Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models

Stochastic particle-resolved methods have proven useful for simulating multi-dimensional systems such as composition-resolved aerosol size distributions. While particle-resolved methods have substantial benefits for highly detailed simulations, these techniques suffer from high computational cost, motivating efforts to improve their algorithmic efficiency. Here we formulate an algorithm for accelerating particle removal processes by aggregating particles of similar size into bins. We present the Binned Algorithm for particle removal processes and analyze its performance with application to the atmospherically relevant process of aerosol dry deposition. We show that the Binned Algorithm can dramatically improve the efficiency of particle removals, particularly for low removal rates, and that computational cost is reduced without introducing additional error. In simulations of aerosol particle removal by dry deposition in atmospherically relevant conditions, we demonstrate about 50-times increase in algorithm efficiency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A fast exact simulation method for a class of Markov jump processes

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Validation of the Poisson Stochastic Radiative Transfer Model

A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.

Zhuravleva, Tatiana↗
DOE OSTI2014

Multi-scenario modelling of uncertainty in stochastic chemical systems

Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Improved Bayesian Infrasonic Source Localization for regional infrasound

The Bayesian Infrasonic Source Localization (BISL) methodology is examined and simplified providing a generalized method of estimating the source location and time for an infrasonic event and the mathematical framework is used therein. The likelihood function describing an infrasonic detection used in BISL has been redefined to include the von Mises distribution developed in directional statistics and propagation-based, physically derived celerity-range and azimuth deviation models. Frameworks for constructing propagation-based celerity-range and azimuth deviation statistics are presented to demonstrate how stochastic propagation modelling methods can be used to improve the precision and accuracy of the posterior probability density function describing the source localization. Infrasonic signals recorded at a number of arrays in the western United States produced by rocket motor detonations at the Utah Test and Training Range are used to demonstrate the application of the new mathematical framework and to quantify the improvement obtained by using the stochastic propagation modelling methods. Moreover, using propagation-based priors, the spatial and temporal confidence bounds of the source decreased by more than 40 per cent in all cases and by as much as 80 per cent in one case. Further, the accuracy of the estimates remained high, keeping the ground truth within the 99 per cent confidence bounds for all cases.

58 GEOSCIENCES↗
DOE OSTI2014

RADIATION TRANSPORT FOR EXPLOSIVE OUTFLOWS: OPACITY REGROUPING

Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) are methods used to stochastically solve the radiative transport and diffusion equations, respectively. These methods combine into a hybrid transport-diffusion method we refer to as IMC-DDMC. We explore a multigroup IMC-DDMC scheme that in DDMC, combines frequency groups with sufficient optical thickness. We term this procedure ''opacity regrouping''. Opacity regrouping has previously been applied to IMC-DDMC calculations for problems in which the dependence of the opacity on frequency is monotonic. We generalize opacity regrouping to non-contiguous groups and implement this in SuperNu, a code designed to do radiation transport in high-velocity outflows with non-monotonic opacities. We find that regrouping of non-contiguous opacity groups generally improves the speed of IMC-DDMC radiation transport. We present an asymptotic analysis that informs the nature of the Doppler shift in DDMC groups and summarize the derivation of the Gentile-Fleck factor for modified IMC-DDMC. We test SuperNu using numerical experiments including a quasi-manufactured analytic solution, a simple 10 group problem, and the W7 problem for Type Ia supernovae. We find that opacity regrouping is necessary to make our IMC-DDMC implementation feasible for the W7 problem and possibly Type Ia supernova simulations in general. We compare the bolometric light curves and spectra produced by the SuperNu and PHOENIX radiation transport codes for the W7 problem. The overall shape of the bolometric light curves are in good agreement, as are the spectra and their evolution with time. However, for the numerical specifications we considered, we find that the peak luminosity of the light curve calculated using SuperNu is ∼10% less than that calculated using PHOENIX.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Space-Time Reduced-Order Modeling for Uncertainty Quantification

This work focuses on the space-time reduced-order modeling (ROM) method for solving large-scale uncertainty quantification (UQ) problems with multiple random coefficients. In contrast with the traditional space ROM approach, which performs dimension reduction in the spatial dimension, the space-time ROM approach performs dimension reduction on both the spatial and temporal domains, and thus enables accurate approximate solutions at a low cost. We incorporate the space-time ROM strategy with various classical stochastic UQ propagation methods such as stochastic Galerkin and Monte Carlo. Numerical results demonstrate that our methodology has significant computational advantages compared to state-of-the-art ROM approaches. By testing the approximation errors, we show that there is no obvious loss of simulation accuracy for space-time ROM given its high computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Markov stochasticity coordinates

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Measuring alpha eigenvalue of a subcritical system by a intense pulsed neutron source

