectral feature, then two, and continuing on with greater and greater numbers of features. Three different classification schemes are used: a standard maximum likelihood Gaussian scheme; the same approach with the mean values of all classes adjusted to be the same; and the use of a minimum distance to means scheme such that mean differences are used.

Landgrebe, David A.↗
DOE OSTI2019

Shape optimization under uncertainty for rotor blades of horizontal axis wind turbines

We present a computational framework for the shape optimization of a Horizontal-Axis Wind Turbine (HAWT) rotor blade under uncertainty. Our framework integrates aerodynamic simulations based on the blade element method which utilizes reduced order models of the blade structure and wind load with design sensitivity analysis and nonlinear programming. The wind velocity is modeled as a stochastic process to account for variations in time and space. An additional stochastic process accounts for uncertainties in the structural material properties. The uncertainty propagation is based on a non-intrusive polynomial chaos expansion that allows accurate estimation of stochastic performance metrics such as generated power and structural compliance. Sensitivities of cost and constraint functions with respect to shape parameters namely twist angles are computed with an efficient scheme to enable gradient based optimization. To demonstrate the effect of uncertainty, designs obtained from optimization under uncertainty are compared to those obtained from deterministic optimization.

42 ENGINEERING↗
DOE OSTI2019

Degradation Modeling and Reliability Assessment of Capacitors

The degradation of capacitors under accelerated stress conditions occur in a monotonic and non-linear fashion. Several efforts have been made to model the degradation behavior of capacitor considering either physics-of-failure models or statistical models and subsequently estimate its reliability and lifetime parameters. But most of these models fail to reflect the physical properties of the degradation path, which varies according to several intrinsic and extrinsic factors. These factors introduce random and temporal uncertainty among the population of capacitors. The gamma stochastic process can model both type of uncertainties among the population of capacitors. In this paper, we model the capacitor degradation by non-homogeneous gamma stochastic process in which both the model parameters (shape and scale) are dependent on stress variables. The model parameters are estimated using the maximum likelihood estimation approach.

42 ENGINEERING↗
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↗