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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Variance estimates for transport in stochastic media by means of the master equation

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

The impact of fuel particle size distribution on neutron transport in stochastic media

This paper presents a study of the particle size distribution impact on neutron transport in three-dimensional stochastic media. An eigenvalue problem is simulated in a cylindrical container consisting of fissile fuel particles with five different size distributions: constant, uniform, power, exponential and Gaussian. We construct 15 cases by altering the fissile particle volume packing fraction and its optical thickness, but keeping the mean chord length of the spherical fuel particle the same at different size distributions. The tallied effective multiplication factor (k{sub eff}) and flux distribution along axial and radial directions are compared between different size distributions. At low packing fraction and low optical thickness, the size distribution has a significant impact on radiation transport in stochastic media, which can cause as high as {approx}270 pcm difference in k{sub eff} value and {approx}2.6% relative error difference in peak flux. As the packing fraction and optical thickness increase, the impact gradually dissipates. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

An Atomic Mix Closure for Stochastic Media Transport Problems

The accurate modeling of stochastic media in radiation transport calculations remains on ongoing research challenge. The Levermore-Pomraning (LP) closure for the statistical transport equation is simple and inexpensive, but it is often inaccurate. More accurate closures have been proposed, but they can be prohibitively expensive. In this work we present a relatively inexpensive closure that we have observed to be more accurate than LP in almost all cases studied. Obtaining solutions to stochastic transport problems can be quite difficult. Transport calculations on an ensemble of explicit realizations generated by Monte Carlo sampling can be prohibitively expensive. Atomic mix or LP calculations are relatively inexpensive, but they can be inaccurate. The present work illustrates an approach that is less expensive than Monte Carlo sampling yet more accurate than atomic mix or LP approximations. We still need to analyze the reasons why the atomic mix closures derived for thicker problems lead to source iteration instabilities. It is not clear if the closure itself induces an ill-posed problem or if it is merely the iterative process that is problematic. We hope to examine alternative source terms to drive the subsidiary calculations. We also want to extend the work to multigroup and multidimensional problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A stochastic model of future extreme temperature events for infrastructure analysis

Applying extreme temperature events for future conditions is not straightforward for infrastructure resilience analyses. This work introduces a stochastic model that fills this gap. The model uses at least 50 years of daily extreme temperature records, climate normals with 10%-90% confidence intervals, and shifts/offsets for increased frequency and intensity of heat wave events. Intensity and frequency are shifted based on surface temperature anomaly from 1850-1900 for 32 models from CMIP6. A case study for Worcester, Massachusetts passed 85% of cases using the two-sided Kolmogorov-Smirnov -value test with 95% confidence for both temperature and duration. Future shifts for several climate scenarios to 2020, 2040, 2060, and 2080 had acceptable errors between the shifted model and 10- and 50-year extreme temperature event thresholds with the largest error being 2.67 degrees C. The model is likely to be flexible enough for other patterns of extreme weather such as extreme precipitation and hurricanes.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Probabilistic Neural Computing with Stochastic Devices

Abstract The brain has effectively proven a powerful inspiration for the development of computing architectures in which processing is tightly integrated with memory, communication is event‐driven, and analog computation can be performed at scale. These neuromorphic systems increasingly show an ability to improve the efficiency and speed of scientific computing and artificial intelligence applications. Herein, it is proposed that the brain's ubiquitous stochasticity represents an additional source of inspiration for expanding the reach of neuromorphic computing to probabilistic applications. To date, many efforts exploring probabilistic computing have focused primarily on one scale of the microelectronics stack, such as implementing probabilistic algorithms on deterministic hardware or developing probabilistic devices and circuits with the expectation that they will be leveraged by eventual probabilistic architectures. A co‐design vision is described by which large numbers of devices, such as magnetic tunnel junctions and tunnel diodes, can be operated in a stochastic regime and incorporated into a scalable neuromorphic architecture that can impact a number of probabilistic computing applications, such as Monte Carlo simulations and Bayesian neural networks. Finally, a framework is presented to categorize increasingly advanced hardware‐based probabilistic computing technologies.

Misra, Shashank↗
DOE OSTI2025

Bayesian Calibration of Stochastic Agent Based Model via Random Forest

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high-dimensional calibration can be computationally prohibitive. This paper presents a random forest-based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented, and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. Further, these results are compared with previous approximate Bayesian calibration (IMABC) results, and their predictive performance is analyzed, showing improved performance with a reduction in computation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Stochastic renormalization group and gradient flow

A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck equations. The result implies a new approach to Monte Carlo RG that is amenable to lattice simulation. Long-distance correlations of the effective theory are shown to approach gradient-flowed correlations, which are simpler to measure. The Markov property of the stochastic RG transformation implies an RG scaling formula which allows for the measurement of anomalous dimensions when transcribed into gradient flow expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models

In this paper we prove a weak necessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke’s generalized gradient of the Hamiltonian and Clarke’s normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum principle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof of the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2022

Stochastic Model for High Temperature Oxidation of Cr–Ni Austenitic Steels Assisted by Spallation

