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DOE OSTI2016

Variational Bayesian strategies for high-dimensional, stochastic design problems

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual difficulties encountered in UQ tasks (e.g. the high computational cost of each forward simulation, the large number of random variables) but also by the need to solve a nonlinear optimization problem involving large numbers of design variables and potentially constraints. We propose a framework that is suitable for a class of such problems and is based on the idea of recasting them as probabilistic inference tasks. To that end, we propose a Variational Bayesian (VB) formulation and an iterative VB–Expectation-Maximization scheme that is capable of identifying a local maximum as well as a low-dimensional set of directions in the design space, along which, the objective exhibits the largest sensitivity. We demonstrate the validity of the proposed approach in the context of two numerical examples involving thousands of random and design variables. In all cases considered the cost of the computations in terms of calls to the forward model was of the order of 100 or less. The accuracy of the approximations provided is assessed by information-theoretic metrics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

Analysis of subgrid models using direct and large-eddy simulations of isotropic turbulence

Direct and large eddy simulations of forced and decaying isotropic turbulence have been performed using a pseudospectral and a finite-difference code. Subgrid models that include a one-equation subgrid kinetic energy model with and without a stochastic backscatter forcing term and a new scale similarity model have been analyzed in both Fourier space and physical space. The Fourier space analysis showed that the energy transfer across the cutoff wavenumber k(sub c) is dominated by local interaction. The correlation between the exact and the modeled (by a spectral eddy viscosity) nonlinear terms and the subgrid energy transfer in physical space was found to be quite low. In physical space, a similar correlation analysis was carried out using top hat filtering. Results show that the subgrid stress and the energy flux predicted by the subgrid models correlates very well with the exact data. The scale similarity model showed very high correlation for reasonable grid resolution. However, with decrease in grid resolution, the scale similarity model became more uncorrelated, when compared to the kinetic energy subgrid model. The subgrid models were then used for large-eddy simulations for a range of Reynolds number. It was determined that the dissipation was modeled poorly and that the correlation with the exact results was quite low for all the models. In general, for coarse grid resolution, the scale similarity model consistently showed very low correlation while the kinetic energy model showed a relatively higher correlation. These results suggest that to use the scale similarity model relatively fine grid resolution may be required, whereas, the kinetic energy model could be used even in coarse grid.

Menon, S.↗

NASA NTRS2006

NASA Tech Briefs, May 2006

T-Shaped Emitter Metal Structures for HBTs Rigorous Estimation of SNR of a PSK Communication Link Advanced Ka-Band Transceiver With Monopulse Tracking EMI Filters for Low-Temperature Applications Lightweight Electronic Camera for Research on Clouds Pilot Weather Advisor System Waveguide Power-Amplifier Module for 80 to 150 GHz Better Back Contacts for Solar Cells on Flexible Substrates Topics covered include:Tunable, Highly Stable Lasers for Coherent Lidar; Improved Photon-Emission-Microscope System; Program Synthesizes UML Sequence Diagrams; Aspect-Oriented Subprogram Synthesizes UML Sequence Diagrams; Updated Computational Model of Cosmic Rays Near Earth; Software for Alignment of Segments of a Telescope Mirror; Simulation of Dropping of Cargo With Parachutes; DAVE-ML Utility Program; Robust Control for the Mercury Laser Altimeter; Thermally Stable Piezoelectric and Pyroelectric Polymers; Combustion Synthesis of Ca3(PO4)2 Net-Shape Surgical Implants; Stochastic Representation of Chaos Using Terminal Attractors; Two High-Temperature Foil Journal Bearings; Using Plates To Represent Fillets in Finite-Element Modeling; Repairing Chipped Silicide Coatings on Refractory Metal Substrates; Simplified Fabrication of Helical Copper Antennas; Graded-Index "Whispering-Gallery" Optical Microresonators; Optical Profilometers Using Adaptive Signal Processing; Manufacture of Sparse-Spectrum Optical Microresonators; Exact Tuning of High-Q Optical Microresonators by Use of UV; Automation for "Direct-to" Clearances in Air-Traffic Control; Improved Traps for Removing Gases From Coolant Liquids; and Lunar Constellation of Frozen Elliptical Inclined Orbits.

