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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP's) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space Double-Struck-Capital-R {sup n}. The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter {epsilon}>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as {epsilon} goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as {epsilon} goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Linearization Techniques for Controlled Piecewise Deterministic Markov Processes; Application to Zubov's Method

We aim at characterizing domains of attraction for controlled piecewise deterministic processes using an occupational measure formulation and Zubov's approach. Firstly, we provide linear programming (primal and dual) formulations of discounted, infinite horizon control problems for PDMPs. These formulations involve an infinite-dimensional set of probability measures and are obtained using viscosity solutions theory. Secondly, these tools allow to construct stabilizing measures and to avoid the assumption of stability under concatenation for controls. The domain of controllability is then characterized as some level set of a convenient solution of the associated Hamilton-Jacobi integral-differential equation. The theoretical results are applied to PDMPs associated to stochastic gene networks. Explicit computations are given for Cook's model for gene expression.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product, the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Deterministic skill of ENSO predictions from the North American Multimodel Ensemble

Hindcasts and real-time predictions of the east-central tropical Pacific sea surface temperature (SST) from the North American Multimodel Ensemble (NMME) system are verified for 1982–2015. Skill is examined using two deterministic verification measures: mean squared error skill score (MSESS) and anomaly correlation. Verification of eight individual models shows somewhat differing skills among them, with some models consistently producing more successful predictions than others. The skill levels of MME predictions are approximately the same as the two best performing individual models, and sometimes exceed both of them. A decomposition of the MSESS indicates the presence of calibration errors in some of the models. In particular, the amplitudes of some model predictions are too high when predictability is limited by the northern spring ENSO predictability barrier and/or when the interannual variability of the SST is near its seasonal minimum. The skill of the NMME system is compared to that of the MME from the IRI/CPC ENSO prediction plume, both for a comparable hindcast period and also for a set of real-time predictions spanning 2002–2011. Comparisons are made both between the MME predictions of each model group, and between the average of the skills of the respective individual models in each group. Acknowledging a hindcast versus real-time inconsistency in the 2002–2012 skill comparison, the skill of the NMME is slightly higher than that of the prediction plume models in all cases. This result reflects well on the NMME system, with its large total ensemble size and opportunity for possible complementary contributions to skill.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

On the Validity of Linear Response Theory in High-Dimensional Deterministic Dynamical Systems

This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory’s assumptions. Here we provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We introduce an exemplary model in which observables of resolved degrees of freedom are weakly coupled to a large, inhomogeneous collection of unresolved chaotic degrees of freedom. By employing statistical limit laws we give conditions under which such systems obey linear response theory even if all the degrees of freedom individually violate linear response. We corroborate our result with numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics

Presented is a system of four ordinary differential equations and a mathematical analysis of microbiological experiments in a four-component chemostat—nutrient n, rods r, cocci c, and predators p. The analysis is consistent with the conclusion that previous experiments produced features of deterministic chaotic and classical dynamics depending on dilution rate. The surrogate model incorporates as much experimental detail as possible, but necessarily contains unmeasured parameters. The objective is to understand better the differences between model simulations and experimental results in complex microbial populations. The key methodology for simulation of chaotic dynamics, consistent with the measured dilution rate and microbial volume averages, was to cause the preference of p for r vs. c to vary with the r and c concentrations, to make r more competitive for nutrient than c, and to recycle some dying p biomass, leading to a modified version of the Monod kinetics model. Our mathematical model demonstrated that the occurrence of chaotic dynamics requires a predator, p, preference for r versus c to increase significantly with increases in r and c populations. Also included is a discussion of several generalizations of the existing model and a possible involvement of the minimum energy dissipation principle. This principle appears fundamental to thermodynamic systems including living systems. Several new experiments are suggested.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Deterministically estimated fission source distributions for Monte Carlo k-eigenvalue problems

The standard Monte Carlo (MC) k-eigenvalue algorithm involves iteratively converging the fission source distribution using a series of potentially time-consuming inactive cycles before quantities of interest can be tallied. One strategy for reducing the computational time requirements of these inactive cycles is the Sourcerer method, in which a deterministic eigenvalue calculation is performed to obtain an improved initial guess for the fission source distribution. This method has been implemented in the Exnihilo software suite within SCALE using the SPNSPN or SNSN solvers in Denovo and the Shift MC code. The efficacy of this method is assessed with different Denovo solution parameters for a series of typical k-eigenvalue problems including small criticality benchmarks, full-core reactors, and a fuel cask. Here it is found that, in most cases, when a large number of histories per cycle are required to obtain a detailed flux distribution, the Sourcerer method can be used to reduce the computational time requirements of the inactive cycles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Calculation of multi-group migration areas in deterministic transport simulations

Recent work on the Cumulative Migration Method (CMM) has demonstrated that it is possible to define multi-group transport cross sections directly from Monte Carlo spectral calculations by utilizing edits of the energy-dependent neutron migration areas. However, it is difficult to demonstrate that downstream deterministic transport calculations actually preserve Monte Carlo migration areas. This paper addresses this issue by: 1) demonstrating the relationship of migration area with the concept of mean squared displacement, 2) deriving, and validating vs. Monte Carlo, an analytic expression for computing one-group migration areas for a homogeneous medium with energy-independent cross sections, 3) deriving, and validating vs. Monte Carlo, an analytic expression for computing multi-group migration areas for a homogenized medium with energy-dependent cross sections, and 4) rigorously proving that energy condensation of multi-group transport cross section must be inverse flux weighted in order to preserve Monte Carlo neutron migration areas.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Home energy management under realistic and uncertain conditions: A comparison of heuristic, deterministic, and stochastic control methods

