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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quantifying Turbine-Level Risk to Golden Eagles Using a High-Fidelity Updraft Model and a Stochastic Behavioral Model

To minimize the effects of wind farms on Golden Eagle (Aquila chrysaetos) populations while enabling sustainable development of renewable energy resources, it is important to understand how eagles interact with atmospheric flows, terrain features, and anthropogenic structures. Models that predict migratory flight paths provide one tool that helps us grasp how the location of wind farms may influence interactions and impacts on migrating Golden Eagles. The current state-of-the-art in predicting migratory flight paths uses a deterministic fluid-flow analogy to predict eagle trajectory using only an orographic updraft potential computed from topographical features. This model does not take into account variables, such as thermal updrafts and time varying atmospheric conditions that are known to influence migratory behavior. In this work, we improve on the model with the objective of developing tools that advance our understanding of how atmospheric flows and terrain features affect migratory eagle behavior and their interactions with wind farms. Specifically, we 1) incorporate both orographic and thermal updraft information in simulating eagle flight paths; 2) incorporate stochasticity into eagle travel patterns to better capture the influence of exogenous factors on, and the inherent stochasticity of eagle behavior; 3) consider spatio-temporal atmospheric data at wind-farm-scale when computing updraft potential; and 4) account for how atmospheric conditions and the direction of migration change seasonally and how these changes affect eagle migratory flight behavior. We tested the model using a 50km by 50km region with 50 m resolution in the western United States. We simulated 900 independent, probabilistic eagle tracks during southerly and northerly migration, assuming eagles solely rely on orographic updrafts. The preliminary results indicate that the inclusion of finer resolution atmospheric data allows for the inclusion of realistic conditions that an eagle experiences. The stochasticity in eagle tracks provides a platform to include uncertainty in eagle decision making and help produce robust eagle presence maps. We will deploy updraft and downdraft velocities computed using a high-fidelity, wind farm scale, computational fluid dynamics solver under development at National Renewable Energy Laboratory. This work is a first step in the development of a predictive and generalizable eagle behavior model at the wind farm scale that does not rely on empirical data collection. Although the current model is intended for migratory eagles, we will extend and refine this model to inform the development of additional behavioral modes, including resident eagle behavior. This modeling approach improves our ability to understand eagle use of the landscape at a fine scale, and it is our hope that this work will ultimately help advance strategies that minimize the impact of wind development on Golden Eagle populations.

49 EE - Wind and Water Power Program - Wind (EE-4W↗
DOE OSTI2020

Sequential Bayesian Parameter Estimation of Stochastic Dynamic Load Models

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms-in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty in the aggregated protection characteristics can be formulated as a stochastic differential equation with process noise. We cast the parameter inversion within a Bayesian parameter estimation framework, and we present methods to include process noise. We demonstrate the benefits of considering stochasticity in the parameter estimation and the risks of ignoring it.

Bayesian Statistics↗
DOE OSTI2021

Implementing a Stochastic Soot Model in a 3D Domain

In this document a highly detailed stochastic soot model limited to 0D simulations is coupled to 3D domains through the use of a Lagrangian parcel-Eulerian fluid method. Although both the stochastic soot model used and the Lagrangian parcel-Eulerian fluid method have long histories of development, their use, as described in this document, is novel and useful. Previous works significant to the model's development include documents from both the stochastic and simpler soot model genre and the fuel, aerosol, and other particle tracking and Lagrangian parcel-Eulerian fluid genres. Developing the theory behind the model is crucial to its implementation because of the unconventional Lagrangian parcel-Eulerian fluid representation. In fact, the Lagrangian parcel-Eulerian fluid coupling is only a means of simplifying the much more difficult theoretical model. Despite the accompanying assumptions, the complete model is validated from the bottom up and then again in a holistic fashion with promising results. Then the model is used in multiple case studies, showcasing capabilities not had by other models. The optical properties of soot generated in a Spray A simulation are calculated to find measured results are likely overpredicting the mass of soot along the central axis via KL extinction measurements. A thermophoresis submodel that calculates force based on the soot particles' shape is installed to find it has a high influence on the path of the heaviest soot particles. Investigations into the HACA mechanism for soot growth and the effect of syngas on soot in 3D domains are performed with much more detail than has been available before.

