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At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Tempered fractional calculus

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Nested polynomial trends for the improvement of Gaussian process-based predictors

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1975

Stochastic stability and instability of model ecosystems

In this work, we initiate a stability study of multispecies communities in stochastic environment by using Ito's differential equations as community models. By applying the direct method of Liapunov, we obtain sufficient conditions for stability and instability in the mean of the equilibrium populations. The conditions are expressed in terms of the dominant diagonal property of community matrices, which is a suitable mechanism for resolving the central problem of 'complexity vs stability' in model ecosystems. As a by-product of this analysis we exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear time-varying perturbations.

Ladde, G. S.↗
DOE OSTI2022

FORCE-DISPATCHES Integration - Initial Demonstration

Integrated energy systems (IES) combine, in mutually beneficial ways, power from variable renewable energy sources and nuclear power plants (NPP) to improve economic viability under uncertain market and weather conditions. The open-source Framework for Optimization of Resources and Economics (FORCE) tool suite, developed at Idaho National Laboratory (INL), has enabled comprehensive modeling and simulation of IES. The capabilities within FORCE include grid portfolio optimization through the Holistic Energy Resource Optimization Network (HERON) and the transient process model analysis library HYBRID, among others. Continuous efforts and investments from the IES programs have been made to expand and improve the versatility of the FORCE toolset in fiscal year 2022. Code-coupling and cross-tool communication have been important methods for improving this versatility. This report focuses on an additional workflow in the HERON tool for capacity and dispatch stochastic optimization through integration with the external tool Design Integration and Synthesis Platform to Advance Tightly Coupled Hybrid Energy Systems (DISPATCHES). DISPATCHES was primarily developed by the National Energy Technology Laboratory, in collaboration with other national laboratories, which included INL, universities, and industry partners. It is coupled to a library of algebraic models for specific plant components, and to a framework for stochastic optimization different from that provided in the current Risk Analysis Virtual Environment (RAVEN)-running-RAVEN algorithm in HERON. HERON currently conducts stochastic optimization via an outer-inner loop: it optimizes over variable capacity on the outer loop, and at each step within the capacity parameter space, conducts an inner optimization over scenarios (of market signals, demand, and/or weather patterns) and hourly dispatch throughout a user-specified number of years. On the other hand, DISPATCHES conducts stochastic optimization via an “all-at-once” strategy in which capacity variables are optimized at the same level as dispatch variables, as all scenarios are considered at once. The latter method works especially well for projects of limited size and project length, as the necessary computational power and memory increases with the number of variables and scenarios. The new capability to use the DISPATCHES workflow in HERON enhances standalone simulations by leveraging FORCE tools—namely, the economic metrics from the Tool for Economic Analysis (TEAL) and reduced-order model (ROM) sampling from RAVEN. The initial demonstration of the DISPATCHES workflow simulates an existing nuclear-case flowsheet within the DISPATCHES repository—this models a NPP with a secondary revenue stream for hydrogen production. Electrical output from the plant is converted to hydrogen via a proton-exchange membrane (PEM) electrolyzer, hydrogen tanks are used for storage, and an additional turbine is added for hydrogen combustion. Continued work regarding this FORCE-DISPATCHES integration will include automatic generation of DISPATCHES models from HERON inputs, offering analysts the option of using either the RAVEN-runsRAVEN or DISPATCHES workflow to solve technoeconomic optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2012

The impacts of population change on carbon emissions in China during 1978-2008

This study examines the impacts of population size, population structure, and consumption level on carbon emissions in China from 1978 to 2008. To this end, we expanded the stochastic impacts by regression on population, affluence, and technology model and used the ridge regression method, which overcomes the negative influences of multicollinearity among independent variables under acceptable bias. Results reveal that changes in consumption level and population structure were the major impact factors, not changes in population size. Consumption level and carbon emissions were highly correlated. In terms of population structure, urbanization, population age, and household size had distinct effects on carbon emissions. Urbanization increased carbon emissions, while the effect of age acted primarily through the expansion of the labor force and consequent overall economic growth. Shrinking household size increased residential consumption, resulting in higher carbon emissions. Households, rather than individuals, are a more reasonable explanation for the demographic impact on carbon emissions. Potential social policies for low carbon development are also discussed. - Highlights: Black-Right-Pointing-Pointer We examine the impacts of population change on carbon emissions in China. Black-Right-Pointing-Pointer We expand the STIRPAT model by containing population structure factors in the model. Black-Right-Pointing-Pointer The population structure includes age structure, urbanization level, and household size. Black-Right-Pointing-Pointer The ridge regression method is used to estimate the model with multicollinearity. Black-Right-Pointing-Pointer The population structure plays a more important role compared with the population size.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2021

Expected Thrust Fraction: Resilient Trajectory Design Applied to the Earth Return Orbiter

Electric propulsion is an enabling technology for NASA’s Mars Sample Return mission that affords an order of magnitude reduction in fuel. Unfortunately, elec- tric propulsion’s low-thrust capabilities require long thrusting arcs that make space- craft susceptible to disturbances resulting in missed thrust events. One method for designing trajectories resilient to such missed thrust events is expected thrust frac- tion, which embeds their stochastic nature into a time-varying duty cycle. This paper investigates the application of expected thrust fraction to the Earth Return Orbiter’s outbound Earth-to-Mars trajectory and compares it with trajectories de- signed using traditional methods to mitigate missed thrust events. Through the use of expected thrust fraction, a trajectory with a baseline 65.4% success rate is im- proved to an 86.6% success rate at the cost of only a 12 kg reduction in delivered mass. Additionally, when expected thrust fraction is used in conjunction with a terminal coast, a 96.0% success rate is achieved, which is higher than any single mitigation technique.