We report home energy management systems (HEMS) have been shown to reduce energy bills and to provide grid services including peak demand reduction and demand flexibility. However, uncertainty in residential energy systems is a significant issue and can reduce the benefits of a HEMS to the homeowner or grid operator. Sources of uncertainty include weather forecasts, predictions of energy-related occupant activities (e.g., hot water draws), and parameter estimation for the building envelope and energy-consuming equipment. This paper tackles the problem of uncertainty by developing a framework that simulates HEMS in uncertain conditions and evaluates the performance of multiple control strategies. A linear, reduced-order residential building model for model predictive control applications is derived and compared to a full-order model. Stochastic model predictive control is shown to perform better than deterministic and heuristic methods when considering realistic forecasts with uncertainty. The framework can evaluate the performance of HEMS in real-world applications, which can help de-risk HEMS deployment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is combining the augmented Lagrangian framework with adaptive sampling, resulting in an efficient optimization methodology validated with practical examples. To achieve the presented efficiency, here we consider inexact solutions for the augmented Lagrangian subproblems, and through an adaptive sampling mechanism, we control the variance in the gradient estimates. Furthermore, we analyze the theoretical performance of the proposed scheme by showing equivalence to a gradient descent algorithm on a Moreau envelope function, and we prove sublinear convergence for convex objectives and linear convergence for strongly convex objectives with affine equality constraints. The worst-case sample complexity of the resulting algorithm, for an arbitrary choice of penalty parameter in the augmented Lagrangian function, is $\mathscr{O}$(ϵ -3-δ ) , where ϵ > 0 is the expected error of the solution and δ > 0 is a user-defined parameter. If the penalty parameter is chosen to be $\mathscr{O}$(ϵ -1 ), we demonstrate that the result can be improved to $\mathscr{O}$(ϵ -2 ) , which is competitive with the other methods employed in the literature. Moreover, if the objective function is strongly convex with affine equality constraints, we obtain $\mathscr{O}$(ϵ -1 log(1/ϵ)) complexity. Finally, we empirically verify the performance of our adaptive sampling augmented Lagrangian framework in machine learning optimization and engineering design problems, including topology optimization of a heat sink with environmental uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A sharp interface model for deterministic simulation of dendrite growth

A high order level set model is developed for deterministic simulation of dendritic growth in unstable solidifying systems. The model captures motion of the front implicitly on a structured finite difference grid, enables calculation of its geometric properties and also applies boundary conditions on the immersed interface. Interfacial capillary effect is incorporated in the model through the Gibbs-Thomson condition. Canonical problems for evaluating grid convergence of the numerical method and validation tests for stability of a growing nucleus in the presence of isotropic surface tension are presented. The growth morphology of solidifying nuclei in undercooled metallic melts is quantitatively analyzed. Effects of crystal anisotropy and melt undercooling on the front geometry, propagation speed and formation of branched dendritic structures are examined. In conclusion, the complex morphological changes, such as remelting of secondary perturbations under specific conditions of undercooling, are also captured during the quantitative analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2018

NSTX-U advances in real-time deterministic PCIe-based internode communication

Distributing control mechanisms across modern commercial off the shelf (COTS) GNU/Linux systems often introduces difficult to mitigate non-deterministic behavior. Existing methods to address this problem involve non-real-time technologies such as Remote Direct Memory Access (RDMA) over Infiniband or custom Ethernet solutions, such as RDMA over Converged Ethernet (RoCE) or userspace Ethernet drivers, that trade determinism for ease of use or lower cost. The National Spherical Torus Experiment Upgrade (NSTX-U) is pursuing a new design that allows direct communication between heterogeneous systems with scalable, microsecond latency with 1 μs of jitter on that latency, outside of the constant transmission delay at the physical layer. The future design of the NSTX-U Real-time Communication System will utilize direct PCIe-to-PCIe communication with kernel support tuned for low overhead, allowing two (or more, through a switch) real-time (RT) systems to communicate and share resources as one larger entity. As a result, this greatly increases the processing capability of the primary Plasma Control System (PCS), turning previously insurmountable computational challenges into a more manageable divide and conquer parallel task.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

Discretization errors in molecular dynamics simulations with deterministic and stochastic thermostats

We investigate the influence of numerical discretization errors on computed averages in a molecular dynamics simulation of TIP4P liquid water at 300 K coupled to different deterministic (Nose-Hoover and Nose-Poincare) and stochastic (Langevin) thermostats. We propose a couple of simple practical approaches to estimating such errors and taking them into account when computing the averages. We show that it is possible to obtain accurate measurements of various system quantities using step sizes of up to 70% of the stability threshold of the integrator, which for the system of TIP4P liquid water at 300 K corresponds to the step size of about 7 fs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S{sub n}) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A multigroup moment-accelerated deterministic particle solver for 1-D time-dependent thermal radiative transfer problems

We introduce an efficient, robust, Lagrangian (characteristic-based) transport solver for 1-D time-dependent thermal radiative transfer (TRT) applications within the context of a moment-accelerated (High-Order/Low-Order, HOLO) algorithm. This novel transport algorithm inherits the best features of both particle methods (e.g., time accuracy, phase-space adaptivity, positivity) and deterministic, grid-based methods (e.g., no stochastic noise). Particles are adapted by the method of characteristics, with a time-dependent weight that accounts for stiff absorption and reemission process self-consistently. As a result, this approach is able to obtain accurate results while employing large time steps and a moderate number of particles (compared to Implicit Monte Carlo).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2026

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