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Results for “Stochastic flow map”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality of the probability space is relatively low. The time-dependent generalized polynomial chaos (TD-gPC) is one such technique that uses an evolving orthogonal basis to better represent the stochastic part of the solution space in time. Here in this paper, we present a new numerical method that uses the concept of enriched stochastic flow maps to track the evolution of the stochastic part of the solution space in time. The computational cost of this proposed flow-driven stochastic chaos (FSC) method is an order of magnitude lower than TD-gPC for comparable solution accuracy. This gain in computational cost is realized because, unlike most existing methods, the number of basis vectors required to track the stochastic part of the solution space does not depend upon the dimensionality of the probability space. Four representative numerical examples are presented to demonstrate the performance of the FSC method for long-time integration of second-order stochastic dynamical systems in the context of stochastic dynamics of structures.

FSC↗
DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗
DOE OSTI2021

Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems

Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time. However, because the random function space is constructed using tensor products, TD-gPC-based methods are known to suffer from the curse of dimensionality. Here, we introduce a new numerical method called the flow-driven spectral chaos (FSC) which overcomes this curse of dimensionality at the random-function-space level. The proposed method is not only computationally more efficient than existing TD-gPC-based methods but is also far more accurate. The FSC method uses the concept of enriched stochastic flow maps to track the evolution of a finite-dimensional random function space efficiently in time. To transfer the probability information from one random function space to another, two approaches are developed and studied herein. In the first approach, the probability information is transferred in the mean-square sense, whereas in the second approach the transfer is done exactly using a new theorem that was developed for this purpose. The FSC method can quantify uncertainties with high fidelity, especially for the long-time response of stochastic dynamical systems governed by ODEs of arbitrary order. Six representative numerical examples, including a nonlinear problem (the Van-der-Pol oscillator), are presented to demonstrate the performance of the FSC method and corroborate the claims of its superior numerical properties. Finally, a parametric, high-dimensional stochastic problem is used to demonstrate that when the FSC method is used in conjunction with Monte Carlo integration, the curse of dimensionality can be overcome altogether.

(nonlinear) stochastic dynamical systems↗
DOE OSTI2022

Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called enriched stochastic flow maps as a means to construct an evolving finite-dimensional random function space that is both accurate and computationally efficient in time. In this paper, we present a multi-element version of the FSC method (the ME-FSC method for short) to tackle (mainly) those dynamical systems that are inherently discontinuous over the probability space. In ME-FSC, the random domain is partitioned into several elements, and then the problem is solved separately on each random element using the FSC method. Subsequently, results are aggregated to compute the probability moments of interest using the law of total probability. To demonstrate the effectiveness of the ME-FSC method in dealing with discontinuities and long-time integration of stochastic dynamical systems, four representative numerical examples are presented in this paper, including the Van-der-Pol oscillator problem and the Kraichnan-Orszag three-mode problem. Results show that the ME-FSC method is capable of solving problems that have strong nonlinear dependencies over the probability space, both reliably and at low computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stochastic reconstruction of fracture network pattern using spatial point processes

Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.

58 GEOSCIENCES↗
DOE OSTI2021

SSRS (Stochastic Soaring Raptor Simulator)

SSRS (Stochastic Soaring Raptor Simulator) is a generalizable, probabilistic, and predictive tool for wind energy developers, ecologists, wildlife managers and industry consultants to estimate the potential for soaring raptors to interact with operating wind turbines, without the need for site-specific data collection. Rapid expansion of wind energy development across the world has exposed the risk of turbine collisions for birds and bats. The risk to obligate soaring raptors such as golden eagles is of particular concern due to their small population and influence on ecological balance. Golden eagles rely heavily on updrafts to subsidize their flight, putting them in direct conflict with operational wind turbines that utilize the same wind resource. Understanding the behavior of soaring raptors with varying atmospheric conditions is crucial for predicting and mitigating the risk of turbine collision. This software contains a predictive movement model that simulates individual flight paths of golden eagles during updraft-subsidized long-distance flight, including migration. For a given set of atmospheric conditions, the model simulates thousands of eagles at turbine-scale spatial resolution (50m) to produce a relative presence density map. The simulated eagles rely on updrafts to pursue uninterrupted directional flight with minimal energy expenditure, following fluid-flow principles. The simulator includes a stochastic model of eagle behavior and a systematic method of accounting for spatiotemporal variations in atmospheric conditions. This framework only requires publicly available atmospheric data to estimate orographic and thermal updrafts, ensuring general usability.