Laipert, Frank↗
DOE OSTI2014

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.

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

Modelling and analysis of turbulent datasets using Auto Regressive Moving Average processes

We introduce a novel way to extract information from turbulent datasets by applying an Auto Regressive Moving Average (ARMA) statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded time series to a discrete version of a stochastic differential equation which is able to describe the correlation structure in the dataset. We introduce a new index Υ that measures the difference between the resulting analysis and the Obukhov model of turbulence, the simplest stochastic model reproducing both Richardson law and the Kolmogorov spectrum. We test the method on datasets measured in a von Kármán swirling flow experiment. We found that the ARMA analysis is well correlated with spatial structures of the flow, and can discriminate between two different flows with comparable mean velocities, obtained by changing the forcing. Moreover, we show that the Υ is highest in regions where shear layer vortices are present, thereby establishing a link between deviations from the Kolmogorov model and coherent structures. These deviations are consistent with the ones observed by computing the Hurst exponents for the same time series. We show that some salient features of the analysis are preserved when considering global instead of local observables. Finally, we analyze flow configurations with multistability features where the ARMA technique is efficient in discriminating different stability branches of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Application of Hybrid Genetic Algorithm Routine in Optimizing Food and Bioengineering Processes

Optimization is a crucial step in the analysis of experimental results. Deterministic methods only converge on local optimums and require exponentially more time as dimensionality increases. Stochastic algorithms are capable of efficiently searching the domain space, however convergence is not guaranteed. This article demonstrates the novelty of hybrid genetic algorithm which combines both stochastic and deterministic routine for improved optimization results. A new hybrid genetic algorithm developed is applied to the Ackley benchmark function as well as case studies in foods, biofuels, and biotechnology processes. For each case study the hybrid genetic algorithm found a better optimum candidate than reported by the sources. In the case of food processing the hybrid genetic predicted 5% higher anthocyanin yield. Optimization of bio-oil production using HGA resulted in a 4.73 % higher yield. In enzyme production process HGA predicted 2.18 IU/gds of higher xylanase yield. In conclusion, hybridization of genetic algorithm with a deterministic algorithm resulted in maximum optimum compared to the statistical methods.

09 BIOMASS FUELS↗
DOE OSTI2025

Emulation of radiation transport in 3D stochastic media using 1D planar Monte Carlo stochastic media radiation transport algorithms

A subset of stochastic media radiation transport problems involves those in which radiation is incident on a thin slab of stochastic material. Particle tracking in 3D for such problems is expensive, and 1D planar models lack accuracy because they only allow the material to change in one dimension. Therefore, we propose dimensional emulation, which through a slight modification allows existing 1D planar geometry stochastic media radiation transport models to reproduce results from the equivalent 3D models by allowing the material to change in all three dimensions, reproducing the fidelity of the 3D model for the low computational cost of the 1D planar model. In this work, we apply dimensional emulation to three Monte Carlo stochastic media radiation transport models: Chord Length Sampling (CLS), the Local Realization Preserving method (LRP), and a variant of Conditional Point Sampling (CoPS). For a common Markovian benchmark set, the 3D emulation variants of these algorithms are numerically verified to reproduce the results of the 3D variants within statistics while running 1.3 to 2 times faster in the implementation within Sandia National Laboratories open-source research code PlaybookMC. The 3D emulation variants are also shown to yield a 72%–92% reduction in error for the thin slab problems in comparison to the 1D benchmark. As a result, the 3D emulation variant of CLS and CoPS-1 are shown to reproduce 3D CLS results that were used to approximate results for a 3D spherical inclusion geometry benchmark set.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Parameter estimation by implicit sampling

© 2015 Mathematical Sciences Publishers. Implicit sampling is a weighted sampling method that is used in data assimilation to sequentially update state estimates of a stochastic model based on noisy and incomplete data. Here we apply implicit sampling to sample the posterior probability density of parameter estimation problems. The posterior probability combines prior information about the parameter with information from a numerical model, e.g., a partial differential equation (PDE), and noisy data. The result of our computations are parameters that lead to simulations that are compatible with the data. We demonstrate the usefulness of our implicit sampling algorithm with an example from subsurface flow. For an efficient implementation, we make use of multiple grids, BFGS optimization coupled to adjoint equations, and Karhunen-Loève expansions for dimensional reduction. Several difficulties of Markov chain Monte Carlo methods, e.g., estimation of burn-in times or correlations among the samples, are avoided because the implicit samples are independent.