Strickland, Tyler↗
DOE OSTI2021

Evaluating Safeguards Statistical Assumptions via Stochastic Simulation

Herein, the authors built and tested a stochastic simulation to estimate achieved detection probabilities (DPs) on a stratum basis, over a tailorable range of diverted amounts from 0 to 2 SQ, using typical IAEA inspection data: i.e., SQ in stratum, number of items, number of gross/partial/bias defect measurements conducted, and realistic relative standard deviation (RSD) values for typical IAEA verification measurements. For bulk strata, the model calculates achieved DP at 0.01 SQ diversion increments; for item strata, the model calculates DP using the smallest realistic diversion increment (e.g., a plate, pin, or coupon). After successfully benchmarking against IAEA deterministic models, the simulation was used to test the sensitivity of DP to certain standard assumptions and selected input parameters. First, the equal defect assumption was tested; the results suggest significant complexity in the effectiveness of partial defect measurements. Next, the authors explored the sensitivity of DP to the assumed RSD of attribute tests. Then, the authors compared non-normal models for instrument performance (e.g., logistic, step, or arbitrary functions) to the typical results from a normal distribution (characterized by RSD). This last comparison was supplemented with experimentally derived performance data for an HM-5. The HM-5 was used to make enrichment measurements on both LEU and HEU MTR fuel elements as plates were removed, and the results fit with logistic and step curves and applied in the simulation. These stochastic DP results were compared to DP estimates from a deterministic model assuming a normal curve and typical RSD, yielding insights that could improve effectiveness in the field. These early results illustrate the potential of stochastic models to better understand achieved DP and to improve safeguards effectiveness.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗
DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. DMMs using deep neural networks to parametrize the transition of Markov probability distributions have recently been shown to provide more expressiveness in modeling sequential data and dynamical system responses. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a rigorous analytical method to prove the necessary and sufficient conditions of DMM's stochastic stability. This task is achieved by spectral analysis of the efficiently computed Jacobians of probabilistic maps modeled by deep neural networks. We make theoretical connections between the eigenvalues of neural network's weights and the different activation function types used on the stability and overall dynamic behavior of DMMs with Gaussian distributions. We empirically substantiate our theoretical results on stochastic stability and eigenvalue spectra via several numerical experiments. Formal stability guarantees of DMMs can substantially improve their robustness and trustworthiness, necessary for reliable use in safety-critical real-world applications.

Drgona, Jan↗
DOE OSTI2024

Searching for cosmological stochastic backgrounds by notching out resolvable compact binary foregrounds with next-generation gravitational-wave detectors

Stochastic gravitational-wave backgrounds can be of either cosmological or astrophysical origin. The detection of an astrophysical stochastic gravitational-wave background with ground-based interferometers is expected in the near future. Perhaps even more excitingly, the detection of stochastic backgrounds of cosmological origin by future ground-based interferometers could reveal invaluable information about the early Universe. From this perspective, the astrophysical background is a {\it foreground} that can prevent the extraction of this information from the data. In this paper, we revisit a time-frequency domain notching procedure previously proposed to remove the astrophysical foreground in the context of next-generation ground-based detectors, but we consider the more realistic scenario where we remove individually detectable signals by taking into account the uncertainty in the estimation of their parameters. We find that time-frequency domain masks can still efficiently remove the astrophysical foreground and suppress it to about $5\%$ of its original level. Further removal of the foreground formed by unresolvable events (in particular, unresolvable binary neutron stars), which is about $10$ times larger than the residual foreground from realistic notching, would require detector sensitivity improvements. Therefore, the main limitation in the search for a cosmological background is the unresolvable foreground itself, and not the residual of the notching procedure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

EXPLORING INTERFEROMETRY DIAGNOSTICS FOR OPTICAL STOCHASTIC COOLING AT FAST/IOTA

Optical Stochastic Cooling (OSC) is an advanced beam-cooling technique that will advance the traditional stochastic cooling. This method leverages optical radiation and high-precision feedback to cool the particles more efficiently than traditional stochastic methods by more than three orders of magnitude. As such, it is an enabler for the development of next generation discovery science machines at the frontiers of energy and intensity. This paper focuses on the development of the second phase of OSC and improving extreme beam cooling techniques in accelerators. The goal was to build and characterize a Mach-Zehnder Interferometer (MZI) in the FAST laser lab using known glass plates thickness which will allow future measurements of unknown phase change due to nonlinear amplification processes.

Teriba, Folashade↗
DOE OSTI2026

Stochastic Thermo-Hydro Modeling and Neural Network Surrogate Development for Thermal Resource Assessment of the Galleries-to-Calories Geobattery

The Galleries-to-Calories Geobattery concept explores the use of abandoned coal mine workings for large-scale thermal energy transport and storage. The system involves injecting waste heat from a supercomputing facility into flooded mine galleries, where groundwater flow can store and transport thermal energy for potential recovery in downgradient district heating and cooling applications. To evaluate the feasibility and performance of the Geobattery under geological and operational uncertainty, we developed a suite of stochastic thermo-hydrological (TH) simulations using Monte Carlo sampling of key uncertain parameters (e.g., permeability, porosity, thermal conductivity, specific heat capacity) and operating conditions (e.g., injection rate, injection temperature). Results identified injection rate and temperature as the most influential parameters governing thermal front propagation, while the geometry of the room-and-pillar structure played a critical role in directing the extent and orientation of thermal advancement. Optimal combinations of material properties for maximizing heat recovery were also determined. To address the high computational cost of coupled-process stochastic modeling, we trained a neural network surrogate model on 24,000 physics-based realizations, achieving an R² > 0.99 and MAE < 0.1 for temperature predictions at monitoring locations. This surrogate enabled an additional 100,000 realizations for global sensitivity analysis and probabilistic thermal resource assessment. The integrated stochastic physics–surrogate modeling framework offers a computationally efficient tool for quantifying uncertainty, identifying key drivers, and informing early-stage design decisions for Geobattery systems.

