Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic sampling”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Improved Fast Randomized Iteration Approach to Full Configuration Interaction

In this work, we present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method’s performance for Ne, H 2 O, and N 2 . The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semistochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.

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

Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function

Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

42 ENGINEERING↗
DOE OSTI2021

A Binomial Stochastic Framework for Efficiently Modeling Discrete Statistics of Convective Populations

Abstract Understanding the coupling between convective clouds and the general circulation, as well as addressing the gray zone problem in convective parameterization, requires insight into the genesis and maintenance of spatial patterns in cumulus cloud populations. In this study, a simple toy model for recreating populations of interacting convective objects as distributed over a two‐dimensional Eulerian grid is formulated to this purpose. Key elements at the foundation of the model include i) a fully discrete formulation for capturing discrete behavior in convective properties at small population sample sizes, ii) object age‐dependence for representing life‐cycle effects, and iii) a prognostic number budget allowing for object interactions and co‐existence of multiple species. A primary goal is to optimize the computational efficiency of this system. To this purpose the object birth rate is represented stochastically through a spatially aware Bernoulli process. The same binomial stochastic operator is applied to horizontal advection of objects, conserving discreteness in object number. The applicability to atmospheric convection as well as behavior implied by the formulation is assessed. Various simple applications of the BiOMi model (Binomial Objects on Microgrids) are explored, suggesting that important convective behavior can be captured at low computational cost. This includes i) subsampling effects and associated powerlaw scaling in the convective gray zone, ii) stochastic predator‐prey behavior, iii) the downscale turbulent energy cascade, and iv) simple forms of spatial organization and convective memory. Consequences and opportunities for convective parameterization in next‐generation weather and climate models are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Astrophysical Insights into Radial Velocity Jitter from an Analysis of 600 Planet-search Stars

Radial velocity (RV) detection of planets is hampered by astrophysical processes on the surfaces of stars that induce a stochastic signal, or “jitter,” which can drown out or even mimic planetary signals. Here, we empirically and carefully measure the RV jitter of more than 600 stars from the California Planet Search sample on a star by star basis. As part of this process, we explore the activity–RV correlation of stellar cycles and include appendices listing every ostensibly companion-induced signal we removed and every activity cycle we noted. We then use precise stellar properties from Brewer et al. to separate the sample into bins of stellar mass and examine trends with activity and with evolutionary state. We find that RV jitter tracks stellar evolution and that in general, stars evolve through different stages of RV jitter: the jitter in younger stars is driven by magnetic activity, while the jitter in older stars is convectively driven and dominated by granulation and oscillations. We identify the “jitter minimum”—where activity-driven and convectively driven jitter have similar amplitudes—for stars between 0.7 and 1.7 M {sub ⊙} and find that more-massive stars reach this jitter minimum later in their lifetime, in the subgiant or even giant phases. Finally, we comment on how these results can inform future RV efforts, from prioritization of follow-up targets from transit surveys like TESS to target selection of future RV surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

In this study, we analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

42 ENGINEERING↗
DOE OSTI2024

A variance deconvolution estimator for efficient uncertainty quantification in Monte Carlo radiation transport applications

Monte Carlo simulations are at the heart of many high-fidelity simulations and analyses for radiation transport systems. As is the case with any complex computational model, it is important to propagate sources of input uncertainty and characterize how they affect model output. Unfortunately, uncertainty quantification (UQ) is made difficult by the stochastic variability that Monte Carlo transport solvers introduce. The standard method to avoid corrupting the UQ statistics with the transport solver noise is to increase the number of particle histories, resulting in very high computational costs. In this contribution, we propose and analyze a sampling estimator based on the law of total variance to compute UQ variance even in the presence of residual noise from Monte Carlo transport calculations. Here, we rigorously derive the statistical properties of the new variance estimator, compare its performance to that of the standard method, and demonstrate its use on neutral particle transport model problems involving both attenuation and scattering physics. We illustrate, both analytically and numerically, the estimator’s statistical performance as a function of available computational budget and the distribution of that budget between UQ samples and particle histories. We show analytically and corroborate numerically that the new estimator is unbiased, unlike the standard approach, and is more accurate and precise than the standard estimator for the same computational budget.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. Risk measures combine objective probabilities with the subjective values of a decision maker to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical approximations obtained from the training data. These surrogate models limit over-confidence in reliability and safety assessments and produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to a stakeholder’s risk preferences and then present an approach, based on stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. Our surrogate models include biases that permit them to conservatively estimate the target risk measures. We provide theoretical results that show that these biases decay at the same rate as the L 2 error in the surrogate model. Numerical demonstrations confirm that risk-adapted surrogate models do indeed overestimate the target risk measures while converging at the expected rate.

42 ENGINEERING↗
DOE OSTI2020

Energy Storage Sizing and Operation of an Integrated Utility-Scale PV+ESS Power Plant

Integration of an energy storage system (ESS) into a large-scale grid-connected photovoltaic (PV) power plant is highly desirable to improve performance of the system and overcome the stochastic nature of PV power generation. Algorithms to size ESS within an integrated PV and ESS ( PV+ESS) power plant, conventionally, require a large number of high-resolution samples of PV generation. These algorithms are computationally expensive. In this paper, a two-day optimization algorithm that utilizes n-step constant power output dispatch every day from the PV+ESS power plant is proposed to size the ESS. Additionally, an n-step power dispatch every day through the one-year timeframe based optimization of the size of ESS is also performed. The proposed methods are computationally cheaper and provide acceptable accuracy with respect to the conventional sizing methods. The economics identified from the proposed methods are compared with the typical day-ahead hourly dispatch-based power production from the PV+ESS power plant. This comparison has shown similar economic performance showcasing the accuracy of the proposed methods in sizing the ESS. It also shows the potential for operating PV+ESS power plant in n-step constant power generation mode.