Source record↗

DOE OSTI2018

Influence of Hydrological Perturbations and Riverbed Sediment Characteristics on Hyporheic Zone Respiration of CO 2 and N 2

Rivers in climatic zones characterized by dry and wet seasons often experience periodic transitions between losing and gaining conditions across the river-aquifer continuum. Infiltration shifts can stimulate hyporheic microbial biomass growth and cycling of riverine carbon and nitrogen leading to major exports of biogenic CO 2 and N 2 to rivers. In this study, we develop and test a numerical model that simulates biological-physical feedback in the hyporheic zone. We used the model to explore different initial conditions in terms of dissolved organic carbon availability, sediment characteristics, and stochastic variability in aerobic and anaerobic conditions from water table fluctuations. Our results show that while highly losing rivers have greater hyporheic CO 2 and N 2 production, gaining rivers allowed the greatest fraction of CO 2 and N 2 production to return to the river. Hyporheic aerobic respiration and denitrification contributed 0.1–2 g/m 2 /d of CO 2 and 0.01–0.2 g/m 2 /d of N 2 ; however, the suite of potential microbial behaviors varied greatly among sediment characteristics. We found that losing rivers that consistently lacked an exit pathway can store up to 100% of the entering C/N as subsurface biomass and dissolved gas. Finally, our results demonstrate the importance of subsurface feedbacks whereby microbes and hydrology jointly control fate of C and N and are strongly linked to wet-season control of initial sediment conditions and hydrologic control of seepage direction. These results provide a new understanding of hydrobiological and sediment-based controls on hyporheic zone respiration, including a new explanation for the occurrence of anoxic microzones and large denitrification rates in gravelly riverbeds.

58 GEOSCIENCES↗

DOE OSTI2015

Effective field model of roughness in magnetic nano-structures

An effective field model is introduced here within the micromagnetics formulation, to study roughness in magnetic structures, by considering sub-exchange length roughness levels as a perturbation on a smooth structure. This allows the roughness contribution to be separated, which is found to give rise to an effective configurational anisotropy for both edge and surface roughness, and accurately model its effects with fine control over the roughness depth without the explicit need to refine the computational cell size to accommodate the roughness profile. The model is validated by comparisons with directly roughened structures for a series of magnetization switching and domain wall velocity simulations and found to be in excellent agreement for roughness levels up to the exchange length. The model is further applied to vortex domain wall velocity simulations with surface roughness, which is shown to significantly modify domain wall movement and result in dynamic pinning and stochastic creep effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Building 235-F Goldsim Fate And Transport Model

Savannah River National Laboratory (SRNL) personnel, at the request of Area Completion Projects (ACP), evaluated In-Situ Disposal (ISD) alternatives that are under consideration for deactivation and decommissioning (D&D) of Building 235-F and the Building 294-2F Sand Filter. SRNL personnel developed and used a GoldSim fate and transport model, which is consistent with Musall 2012, to evaluate relative to groundwater protection, ISD alternatives that involve either source removal and/or the grouting of portions or all of 235-F. This evaluation was conducted through the development and use of a Building 235-F GoldSim fate and transport model. The model simulates contaminant release from four 235-F process areas and the 294-2F Sand Filter. In addition, it simulates the fate and transport through the vadose zone, the Upper Three Runs (UTR) aquifer, and the Upper Three Runs (UTR) creek. The model is designed as a stochastic model, and as such it can provide both deterministic and stochastic (probabilistic) results. The results show that the median radium activity concentrations exceed the 5 ?Ci/L radium MCL at the edge of the building for all ISD alternatives after 10,000 years, except those with a sufficient amount of inventory removed. A very interesting result was that grouting was shown to basically have minimal effect on the radium activity concentration. During the first 1,000 years grouting may have some small positive benefit relative to radium, however after that it may have a slightly deleterious effect. The Pb-210 results, relative to its 0.06 ?Ci/L PRG, are essentially identical to the radium results, but the Pb-210 results exhibit a lesser degree of exceedance. In summary, some level of inventory removal will be required to ensure that groundwater standards are met.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Stochastic Price Generation for Evaluating Wholesale Electricity Market Bidding Strategies