15 - GEOTHERMAL ENERGY↗
DOE OSTI2015

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations

We explore the dynamics of elastic microstructures within a fluid that are subjected to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the coupling forces that transfer momentum between the fluid and microstructures are strong, (ii) the mass of the microstructures is small relative to the displaced mass of the fluid, and (iii) the response to stresses results in hydrodynamics that relax rapidly to a quasi-steady-state relative to the motions of the microstructure. Furthermore, we derive effective equations using a singular perturbation analysis of the backward Kolmogorov equations of the stochastic process. Our continuum mechanics description is based on the stochastic Eulerian--Lagrangian method which provides a framework for approximation of the fluid-structure interactions when subject to thermal fluctuations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble when applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Data-Consistent Solutions to Stochastic Inverse Problems Using a Probabilistic Multi-Fidelity Method Based on Conditional Densities

In this work, we build upon a recently developed approach for solving stochastic inverse problems based on a combination of measure-theoretic principles and Bayes' rule. We propose a multi-fidelity method to reduce the computational burden of performing uncertainty quantification using high-fidelity models. This approach is based on a Monte Carlo framework for uncertainty quantification that combines information from solvers of various fidelities to obtain statistics on the quantities of interest of the problem. In particular, our goal is to generate samples from a high-fidelity push-forward density at a fraction of the costs of standard Monte Carlo methods, while maintaining flexibility in the number of random model input parameters. Key to this methodology is the construction of a regression model to represent the stochastic mapping between the low- and high-fidelity models, such that most of the computations can be leveraged to the low-fidelity model. To that end, we employ Gaussian process regression and present extensions to multi-level-type hierarchies as well as to the case of multiple quantities of interest. Finally, we demonstrate the feasibility of the framework in several numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Stochastic Modeling of Radioactive Material Releases

Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was funded through a grant from the DOE Nuclear Safety Research and Development Program.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗
DOE OSTI2014

Stochastic Parameterization for Light Absorption by Internally Mixed BC/dust in Snow Grains for Application to Climate Models

A stochastic approach to model the positions of BC/dust internally mixed with two snow-grain types has been developed, including hexagonal plate/column (convex) and Koch snowflake (concave). Subsequently, light absorption and scattering analysis can be followed by means of an improved geometric-optics approach coupled with Monte Carlo photon tracing to determine their single-scattering properties. For a given shape (plate, Koch snowflake, spheroid, or sphere), internal mixing absorbs more light than external mixing. The snow-grain shape effect on absorption is relatively small, but its effect on the asymmetry factor is substantial. Due to a greater probability of intercepting photons, multiple inclusions of BC/dust exhibit a larger absorption than an equal-volume single inclusion. The spectral absorption (0.2 – 5 um) for snow grains internally mixed with BC/dust is confined to wavelengths shorter than about 1.4 um, beyond which ice absorption predominates. Based on the single-scattering properties determined from stochastic and light absorption parameterizations and using the adding/doubling method for spectral radiative transfer, we find that internal mixing reduces snow albedo more than external mixing and that the snow-grain shape plays a critical role in snow albedo calculations through the asymmetry factor. Also, snow albedo reduces more in the case of multiple inclusion of BC/dust compared to that of an equal-volume single sphere. For application to land/snow models, we propose a two-layer spectral snow parameterization containing contaminated fresh snow on top of old snow for investigating and understanding the climatic impact of multiple BC/dust internal mixing associated with snow grain metamorphism, particularly over mountains/snow topography.

climate models↗
DOE OSTI2022

Process-oriented stochastic perturbations applied to the parametrization of turbulence and shallow convection for ensemble prediction

Weather forecasting nowadays often requires some estimation of uncertainties associated with the output of meteorological models, in order to better inform decision making, especially in the context of intense weather events. Ensemble prediction systems provide such information through sets of possible scenarios which are designed to represent various uncertainty sources, including model uncertainties. A wide variety of methods have been proposed to estimate model uncertainties, among which perturbation methods targeting uncertain processes are a promising research field. Here, we focus on the representation of small-scale variability by process-oriented perturbation schemes applied to two key physical processes, namely turbulence and shallow convection. The perturbations are applied to a single-column version of the convection-permitting AROME model, in three idealized boundary-layer cases. Large-eddy simulations (LESs) of the same cases serve as a reference for the subgrid variability that has to be represented, and the results are also compared to those given by the Stochastically Perturbed Parametrization Tendencies (SPPT) method, which is a method commonly used by weather forecast centres to represent model uncertainty. The spread produced by our process-oriented perturbations of turbulence and shallow convection does not represent all the small-scale variability implied by the LESs for temperature and humidity. However, it is of a similar order of magnitude for the wind, thanks to perturbations generated by the stochastic turbulence scheme. The dispersion is structurally different from what is obtained with SPPT. It is non-negligible in the lower levels, where SPPT perturbations are usually suppressed because of numerical instabilities, indicating a possible complementarity between the schemes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. Here we adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochastic Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, P(Φ), for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-N models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order H 4 at late times and so does not generate a dramatic gravitational back-reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

The quantum Fokker-Planck equation of stochastic inflation

We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