Sandhu, Rimple↗
DOE OSTI2022

Learning the temporal evolution of multivariate densities via normalizing flows

In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced by integrating local or nonlocal Fokker–Planck equations). Here, we analyze this evolution through machine learning assisted construction of a time-dependent mapping that takes a reference distribution (say, a Gaussian) to each and every instance of our evolving distribution. If the reference distribution is the initial condition of a Fokker–Planck equation, what we learn is the time-T map of the corresponding solution. Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time. We demonstrate that this approach can approximate probability density function evolutions in time from observed sampled data for systems driven by both Brownian and Lévy noise. We present examples with two- and three-dimensional, uni- and multimodal distributions to validate the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Evaluation of Two-Dimensional to One-Dimensional Site Response for Idaho National Laboratory

We perform two-dimensional (2D) site response analyses accounting for spatial variability of soil properties and subsurface geometry of the Eastern Snake River Plane (ESRP), and quantify their effects on ground surface motion relative to one-dimensional (1D) site response analyses at the Idaho National Laboratory (INL). We first present the development of random field idealizations of the repeated basalt lava flows, heterogeneously inter-layered with sediments, from seismic velocity data collected over four decades in the ESRP. Using realizations of the stochastic fields mapped on 2D deterministic finite element models, we perform 2D viscoelastic and equivalent-linear wave propagation simulations, and quantify the mean and variance of site response aggravation factors, defined as the response spectral ratio of 2D to 1D analyses on the ground surface. Results are shown to be insensitive to the constitutive material behavior considered here, for strains induced by rock outcrop peak ground acceleration (PGA) as high as 0.7g: viscoelastic and equivalent-linear analyses predict peak mean 2D/1D aggravation factor 1.05 at period T=0.075 sec (i.e. the 2D response spectrum is 5% higher than the corresponding 1D at that period, on average), which corresponds to the wavelength of the horizontal correlation length of the random field (50m). For periods longer than the fundamental period of the site (here, T 1 =0.3125 sec), the propagating wavelengths are too long to be affected by the 1D site response and the aggravation factor becomes equal to 1. The standard deviation of the natural logarithms of the 2D/1D aggravation factors is ~0.15 for periods shorter than the fundamental period of the site, and decays thereafter at a steady rate.

58 GEOSCIENCES↗
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↗
DOE OSTI2020

A statistical model to predict ignition probability

Ignition capability is a critical design constraint for aeronautical gas turbines. However the current trend toward overall lean burn is detrimental to the engine ignition and relight and the ignition system must be adapted to ensure a fast and reliable light-round in all circumstances. As ignition is a stochastic phenomenon, the optimization of an ignition system requires to build ignition probability maps, which is difficult and costly with either experiment or numerical simulation as both require many tests. Here, this work proposes a model to predict the ignition probability map, knowing only flow statistics in non-reacting conditions, i.e., with only one test. The originality of the model is to construct statistics of the flame kernel trajectory, which are then combined with local flow indicators to evaluate the ignition probability at the considered sparking location. Application to a swirled burner operated in premixed, non-premixed and spray combustion modes illustrates the model concepts and demonstrates its ability to recover the experimental ignition map with good accuracy.