This work presents a novel method for generating electricity price scenarios from statistical properties of past electricity prices using a hybrid statistical and reduced-form stochastic model. Previous work in applying stochastic differential equations (SDE) to model electricity prices has focused on daily average prices. To extend stochastic price generation methods to hourly or sub-hourly pricing, we address several weaknesses in the state-of-the-art: (1) we replace the mean-reversion component of the SDE with an ARIMA process that is better able to characterize the daily and weekly trends; (2) we extend the price-spike, or jump process to account for conditional probabilities of price spikes occurring in consecutive time steps by replacing the traditional Poisson process for modeling jumps with a generalized point process model inspired by brain neuron models; and (3) we replace the traditional method of estimating spike intensity with empirical variance with a Markov process based on observed price spike intensity transitions. The method is demonstrated with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the day-ahead and real-time energy markets of ERCOT using stochastic optimization methods. Results show that the the synthetic price model out performs a (naive) persistence forecast model by resulting in 24% to 47% more in profits over 168 simulated days.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2012

QB1 - Stochastic Gene Regulation

Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2013

Test particle study of ion transport in drift type turbulence

Ion transport regimes in drift type turbulence are determined in the frame of a realistic model for the turbulence spectrum based on numerical simulations. The model includes the drift of the potential with the effective diamagnetic velocity, turbulence anisotropy, and dominant waves. The effects of the zonal flow modes are also analyzed. A semi-analytical method that is able to describe trajectory stochastic trapping or eddying is used for obtaining the transport coefficients as function of the parameters of the turbulence. Analytical approximations of the transport coefficients are derived from the results. They show the transition from Bohm to gyro-Bohm scaling as plasma size increases in very good agreement with the numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Challenges and opportunities in verification and validation of low temperature plasma simulations and experiments

This paper describes the verification and validation (V&V) framework developed for the stochastic Particle-in-Cell, Direct Simulation Monte Carlo code Aleph. An ideal framework for V&V from the viewpoint of the authors is described where a physics problem is defined, and relevant physics models and parameters to the defined problem are assessed and captured in a Phenomena Identification and Ranking Table (PIRT). Furthermore, numerous V&V examples guided by the PIRT for a simple gas discharge are shown to demonstrate the V&V process applied to a real-world simulation tool with the overall goal to demonstrably increase the confidence in the results for the simulation tool and its predictive capability. Although many examples are provided here to demonstrate elements of the framework, the primary goal of this work is to introduce this framework and not to provide a fully complete implementation, which would be a much longer document. Comparisons and contrasts are made to more usual approaches to V&V, and techniques new to the low-temperature plasma community are introduced. Specific challenges relating to the sufficiency of available data (e.g., cross sections), the limits of ad hoc validation approaches, the additional difficulty of utilizing a stochastic simulation tool, and the extreme cost of formal validation are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Evaluation of D and D alternatives for a DOE nuclear material processing facility - 15265

Ten scenarios for SRS Building 235-F were evaluated relative to groundwater protection through use of a 235-F GoldSim{sup TM} fate and transport model. The scenarios included two extreme scenarios, a no action scenario, four D and D grouting scenarios, and three D and D inventory removal scenarios. The fate and transport model simulated contaminant release from four 235-F process areas and the 294-2F Sand Filter and fate and transport through the vadose zone, the Upper Three Runs (UTR) aquifer, and the UTR creek. The model was a stochastic model for which 1,000 realizations were run over 100,000 years for each scenario. In association with the seven D and D alternatives only three groundwater standards out of 25 were exceeded, with the combined radium standard showing the greatest exceedance. The standards were only exceeded at the edge of the building after 10,000 years. It was estimated that there was a 90% likelihood that the combined radium standard would be exceeded for all four D and D grouting scenarios and that a 95% inventory removal from process cells 1-5 would result in an essentially zero percent likelihood that any standards would be exceeded. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2014