Xia, Qian↗
DOE OSTI2022

Random field optimization

Herein we present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Improved performance of stellarator coil design optimization

Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Embedded training of neural-network subgrid-scale turbulence models

We report that the weights of a deep neural-network model are optimized in conjunction with the governing flow equations to provide a model for subgrid-scale stresses in a temporally developing plane turbulent jet at Reynolds number Re 0 = 6000 . The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier-Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered subgrid-scale stresses, without the constraint of being embedded within the flow equations during the training, fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

42 ENGINEERING↗
DOE OSTI2022

A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Surrogate Modeling For Efficiently Accurately and Conservatively Estimating Measures of Risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L 2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dynamical Mass Estimates of the β Pictoris Planetary System through Gaussian Process Stellar Activity Modeling

Nearly 15 yr of radial velocity (RV) monitoring and direct imaging enabled the detection of two giant planets orbiting the young, nearby star β Pictoris. The δ Scuti pulsations of the star, which overwhelm planetary signals, need to be carefully suppressed. In this work, we independently revisit the analysis of the RV data following a different approach than available in the literature to model the activity of the star. We show that a Gaussian process (GP) with a stochastically driven damped harmonic oscillator kernel can model the δ Scuti pulsations. It provides similar results to parametric models but with a simpler framework, using only three hyperparameters. It also enables us to model poorly sampled RV data that were excluded from previous analyses, hence extending the RV baseline by nearly five years. Altogether, the orbit and mass of both planets can be constrained from RV only, which was not possible with the parametric modeling. To characterize the system more accurately, we also perform a joint fit of all available relative astrometry and RV data. Our orbital solutions for β Pic b favor a low eccentricity of 0.029$_{−0.024}^{+0.061}$ and a relatively short period of 21.1$_{−0.8}^{+2.0}$ yr. The orbit of β Pic c is eccentric with 0.206$_{−0.063}^{+0.074}$ with a period of 3.36 ± 0.03 yr. We find model-independent masses of 11.7 ± 1.4 and 8.5 ± 0.5 M Jup for β Pic b and c, respectively, assuming coplanarity. The mass of β Pic b is consistent with the hottest start evolutionary models, at an age of 25 ± 3 Myr. A direct detection of β Pic c would provide a second calibration measurement in a coeval system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Efficient Bayesian inference with latent Hamiltonian neural networks in No-U-Turn Sampling

When sampling for Bayesian inference, one popular approach in the computational field is to use Hamiltonian Monte Carlo (HMC) and specifically the No-U-Turn Sampler (NUTS), which automatically decides the end time of the Hamiltonian trajectory. However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice when relying on computationally expensive forward models. We propose Latent Hamiltonian neural networks (L-HNNs) with HMC and NUTS for solving Bayesian inference problems. Once trained, L-HNNs do not require numerical gradients of the target density during sampling, and hence numerous evaluations of the forward computational model. Moreover, L-HNNs satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well-suited for use within HMC and NUTS because stationarity can be shown. We also propose the integration of L-HNNs in an online error monitoring scheme, in which numerical gradients of the target density are used for a few samples whenever the L-HNNs prediction errors are large. This online error monitor scheme prevents sample degeneracy in regions of low probability density and ensures robust uncertainty quantification. We demonstrate L-HNNs in NUTS with online error monitoring on several analytical examples involving complex, heavy-tailed, and high-local-curvature probability densities. We then demonstrate the applicability of L-HNNs in NUTS to two computational case studies, namely the Allen-Cahn stochastic partial differential equation and an elliptic partial differential equation with 25 and 50 inference parameters, respectively. Overall, the L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. In conclusion, compared to traditional NUTS, L-HNNs in NUTS with online error monitoring required 1–2 orders of magnitude fewer numerical gradients of the target density and improved the effective sample size (ESS) per gradient (which is a measure of both the sampling quality and the computational expense) by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assembly of the Populus Microbiome Is Temporally Dynamic and Determined by Selective and Stochastic Factors

Recent work shows that the plant microbiome, particularly the initial assembly of this microbiome, influences plant health, survival, and fitness. Here, we characterize the initial assembly of the Populus microbiome across ten genotypes belonging to two poplar species in a common garden using 16S rRNA gene and ITS2 region amplicon sequencing of the leaf endosphere, leaf surface, root endosphere, and rhizosphere. We sampled these microbiomes three times throughout the first growing season and found that the composition of the microbiome changed dramatically over time across all plant-associated habitats and host genotypes. For archaea and bacteria, these changes were dominated by strong homogenizing selection (accounting for 29 to 62% of pairwise comparisons). However, fungal assembly was generally characterized by multiple ecological assembly processes (i.e., a mix of weak selective and dispersal processes). Interestingly, genotype, while a significant moderator of microbiome composition, generally explained less variation than sample date across plant-associated habitats. We defined a set of core genera that accounted for, on average, 36% of the microbiome. The relative abundance of this core community was consistent over time. Additionally, using source tracking modeling, we determined that new microbial taxa colonize from both aboveground and belowground sources, and combined with our ecological assembly null models, we found that both selective and dispersal processes explained the differences between exo- (i.e., leaf surface and rhizosphere) and endospheric microbiomes. Taken together, our results suggest that the initial assembly of the Populus microbiome is time-, genotype-, and habitat-dependent and is moderated by both selective and stochastic factors.

16S rRNA↗
DOE OSTI2022

Physics-Informed Sparse Gaussian Process for Probabilistic Stability Analysis of Large-Scale Power System with Dynamic PVs and Loads

This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.

24 POWER TRANSMISSION AND DISTRIBUTION↗