Uncertainty Propagation in Dynamical Systems via Stochastic Collocation on Model Dynamics.
Abstract not provided.
De, Saibal↗
SEARCH · Engineering Papers
Results for “Stochastic modelling”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics
We introduce adversarial learning methods for data-driven generative modeling of dynamics of nth-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.
• Artificial intelligence (AI) / machine learning ↗
Stochastic parametric skeletal dosimetry model for humans: Anatomical-morphological basis and parameter evaluation
Radiation exposure of the hematopoietic system that results in a radiation dose to bone marrow of more than 100 mGy leads to an increase in the risk of leukemia in humans. Excess relative risk of leukemia was observed in cohorts whose members lived in the territories of the Southern Urals that were radioactively contaminated in the 1950s. As part of the dosimetric support of epidemiological studies of these cohorts, an original methodology for stochastic bone dosimetric modeling was developed, termed the Stochastic Parametric Skeletal Dosimetry (SPSD) model. The purpose of this work was to present the anatomical and morphological bases of the SPSD model, which includes an assessment of the parameters of the microstructure of the trabecular bone in the hematopoietic areas of the human skeleton, as well as a description of the macrostructural division (segmentation) of hematopoietic areas into simple bone segments. As a result, an anatomical-morphological basis of the SPSD model was created based on published data. Data collection work included the analysis of original articles, atlases, manuals, monographs and the formation of primary data files. Data on the duration of hematopoiesis in various parts of the skeleton; and data on age-related changes in the microstructure and linear dimensions of human bones and their segments were analyzed. The paper describes the full set of parameters to be used for the dosimetric model for newborns, children aged 1, 5 and 10 years, as well as for adolescents aged 15 years and adults; for the latter, sex differences in bone size were considered. In total, the SPSD model includes 289 unique basic (bone) phantom segments, each of which is described by 7 or more parameters describing the microstructure, thickness of the cortical layer and linear dimensions. Population variability was estimated for each parameter. The approach to SPSD modeling, i.e., the use of simple geometric shapes, was successfully verified using independent datasets on bone masses and volumes.
Science & Technology - Other Topics↗
Bounds on galaxy stochasticity from halo occupation distribution modeling
The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce RED M A G I C-like galaxy catalogs within the A BACUS S UMMIT suite of N -body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.
Britt, Dylan (ORCID:000000019905601X)↗
Stochastic parametric skeletal dosimetry model for humans: Pediatric and adult computational skeleton phantoms for internal bone marrow dosimetry
Currently, computational phantoms that simulate skeletal tissues are used in active red bone marrow (AM) internal dosimetry. Up-to-date reference computational phantoms recommended by the ICRP are based on the analysis of CT-images of cadavers. Such phantoms have significant disadvantages. One disadvantage is that the assessment of uncertainty due to the population variability of skeleton dimensions and microstructure results from the limited availability of autopsy material. Another disadvantage is the simplified modelling of cortical layer and bone microarchitecture. A method of stochastic parametric skeletal dosimetry modelling of the bone structures – SPSD modelling – has been developed as an alternative to the ICRP reference phantoms. In the framework of this approach, skeletal phantom parameters are evaluated based on extensively reviewed results of published measurements of real bones. The SPSD approach allows for the assessment of both population-average values and their variability. SPSD-phantoms of the skeleton are modelled in voxel representation. They consist of smaller phantoms of the bone sites – segments – described by simple geometric shapes with uniform microarchitecture parameters. Such segmentation makes it possible to account for non-homogeneous skeletal microarchitecture and to model the bone structure with the required voxel resolution to elaborate suitable skeletal phantoms. The current study presents the parameters of the SPSD skeletal phantoms for the following age-groups: newborn, 1-year-old, 5-year-old, 10-year-old, 15-year-old (male and female), and adult (male and female). This skeletal phantom can be used for dosimetry as an alternative to available reference phantoms for bone-seeking radionuclides. The above-mentioned age- and sex-specific skeletal phantoms are comprised of 289 unique segments. The characteristics of the SPSD phantoms do not contradict published data and are in good agreement with the measurement results of real bones.