Abstract Cr–Ni austenitic steels offer significant high temperature corrosion protection by forming a surface oxide layer. However, above critical service conditions (temperature, atmosphere, thermal cycling), oxidized surface can experience intensive degradation because of scale spallation, which could be detrimental to the in-service life. To predict the effect of scale spallation on oxidation kinetics, a simulation was implemented using a stochastic model. The model considers topological parameters and intensity of spallation which can occur, while delivering a true oxidation constant. The experimental procedure identified the amount of formed spalled scale and topology of spallation based on the use of element mapping of the surface. This information was used to determine a true kinetic constant for a corresponding spallation intensity in oxidized Cr–Ni austenitic steel. To illustrate the capability of the stochastic model, a parametric analysis was performed. The model verified how the spallation parameters could change the oxidation processes from parabolic growth of an adhered oxide layer without spallation to a mixed linear-parabolic, or with a constant thickness of residual scale at high spallation intensity. The spallation model will be used in a separate article to characterize high temperature surface degradation of several Cr–Ni austenitic steels during harsh oxidation environments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems—like fixation of cells coupled with fluorescence microscopy—provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. In this study, these snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Stochastic joint inversion of hydrogeophysical data for salt tracer test monitoring and hydraulic conductivity imaging

The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity field. We used a stochastic joint inversion of Direct Current (DC) resistivity and Self-Potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field between two wells. The pilot point parameterization was used to avoid over-parameterization of the inverse problem. Bounds on the model parameters were used to promote a consistent Markov chain Monte Carlo sampling of the model parameters. To evaluate the effectiveness of the joint inversion process, we compared 8 cases in which the geophysical data are coupled or not to the in situ sampling of the salinity to map the hydraulic conductivity. We first tested the effectiveness of the inversion of each type of data alone (concentration sampling, self-potential, and DC resistivity), and then we combined the data two by two. We finally combined all the data together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. We also investigated a case in which the data were contaminated with noise and the variogram unknown and inverted stochastically. The results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity field especially when the self-potential data were combined to the salt concentration measurement in the second well or to the time-lapse cross-well electrical resistivity data. Various tests were also performed to quantify the uncertainty in the inverted hydraulic conductivity field.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Markov stochasticity coordinates

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Stochastic risk-sensitive market integration for renewable energy: Application to ocean wave power plants

With the expected increase of intermittent renewable energy resources on the electric power grid, short-term reserve markets can prove to be a critical reliability asset. This paper introduces and tests a potential market structure that includes a short-term reserve market for renewable resources where the realized energy is drawn within the bounds of the hourly capacity offered. The study presents a risk-aware stochastic model that determines, based on the day-ahead offer derived using a classic newsvendor formula, the best intraday offers for a renewable energy power plant. The stochastic approach takes into account the uncertainties of energy production and market prices. The proposed risk-sensitive model aims to maximize the renewable power plant's revenues and minimize potential risks of loss in a multi-product multi-timescale market setup. To demonstrate the effectiveness of the proposed formulation, we study the case of a hypothetical 750-kW wave power plant coupled with energy storage. The study shows that the risk of profit loss is not uniformly distributed across the risk-aversion factor space. We also find that the introduction of the short-term reserve market results in a wider range of conditional value at risk while inducing 5% profit increase and a lower profit reduction across the risk range. In addition, the study reveals that the short-term reserve market is profitable for both the system operator and the wave energy power plant considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Assessment of wind power scenario creation methods for stochastic power systems operations

Probabilistic scenarios of renewable energy production, such as wind, have been gaining popularity for use in stochastic variants of power systems operations scheduling problems, allowing for optimal decision-making under uncertainty. The quality of the scenarios has a direct impact on the value of the resulting decisions, but until now, methods for creating scenarios have not been compared under realistic operational conditions. Here, we compare the quality of scenario sets created using three different methods, based on a simulated re-enactment of stochastic day-ahead unit commitment and subsequent dispatch for a realistic test system. We create scenarios using a dataset of forecasted and actual wind power values, scaled to evaluate the effects of increasing wind penetration levels. We show that the choice of scenario set can significantly impact system operating cost, renewable energy use, and the ability of the system to meet demand. This result has implications for the ability of system operators to efficiently integrate renewable production into their day-ahead planning, highlighting the need for the use of performance-based assessments for scenario evaluation.

17 WIND ENERGY↗
DOE OSTI2022

A hierarchical stochastic modeling approach for representing point bar geometries and petrophysical property variations

The flow of fluids in point bars is affected by the existence of heterogeneities like shale drapes that are found on the surfaces of inclined heterolithic stratifications. In fact, these shale drapes can act as fluid flow baffles; therefore, developing a framework for modeling point bars and their associated heterogeneities is vital. In this study, a stochastic process-based modeling approach is presented for capturing the main point bar heterogeneities: accretion surfaces (i.e., the aerial heterogeneity) and inclined heterolithic stratifications (i.e., the vertical heterogeneity). The former was modeled using a sine-generation function and the latter, with a sigmoidal function after which they were combined into a 3D point bar model. To ensure proper modeling of petrophysical properties, we developed a more representative gridding scheme which generates curvilinear grids representative of the point bar geometry. This grid was then transformed into a rectilinear grid to allow for geostatistical simulation after which all petrophysical properties were mapped back into the original curvilinear grid. An essential element of this modeling approach is the stochastic representation of shale drapes at the interface between successive accretion surfaces. The workflow was tested using a real field dataset for the Cranfield field, Mississippi. The constructed model was then subjected to a flow simulation study mimicking a CO 2 storage scenario. Various sensitivities were simulated to evaluate the effect of heterogeneities on CO 2 flow within the point-bar. Results demonstrate the importance of representing point-bar related heterogeneity and the spatial distribution of shale drapes on CO 2 plume migration and storage.

58 GEOSCIENCES↗