Morzfeld, Matthias↗
DOE OSTI2016

Predictive Modeling of Aging and Degradation of Materials in Extreme Environments.

In order to accurately describe defect accumulation in heterogeneous microstructures and under complex irradiation conditions, simulation methods are needed that can explicitly account for the effect of nonhomogeneous microstructures on damage accumulation. In this project, an advanced simulation tool called spatially resolved stochastic cluster dynamics (SRSCD) is developed for this purpose. The proposed approach relies on solving spatially resolved coupled rate equations of standard cluster dynamics methods in a kinetic Monte Carlo scheme. Large-scale simulations of radiation damage in polycrystalline materials are enabled through several improvements made to this method, including a pseudo-adaptive meshing scheme for cascade implantation and implementation of this method in a synchronous parallel kinetic Monte Carlo framework.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Facile method to stain the bacterial cell surface for super-resolution fluorescence microscopy

A method to fluorescently stain the surfaces of both Gram-negative and Gram-positive bacterial cells compatible with super-resolution fluorescence microscopy is presented. This method utilizes a commercially-available fluorescent probe to label primary amines at the surface of the cell. We demonstrate efficient staining of two bacterial strains, the Gram-negative Shewanella oneidensis MR-1 and the Gram-positive Bacillus subtilis 168. Using structured illumination microscopy and stochastic optical reconstruction microscopy, which require high quantum yield or specialized dyes, we show that this staining method may be used to resolve the bacterial cell surface with sub-diffraction-limited resolution. We further use this method to identify localization patterns of nanomaterials, specifically cadmium selenide quantum dots, following interaction with bacterial cells.

Bacterial↗
DOE OSTI2022

Switching Dynamics in Vanadium Dioxide-Based Stochastic Thermal Neurons

We report on switching dynamics of individual and coupled vanadium dioxide (VO 2 ) devices subject to voltage pulses as the temperature is systematically varied from room temperature spanning the insulator–metal transition (IMT) temperature. The switching voltage of single devices has a strong relationship with both temperature and voltage pulsewidth. Two-step switching in connected VO 2 devices has been noted in current transient plots and was found to depend on temperature, pulsewidth, and pulse amplitude. Experimental switching behavior measured from VO 2 artificial neurons was implemented into a spiking neural network (SNN). During training, modulating the switching voltage via temperature affords a novel method to implement homeostasis with the coupled devices. Simulation results show the efficacy of the stochastic neuronal characteristics and the proposed homeostasis mechanism on a standard digit recognition task. As a result, these studies contribute to ongoing efforts in neuromorphic computing exploiting collective phase transitions.

42 ENGINEERING↗
DOE OSTI2020

Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates

Herein, the use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals as well as their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated for MC-MP2 and MC-MP3, respectively, by systematically replacing one or more two-electron-integral vertexes of certain configurations by zero-valued overlap-integral vertexes in their Goldstone diagrams. The variances and co- variances of these control variates are computed at a marginal cost, enhancing the overall efficiency of the MC-MP2 and MC-MP3 calculations by a factor of up to 14 and 20, respectively.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

A Novel LDPP-MADDPG Approach for Distributed Power Allocation in mmWave Cellular Networks

This paper considers the problem of distributed beam scheduling and power allocation problem in millimeter- Wave (mmWave) cellular networks, in which multiple Base Stations (BSs) operate as individual operators over a shared spectrum. We propose a novel learning-aided approach that integrates the Lyapunov Drift-Plus-Penalty (LDPP) framework and Multi-agent Deep Deterministic Policy Gradient (MADDPG) reinforcement learning algorithms. This offers a powerful approach to learning stable and constraint-aware policies, reaping the joint benefit of both LDPP and MADDPG, in complex multiagent environments. The major challenge for this approach is to integrate these two approaches in a meaningful and effective manner. The key idea to solve this problem is to introduce a novel feature of local observation that incorporates potential negative value of the reward function due to the stochastic constraints introduced by the LDPP framework. Empirical results demonstrate that our proposed scheme outperforms the baseline methods under various conditions.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2014

A stochastic analysis of steady and transient heat conduction in random media using a homogenization approach

We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total number N. Both steady and transient solutions T are expressed in terms of the homogenized solution (symbol) and its spatial derivatives (equation), where homogenized solution (symbol) is obtained by solving the homogenized equation with effective thermal conductivity. Both mean and variance of stochastic solutions can be obtained analytically for K field consisting of independent identically distributed (i.i.d) random variables. The mean and variance of T are shown to be dependent only on the mean and variance of these i.i.d variables, not the particular form of probability distribution function of i.i.d variables. Variance of temperature field T can be separated into two contributions: the ensemble contribution (through the homogenized temperature (symbol)); and the configurational contribution (through the random variable Ln(x)Ln(x)). The configurational contribution is shown to be proportional to the local gradient of (symbol). Large uncertainty of T field was found at locations with large gradient of (symbol) due to the significant configurational contributions at these locations. Numerical simulations were implemented based on a direct Monte Carlo method and good agreement is obtained between numerical Monte Carlo results and the proposed stochastic analysis.

99 GENERAL AND MISCELLANEOUS↗