Propagation of ultra-short solitons in stochastic Maxwell's equations

We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1997

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗

DOE OSTI2020

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced, and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. Here, we discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Reconstruction of effective potential from statistical analysis of dynamic trajectories

The broad incorporation of microscopic methods is yielding a wealth of information on the atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here, we develop a method for the stochastic reconstruction of effective local potentials solely from observed structural data collected from molecular dynamics simulations (i.e., data analogous to those obtained via atomically resolved microscopies). Using the silicon vacancy defect in graphene as a model, we apply the statistical framework presented herein to reconstruct the free energy landscape from the calculated atomic displacements. Evidence of consistency between the reconstructed local potential and the trajectory data from which it was produced is presented, along with a quantitative assessment of the uncertainty in the inferred parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2015

A cosmic ALP background and the cluster soft X-ray excess in A665, A2199 and A2255

It has been proposed that an excess in soft X-ray emission observed from many galaxy clusters can be explained by conversion into photons of axion-like particles (ALPs) in the cluster's magnetic field. Previously it has been shown that conversion of this primordially-generated background of relativistic ALPs—a cosmic ALP background (CAB)—can explain the observed soft X-ray excess in both the centre and the outskirts of the Coma cluster. Here we extend this work to the three clusters A665, A2199 and A2255. We use a stochastic, power law model of the cluster magnetic field to numerically calculate ALP-photon conversion probabilities to predict the CAB-generated soft X-ray flux in these clusters. The simulated magnetic fields include models with non-standard (i.e. not turbulent Kolmogorov) power spectra, the index of the spectrum changes from cluster to cluster and even within the cluster A2255. We compare this flux to ROSAT PSPC observations of the three clusters, and use these observations to constrain the CAB parameter space. Assuming these non-standard magnetic field power spectra are valid, we find the CAB can reproduce the magnitude of the observed excess in A2199 and A2255 for the same CAB parameters that match the observed soft excess in the Coma cluster. We also find good fit to the morphology of the excesses in these clusters. Simulation of CAB conversion in the cluster A665 is in mild tension with the other clusters due to producing a small but observable excess at large radii where none is observed. This tension is alleviated considering the uncertainty on predicting the count rate in the ROSAT detector, and on the systematics affecting the magnetic field determination. Overall we find good agreement between the CAB parameters for the four clusters studied so far.

79 ASTRONOMY AND ASTROPHYSICS↗

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 OSTI2025

Stochastic Adaptive Droop Control in Frequency Regulation of Power Systems With Intermittent Generators

Modern power systems (MPSs), including microgrids (MGs), are increasingly incorporating multiple renewable energy sources (RESs) such as wind and solar power, as well as battery storage and controllable loads. While environmentally beneficial, these sources pose challenges for control and management due to their intermittent and stochastic nature, especially in maintaining frequency stability with multiple interconnected generators of varying capacities. Traditional droop control methods are effective in systems with generators that are dispatchable and have fixed generation capacities, but they fall short when applied to systems with RESs, where generation capacities are dynamic and affected by unpredictable environmental conditions. To address these challenges, this paper introduces a novel stochastic adaptive droop control (SADC) method for load frequency control (LFC). The proposed method adapts droop coefficients in real time, based on the measured stochastic data of power generation capacities, enabling more effective frequency regulation in systems with variable and intermittent power generation. Unlike traditional adaptive control methods, which assume constant or slowly-varying system parameters, this approach accounts for stochastic processes by modeling them as Markov chains, enabling robust performance under highly dynamic and unpredictable conditions. The key contributions of this work include the development of real-time droop coefficient adaptation algorithms, derivation of their stability and convergence properties, and the demonstration of the advantages of the method through simulations. Case studies highlight the improved performance of frequency regulation, particularly in addressing the impact of stochastic weather conditions and the benefits of reducing dependence on battery reserves in dealing with intermittency of RESs. Finally, this paper provides a comprehensive analysis of the theoretical foundations of the method, as well as practical implementation insights for future power systems with high penetration of RESs.

24 POWER TRANSMISSION AND DISTRIBUTION↗