Intense-Pulsed-Neutron-Source (IPNS) technique is a new approach to measure the subcriticality of a reactor system, which has been theoretically analyzed by us while not been verified in experiment in other reference. In INPS technique the reactivity is derived via the system response to a prompt pulsed neutron source. The method utilizes very intense neutron pulses (about 1010 neutrons/pulse) with the duration ranging from 10 ns to 100 ns, which are generated by the dense plasma focus (DPF) device filled with pure DT mixture as the working gas. The neutron pulse in high intensity provides the opportunity to measure the signal using a scintillator and a photo-multiplier tube (PMT) (the intense pulse radiation measure method) with the flight distance of only twenty centimeters. The attenuation of the dense plasma focus device must be faster than the subcritical system so that the attenuation of the system can be researched. In this paper, after a neutron pulse is injected into the subcritical reactor, the subcriticality is determined by measuring the instantaneous characteristics of the leaking reactor neutron. The Monte Carlo analysis shows that, with the linear arrangement of the dense plasma focus, the subcritical system and the detector, the signal-to-noise ratio at the measure point meets the investigate requirement, in which the 14 MeV neutrons are attenuated by the subcritical system. The detector is close with the subcritical system to reduce the influence of the outer background and the spread of time-of-flight of the neutrons. The measure system utilizing gated detection technology is characterized with fast attenuation time and large linear current, the a value obtained with this method is 2.05 μs{sup -1} while the measurements using the {sup 252}Cf stochastic pulsed source method and the Rossi-a method were 2.18μs{sup -1} and 2.16μs{sup -1}.It showed that the measured result obtained with dense plasma focus instantaneous pulsed source is consistent with those obtained with the other two traditional methods. This new method utilized only a single-shot pulse to determine the a value of the reactor system. Therefore, this quick measure method is recommendable. The influence caused by energy response of the detector should been taken into account since the measured result reflects the time behavior of group particle. The influence is discussed preliminarily in this paper. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2014

A High-Performance Embedded Hybrid Methodology for Uncertainty Quantification With Applications

Multiphysics processes modeled by a system of unsteady differential equations are naturally suited for partitioned (modular) solution strategies. We consider such a model where probabilistic uncertainties are present in each module of the system and represented as a set of random input parameters. A straightforward approach in quantifying uncertainties in the predicted solution would be to sample all the input parameters into a single set, and treat the full system as a black-box. Although this method is easily parallelizable and requires minimal modifications to deterministic solver, it is blind to the modular structure of the underlying multiphysical model. On the other hand, using spectral representations polynomial chaos expansions (PCE) can provide richer structural information regarding the dynamics of these uncertainties as they propagate from the inputs to the predicted output, but can be prohibitively expensive to implement in the high-dimensional global space of uncertain parameters. Therefore, we investigated hybrid methodologies wherein each module has the flexibility of using sampling or PCE based methods of capturing local uncertainties while maintaining accuracy in the global uncertainty analysis. For the latter case, we use a conditional PCE model which mitigates the curse of dimension associated with intrusive Galerkin or semi-intrusive Pseudospectral methods. After formalizing the theoretical framework, we demonstrate our proposed method using a numerical viscous flow simulation and benchmark the performance against a solely Monte-Carlo method and solely spectral method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Linear regulator design for stochastic systems by a multiple time-scales method

This short paper develops a hierarchically structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short-period modes of the longitudinal dynamics of the F-8 aircraft.

Teneketzis, D.↗
DOE OSTI2024

Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations

Here, we present an approach for GW calculations of quasiparticle energies with quasi-quadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS 2 bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Robustness analysis of an air heating plant and control law by using polynomial chaos

This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputs (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

An investigation of Newton-Sketch and subsampled Newton methods

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Impact of parametric uncertainty on estimation of the energy deposition into an irradiated brain tumor

Predictions of the total energy deposited into a brain tumor through X-ray irradiation are notoriously error-prone. We investigate how this predictive uncertainty is affected by uncertainty in both the location of the region occupied by a dose-enhancing iodinated contrast agent and the agent's concentration. This is done within the probabilistic framework in which these uncertain parameters are modeled as random variables. We employ the stochastic collocation (SC) method to estimate statistical moments of the deposited energy in terms of statistical moments of the random inputs, and the global sensitivity analysis (GSA) to quantify the relative importance of uncertainty in these parameters on the overall predictive uncertainty. A nonlinear radiation–diffusion equation dramatically magnifies the coefficient of variation of the uncertain parameters, yielding a large coefficient of variation for the predicted energy deposition. This demonstrates that accurate prediction of the energy deposition requires a proper treatment of even small parametric uncertainty. Our analysis also reveals that SC outperforms standard Monte Carlo, but its relative efficiency decreases as the number of uncertain parameters increases from one to three. A robust GSA ameliorates this problem by reducing this number.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Stochastically Realized Observables for Excitonic Molecular Aggregates

In this work, we show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as $\mathcal{O}$($N$ 3 ) for $N$ dye molecules. Our approach scales much more efficiently as $\mathcal{O}$($N$ log($N$)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