Science & Technology - Other Topics↗
Development and Integration of a Stochastic Clad Damage Propagation Model into PRONGHORN-SC Subchannel Analysis Code
The failure of fuel pins in nuclear reactors is intrinsically stochastic. Typically, a combination of variation in manufacturing that affects the material characteristics and the fuel assembly dimensions, variation in operating conditions, such as local power, coolant flow rate, and irradiation induced changes in material properties lead to a large uncertainty in failure margin of the fuel pins. Failure, therefore, may occur in exceptional pins with adverse combinations of these variations. Upon a metal fuel pin (U-Pu-Zr/HT9) failure, depressurization of the fuel pin takes place by release of fission gas, liquid sodium bond, and potentially solid fuel particles or molten/eutectic fuel droplets through the hole in cladding. The effect of a fission gas jet on neighbor fuel pins and possible propagation of a clad damage during normal operation was studied experimentally in 1970s and it was found that the post-failure fission gas jet insulates the jet impingement area of the target fuel pin surface and could increase the target pin’s surface temperature by as much as 100 – 200 K during the failed pin depressurization. It was concluded that the effect should not lead to fuel pin failure propagation during normal operation. In accident scenarios of sodium and lead fast reactors such as Unprotected Loss-Of-Flow (ULOF) or Unprotected Transient Over Power (UTOP), the fuel pins can be subjected to higher clad temperatures and fuel pin pressures or fuel clad mechanical/chemical interaction where thermal creep margin becomes significantly lower compared to the normal operation conditions. Therefore, possible stochastic failure and the post-failure fission gas/fuel jet impingement could be critical in order to predict fuel pin failure propagation. Pin depressurization due to fission gas release may degrade the heat transfer by formation of a gas blanket on a neighboring pin surface, which is a local phenomenon, and by causing coolant flow deceleration and starvation, which could affect a surrounding region as well. Furthermore, the potential presence of solid fuel particles or molten fuel at the time of clad failure could boost post-failure jet induced degradation even further. The present study models the U-Pu-Zr/HT9 metal fuel pin failure and stochastic clad damage propagation by biased sampling based on a Cumulative Damage Fraction (CDF) type clad failure criterion and the normal distribution of fuel failure probability density as a function of logarithm of Cumulative Damage Fraction. In addition, the effect of post-failure fission gas jet on heat transfer degradation is modeled for the target pins. This model is called stochastic Clad Damage Propagation (CDAP). The CDAP model is now fully integrated into developmental version of PRONGHORN-SC subchannel analysis code, allowing for modeling local failures and its propagation potential. Section 2 describes the components of the CDAP models. Section 3 describes the model implementation to PRONGHORN-SC and input specifications. Section 4 describes the CDAP model validation coupled to PRONGHORN-SC.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market
In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.
Bilevel multistage stochastic programming problem↗
A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution
Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.
97 MATHEMATICS AND COMPUTING↗
A Stochastic Charging Station Deployment Model for Electrified Taxi Fleets in Coupled Urban Transportation and Power Distribution Networks
Metropolitansworldwide are increasingly adopting electric taxis (ET) to address concerns about transportation-related emissions. However, the widespread deployment of electric taxis presents challenges in terms of increased electricity demand and changing demand profiles. This transition impacts both the urban transportation network (TN) and the electricity power distribution network (PDN), highlighting the interdependence between these two systems. Here, in this paper, we propose a two-stage stochastic programming planning model that aims to optimize both the TN and PDN, enabling efficient deployment of charging stations and grid upgrades. Our model seeks to strike a balance between meeting ET drivers' charging preferences, minimizing the costs associated with infrastructure deployment and grid expansion, and harmonizing the coordination between the TN and PDN. Additionally, we explore the potential benefits of utilizing an autonomous ET fleet to enhance overall system performance.
33 ADVANCED PROPULSION SYSTEMS↗
Stochastic fracture generation and thermo-hydro-mechanical modeling in an equivalent continuum framework for enhanced geothermal systems
Enhanced geothermal systems (EGS) involve fracturing low permeability material to establish well connectivity and then injecting and circulating fluid into the fractured subsurface for geothermal power production. Changes in fracture aperture from contraction of the cooling matrix rock may alter network connectivity and risk thermal short-circuiting. Thermo-hydro-mechanical (THM) models are a useful tool to study these processes. However, as fracture networks are complex, and data may be limited, fracture networks in THM models are often stochastically generated. Given reliance on stochastic fracture networks and THM modeling to represent the subsurface and assess productivity of EGS, increased understanding of the influence of such statistically derived fracture networks on flow and heat transport in THM models is needed. Here, a new fracture process model is developed in the reactive transport code PFLOTRAN to stochastically generate fracture families and simulate changes in fracture aperture over time due to temperature changes of the rock matrix. Sixty-four different fracture networks ranging from well to poorly-connected, are modeled in PFLOTRAN with and without mechanical processes (THM vs TH). Results indicate that for well-connected fracture networks, thermal short-circuiting is less of a concern due to the abundance of available alternative flowpaths. For poorly-connected fracture networks, inclusion of mechanical processes showed steep thermal drawdown coincident with increase in fracture aperture along developing colder flowpaths, demonstrating the risk of thermal short-circuiting. Simulations with additional, larger fractures engineered to establish connectivity in a poorly-fractured subsurface, indicate that while stochastic variation of fracture orientation of the background network had limited influence, such variation in the engineered fractures significantly affected flow and heat transport.
