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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions

As simulations of kinetic plasmas continue to increase in scope and complexity, a rigorous and straightforward method for verifying particle-in-cell (PIC) implementations is necessary to ensure their correctness. Here, in this paper, we present a deterministic method for the rigorous verification of multidimensional, multispecies, electrostatic particle-in-cell codes based on the method of manufactured solutions. Specifically, we prove that rigorous verification is possible through the exclusive examination of errors of grid quantities (i.e., moments and/or fields), allowing for a very light-weight and non-intrusive implementation in existing PIC codes. This is a marked improvement over earlier PIC verification approaches (only demonstrated with one species in 1D-1V), which rely on the comparison of cumulative distribution functions, and are invasive on the code base, introduce additional stochastic noise, are significantly more computationally expensive, and lack rigorous convergence properties. Interestingly, we show that different grid quantities feature different rates of convergence with the number of particles and mesh size, impacting the verification process. These theoretical results are confirmed numerically with a multi-species 2D-2V particle-in-cell code, including the ability of the method to detect order reduction due to an incorrect implementation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

A decomposition approach based on meta-heuristics and exact methods for solving a two-stage stochastic biofuel hub-and-spoke network problem

An alternative to the production of fossil transportation fuels is the production of biofuels, particularly, bioethanol. One of the main opportunity areas is the reduction in the overall cost of biofuel. An approach to reduce this cost is to design and implement a supply chain (SC) that considers the quality-related properties of the biomass as well as the economies of scale to minimize the logistics and quality-related costs. This problem is formulated as a hub location problem, which has been classified as an NP-hard problem, thus, meta-heuristics are a suitable approach to solve this problem. We propose a hybrid meta-heuristic solution procedure to solve large-scale instances of a two-stage stochastic biomass-to-biorefinery hub-and-spoke network problem. This solution procedure is proposed to support the large-scale production and distribution of bioethanol by considering the variability in its moisture and ash contents. The hybrid method utilizes a simulated annealing-simplex method to find an initial solution and a tabu search-simplex method to improve the solution. Numerical experimentation was performed on a realistic case study in Texas. The findings demonstrate that the hybrid procedure outperforms the standard L-shaped (LS) method. The meta-heuristic combining simulated annealing and tabu search with the simplex method (SATS-SM) achieved 2.48% lower costs and required 96.57% less time, on average, when compared to the results from using the LS.

09 BIOMASS FUELS↗
DOE OSTI2024

Adaptive tau-leaping methods for microscopic-lattice kinetic Monte Carlo simulations

Traditional Kinetic Monte Carlo (KMC) approaches, rooted in Gillespie’s stochastic simulation algorithm, become computationally demanding in systems with a large range of timescales. The goal of this work is to propose and study new adaptive lattice-KMC time integration strategies for spatially non-uniform systems. To that end, two novel adaptive tau-leaping methods and their corresponding time integration strategies are developed based on the idea of the “n-fold” direct KMC method. These strategies allow for the simultaneous execution of multiple reactions, advancing time by adaptively selected coarse increments. We present numerical experiments comparing the proposed methods with existing approaches in a catalytic surface kinetics application involving ammonia decomposition.

Bimolecular reactions↗
DOE OSTI2017

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Large scale Brownian dynamics of confined suspensions of rigid particles

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217–296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its “square” root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose height above the wall is set by a combination of thermal noise and active flows. We find the existence of two populations of active particles, slower ones closer to the bottom and faster ones above them, and demonstrate that our method provides quantitative accuracy even with relatively coarse resolutions of the particle geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Observer-based H{sub ∞} control for nonlinear Markovian jump systems with time-delay and input saturation

This paper focus on the problem of observer-based H{sub ∞} control for uncertain nonlinear Markovian jump systems with time-delay and actuator saturation. A delay-dependent sufficient condition is proposed which guarantees that the uncertain nonlinear Markovian jump system with time-delay and input saturation is stochastically stable via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region and the design method of observer-based H{sub ∞} controller are given by solving LMIs and convex optimization problems. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Model averaging approaches to data subset selection

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models across different subsets of the data. Two different criteria have been proposed in the literature for how the data subsets should be weighted. We compare the two criteria closely in a unified treatment based on the Kullback-Leibler divergence and conclude that one of them is subtly flawed and will tend to yield larger uncertainties due to loss of information. Here, analytical and numerical examples are provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Model Agnostic Bayesian Framework for Online Anomaly/Event Detection in PMU Data

Phasor measurement units (PMU) are integral to the modernization and automation plan of the electric power industry. A PMU data signature contains system-level events (e.g., faults, generation/load change, etc.) and any measurement/device-related errors. Therefore, the reliable and resilient operation of power systems is equivalent to the quality of the PMU data and the situation awareness provided by its data signature. Despite recent progress, current state-of-the-art methods are not fool-proof and have certain limitations tracing an error/abnormality to sensor sub-components and grid systems. This is because of technical challenges imposed by the scarcity of the labeled information, loss of data quality, and non-stationarity of data. In this paper, we consider the online PMU data stream as an output of a stochastic process and pose the anomaly/event detection as a changepoint detection problem dealing with detecting parameter changes in the underlying stochastic processes. The proposed model-agnostic framework relies on: (a) feature extraction utilizing the minimum volume enclosing ellipsoids (MVEE) method from raw PMU observations and (b) a Bayesian framework of changepoint detection. The validity of the proposed methodology is discussed through numerical experiments on real-world utility-scale PMU data.

Hossain, Ramij Raja↗
DOE OSTI2022

Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. Here this article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

In light of the recently published complete set of statistically correct Grønbech–Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely, the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Finally, numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite Los Alamos Transferable Tight-Binding for Energetics, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time-step-independent stochastic integrators to QMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Modeling electrokinetic flows with the discrete ion stochastic continuum overdamped solvent algorithm

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Herein, several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a “dry diffusion” approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Statistical Distributions for Mesh Independent Solutions in ALEGRA

The representation of material heterogeneity (also referred to as "spatial variation") plays a key role in the material failure simulation method used in ALEGRA. ALEGRA is an arbitrary Lagrangian-Eulerian shock and multiphysics code developed at Sandia National Laboratories and contains several methods for incorporating spatial variation into simulations. A desirable property of a spatial variation method is that it should produce consistent stochastic behavior regardless of the mesh used (a property referred to as "mesh independence"). However, mesh dependence has been reported using the Weibull distribution with ALEGRA's spatial variation method. This report describes efforts towards providing additional insight into both the theory and numerical experiments investigating such mesh dependence. In particular, we have implemented a discrete minimum order statistic model with properties that are theoretically mesh independent.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