42 ENGINEERING↗
DOE OSTI2023

A data-driven framework for permeability prediction of natural porous rocks via microstructural characterization and pore-scale simulation

Understanding the microstructure–property relationships of porous media is of great practical significance, based on which macroscopic physical properties can be directly derived from measurable microstructural informatics. However, establishing reliable microstructure–property mappings in an explicit manner is difficult, due to the intricacy, stochasticity, and heterogeneity of porous microstructures. In this paper, a data-driven computational framework is presented to investigate the inherent microstructure–permeability linkage for natural porous rocks, where multiple techniques are integrated together, including microscopy imaging, stochastic reconstruction, microstructural characterization, pore-scale simulation, feature selection, and data-driven modeling. A large number of 3D digital rocks with a wide porosity range are acquired from microscopy imaging and stochastic reconstruction techniques. A broad variety of morphological descriptors are used to quantitatively characterize pore microstructures from different perspectives, and they compose the raw feature pool for feature selection. Here high-fidelity lattice Boltzmann simulations are conducted to resolve fluid flow passing through porous media, from which reliable permeability references are obtained. The optimal feature set that best represents permeability is identified through a performance-oriented feature selection process, upon which a cost-effective surrogate model is rapidly fitted to approximate the microstructure-permeability mapping via data-driven modeling. This surrogate model exhibits great advantages over empirical/analytical formulas in terms of prediction accuracy and generalization capacity, which can predict reliable permeability values spanning four orders of magnitude. Besides, feature selection also greatly enhances the interpretability of the data-driven prediction model, from which new insights into the mechanism of how microstructural characteristics determine intrinsic permeability are obtained.

58 GEOSCIENCES↗
DOE OSTI2022

Discovering causal structure with reproducing-kernel Hilbert space ε -machines

We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Deep Direct-Use Feasibility Study Reservoir Productivity Uncertainty Analysis for the Tuscarora Sandstone, Morgantown, WV

This dataset contains figures that summarize the Tuscarora Sandstone core permeability data collected from the Preston 119 well in Preston County, WV, and summary results of a stochastic analysis that was used to estimate reservoir productivity for the currently unexplored Tuscarora Sandstone below Morgantown, West Virginia. Uncertainties in reservoir productivity considered the thickness of the reservoir, rock permeability, and fluid viscosity. A Monte Carlo analysis of these uncertain properties was used to predict reservoir flow productivity for the case of a matrix-dominated reservoir, and a fracture-dominated reservoir. These results are summarized in figures, spreadsheets, and maps.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids

In this work, we introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system's behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs

Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models. The geographic extent, spatial heterogeneity, and multiple correlation length scales of the Hanford Site require training a computationally intensive GAN model to thousands of dimensions. We develop a highly optimized implementation that scales to {\herogpucount} NVIDIA Volta GPUs. We develop a hierarchical scheme based on a multi-player game-theoretic approach for exploiting domain parallelism, map discriminators and generators to multiple GPUs, and employ efficient communication schemes to ensure training stability and convergence. Our implementation scales to {\heronodecount} nodes on the Summit supercomputer with a \weakscalingeff\% scaling efficiency, achieving peak and sustained half-precision rates of {\heropeakperf} PF/s and {\herosustainedperf} PF/s.

physics informed ML, machine learning, generative ↗
DOE OSTI2025

Mapping Local Dissipation and Entropy Production in Complex and Active Fluids

While global entropy production provides a measure of irreversibility, its partitioning into contributions from local regions is key to understanding the mechanisms underlying time-reversal symmetry breaking in complex systems and active matter. Here, by analyzing local heat flows and fluxes, we propose a framework that enables the mapping of local dissipation and entropy production in a nonequilibrium system. We test this approach in simulations of fluids driven through complex environments and active systems. We connect the results across the local and global scales by showing that local dissipation and entropy production satisfy a local version of the usual (global) fluctuation theorem, which accounts for the correlations between the local region and its surroundings. Interestingly, in the case of the active fluid, our analysis reveals that these correlations are of opposite signs for the active (stochastic) and passive (deterministic) contributions to local dissipation.

Entropy↗
DOE OSTI2022

Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code

Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

An Efficient Three-Dimensional CFD-Based Numerical Wave Tank for a Wave Energy Converter in Extreme Irregular Waves

A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high-fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not predicted by potential flow engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.

CFD↗