Discrete fracture networks (DFN)↗
A Generalization of Threshold-Based and Probability-Based Models of Information Diffusion
Diffusion of information through complex networks is of interest in studies such as propagation prediction and influence maximization, both of which have applications in viral marketing and rumor controlling. There are a variety of information diffusion models, all of which simulate the adoption and spread of information over time. However, there is a lack of understanding of whether, despite their conceptual differences, these models represent the same underlying generative structures. For instance, if two different models utilize different conceptual mechanisms, but generate the same results, does the choice of model matter? A classification of diffusion of information models is developed based on the neighbor knowledge of the model infection requirement and the stochasticity of the model. This classification allows for the identification of models that fall into each respective category. The study involves the analysis of the following agent-based models on directed scale-free networks: (1) a linear absolute threshold model (LATM), (2) a linear fractional threshold model (LTFM), (3) the independent cascade model (ICM), (4) Bass-Rand-Rust model (BRRM) (5) a stochastic linear absolute threshold model (SLATM) (6) a stochastic fractional threshold model (SLFTM), and (7) Dodds–Watts model (DWM). Through the execution of simulations and analysis of the experimental results, the distinctive properties of each model are identified. Our analysis reveals that similarity in conceptual design does not imply similarity in behavior concerning speed, final state of nodes and edges, and sensitivity to parameters. Therefore, we highlight the importance of considering the unique behavioral characteristics of each model when selecting a suitable information diffusion model for a particular application.
97 MATHEMATICS AND COMPUTING↗
Structure–Property Relationships of Recycled Lithium-Ion Battery Cathodes: Microstructure Optimization Using Virtual Materials Testing
The increasing demand for sustainable battery technologies requires effective recycling strategies for end-of-life lithium-ion battery cathodes. In this study, virtual materials testing, a well-established framework for modeling conventionally manufactured NMC-based cathodes, is applied to partially recycled cathodes. To this end, virtual cathodes consisting of mixtures of pristine and recycled NMC particles are utilized to systematically analyze structure–property relationships depending on mixing ratios and different spatial arrangement strategies. For this purpose, a stochastic 3D model is developed that is capable of generating virtual cathodes with arbitrary volume fractions of active materials and mixing ratios of pristine and recycled NMC particles. Particularly, the stochastic 3D model can mimic the different size distributions of pristine and recycled particles that are observed in image data. Additionally, the model allows the structuring of pristine and recycled NMC either uniformly mixed or layer-wise arranged, mimicking single- and dual-layer cathodes. Subsequently, a systematic computational analysis is conducted to assess the influence of increasing active material ratios of recycled particles, ranging from 0 % to 100 %, while maintaining a constant overall active material volume fraction. The impact of particle mixing on cathode performance is evaluated by examining transport-relevant geometrical descriptors and effective properties, such as geodesic tortuosity, specific surface area, and tortuosity factor.
25 ENERGY STORAGE↗
Modeling of the Optical Stochastic Cooling at the IOTA Storage Ring Using ELEGANT
In support of the Optical Stochastic Cooling (OSC) experiment at IOTA, we implemented a high-fidelity model of OSC in ELEGANT. The element is generalizable to any OSC experiment and captures three main behaviors; (i) the longitudinal time of flight OSC, (ii) the effects between the transverse motion of particles in the beam and the transverse distribution of undulator radiation, and (iii) the incoherent contributions of neighboring particles. Together these produce a highly accurate model of OSC and were benchmarked using the results from the IOTA OSC experiment.
43 PARTICLE ACCELERATORS↗
Training models using forces computed by stochastic electronic structure methods
Abstract Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enables us to estimate the errors in the model. We conclude with a discussion of future research problems.
Ceperley, David M. (ORCID:0000000150826271)↗
Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties
Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar’s brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.
79 ASTRONOMY AND ASTROPHYSICS↗
ANN-based ground motion model for Turkey using stochastic simulation of earthquakes
SUMMARY Turkey is characterized by a high level of seismic activity attributed to its complex tectonic structure. The country has a dense network to record earthquake ground motions; however, to study previous earthquakes and to account for potential future ones, ground motion simulations are required. Ground motion simulation techniques offer an alternative means of generating region-specific time-series data for locations with limited seismic networks or regions with seismic data gaps, facilitating the study of potential catastrophic earthquakes. In this research, a local ground motion model (GMM) for Turkey is developed using region-specific simulated records, thus constructing a homogeneous data set. The simulations employ the stochastic finite-fault approach and utilize validated input-model parameters in distinct regions, namely Afyon, Erzincan, Duzce, Istanbul and Van. To overcome the limitations of linear regression-based models, artificial neural network is used to establish the form of equations and coefficients. The predictive input parameters encompass fault mechanism (FM), focal depth (FD), moment magnitude (Mw), Joyner and Boore distance (RJB) and average shear wave velocity in the top 30 m (Vs30). The data set comprises 7359 records with Mw ranging between 5.0 and 7.5 and RJB ranging from 0 to 272 km. The results are presented in terms of spectral ordinates within the period range of 0.03–2.0 s, as well as peak ground acceleration and peak ground velocity. The quantification of the GMM uncertainty is achieved through the analysis of residuals, enabling insights into inter- and intra-event uncertainties. The simulation results and the effectiveness of the model are verified by comparing the predicted values of ground motion parameters with the observed values recorded during previous events in the region. The results demonstrate the efficacy of the proposed model in simulating physical phenomena.
Karimzadeh, Shaghayegh (ORCID:0000000337531676)↗
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↗
Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets
Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.
25 ENERGY STORAGE↗