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Results for “Monte Carlo Sampling”

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All sources NASA NTRS DOE OSTI

DOE OSTI2016

Efficient Uncertainty Quantification in Stochastic Economic Dispatch

Stochastic economic dispatch models usually address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate evaluations of expectations or higher order moments for quantities of interest, e.g., generating cost, can require a prohibitively large number of samples. We propose an alternative to Monte Carlo sampling based on polynomial chaos expansions. These representations enable efficient and accurate propagation of uncertainties in model parameters, using sparse quadrature methods. Furthermore, we use Karhunen-Loève expansions for efficient representation of uncertain renewable energy generation that follows geographical and temporal correlations derived from historical data at each wind farm. Considering expected production cost, we show that the proposed approach can yield several orders of magnitude reduction in computational cost for solving stochastic economic dispatch relative to Monte Carlo sampling, for a given target error threshold.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2014

Advanced probabilistic risk analysis using RAVEN and RELAP-7

RAVEN, under the support of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program [1], is advancing its capability to perform statistical analyses of stochastic dynamic systems. This is aligned with its mission to provide the tools needed by the Risk Informed Safety Margin Characterization (RISMC) path-lead [2] under the Department Of Energy (DOE) Light Water Reactor Sustainability program [3]. In particular this task is focused on the synergetic development with the RELAP-7 [4] code to advance the state of the art on the safety analysis of nuclear power plants (NPP). The investigation of the probabilistic evolution of accident scenarios for a complex system such as a nuclear power plant is not a trivial challenge. The complexity of the system to be modeled leads to demanding computational requirements even to simulate one of the many possible evolutions of an accident scenario (tens of CPU/hour). At the same time, the probabilistic analysis requires thousands of runs to investigate outcomes characterized by low probability and severe consequence (tail problem). The milestone reported in June of 2013 [5] described the capability of RAVEN to implement complex control logic and provide an adequate support for the exploration of the probabilistic space using a Monte Carlo sampling strategy. Unfortunately the Monte Carlo approach is ineffective with a problem of this complexity. In the following year of development, the RAVEN code has been extended with more sophisticated sampling strategies (grids, Latin Hypercube, and adaptive sampling). This milestone report illustrates the effectiveness of those methodologies in performing the assessment of the probability of core damage following the onset of a Station Black Out (SBO) situation in a boiling water reactor (BWR). The first part of the report provides an overview of the available probabilistic analysis capabilities, ranging from the different types of distributions available, possible sampling strategies, and post processing analysis capabilities. The first part of the report provides an extensive description of two major developments introduced this year: adaptive sampling for limit surface sampling and multi variate distributions. The document concludes with a description of the demo case (BWR-SBO) and a discussion of the results obtained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Empirical investigation of nuclear correlation function distributions in lattice QCD

Two-point correlation functions of systems with baryon number 𝐵 ∈ {1,2,3,4} are investigated using lattice quantum chromodynamics (QCD). In particular, the empirical distributions of importance-sampling Monte-Carlo samples of these correlation functions are examined as a function of the spacetime separation between the two points and the baryon number. While the exact forms of these distributions are not known for QCD, recent work has determined asymptotic expressions for analogous correlation function distributions in simpler theories such as scalar field theory and the disordered phase of the 𝑂⁡(𝑁) model. The theoretical 𝑂⁡(𝑁) model distributions are found to provide an accurate description of the empirical QCD distributions at zero momentum over a wide range of temporal separations for each baryon number when assessed with a range of different statistical tests. In particular, the behavior of the baryon number 𝐵 QCD correlation function at large temporal separation is well reproduced by the 𝑂⁡(𝑁 ∼ 2/𝐵) model distribution.

Lattice field theory↗

DOE OSTI2016

Multilevel ensemble Kalman filtering

This study embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. Finally, the resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.

ltering↗

DOE OSTI2024

Correlation function distributions for O ( N ) lattice field theories in the disordered phase

Numerical computations in strongly interacting quantum field theories are often performed using Monte Carlo sampling methods. A key task in these calculations is to estimate the value of a given physical quantity from the distribution of stochastic samples that are generated using the Monte Carlo method. Typically, the sample mean and sample variance are used to define the expectation values and uncertainties of computed quantities. However, the Monte Carlo sample distribution contains more information than these basic properties, and it is useful to investigate it more generally. In this work, the exact form of the probability distributions of two-point correlation functions at zero momentum in O ( N ) lattice field theories in the disordered phase and in infinite volume are determined. These distributions allow for a robust investigation of the efficacy of the Monte Carlo sampling procedure and are shown also to allow for improved estimators of the target physical quantity to be constructed. The theoretical expectations are shown to agree with numerical calculations in the O ( 2 ) model. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2025

Quantitative Modeling of High-Energy Electron Scattering in Thick Samples Using Monte Carlo Techniques

Cryo-electron microscopy (cryo-EM) is a powerful tool for imaging biological samples but is typically limited by sample thickness, which is restricted to a few hundred nanometers depending on the electron energy. However, there is a growing need for imaging techniques capable of studying biological samples up to 10 µm in thickness while maintaining nanoscale resolution. This need motivates the use of mega-electron-volt scanning transmission electron microscopy (MeV-STEM), which leverages the high penetration power of MeV electrons to generate high-resolution images of thicker samples. In this study, we employ Monte Carlo simulations to model electron–sample interactions and explore the signal decay of imaging electrons through thick specimens. By incorporating material properties, interaction cross-sections for energy loss, and experimental parameters, we investigate the relationship between the incident and transmitted beam intensities. Key factors such as detector collection angle, convergence semi-angle, and the material properties of samples were analyzed. Our results demonstrate that the relationship between incident and transmitted beam intensities follows the Beer–Lambert law over thicknesses ranging from a few microns to several tens of microns, depending on material composition, electron energy, and collection angles. The linear depth of silicon dioxide reaches 3.9 µm at 3 MeV, about 6 times higher than that at 300 keV. Meanwhile, the linear depth of amorphous ice reaches 17.9 µm at 3 MeV, approximately 11.5 times higher than that at 300 keV. These findings are crucial for advancing the study of thick biological and semiconductor samples using MeV-STEM.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Sensitivity Analyses for Monte Carlo Sampling-Based Particle Simulations

Computational design-based optimization is a well-used tool in science and engineering. Our report documents the successful use of a particle sensitivity analysis for design-based optimization within Monte Carlo sampling-based particle simulation—a currently unavailable capability. Such a capability enables the particle simulation communities to go beyond forward simulation and promises to reduce the burden on overworked analysts by getting more done with less computation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

MCCCS-MN

The MCCCS‒MN (Monte Carlo for Complex Chemical Systems‒Minnesota) software is developed by the Siepmann research group at the University of Minnesota. MCCCS‒MN allows for the simulation of multi-component molecular systems in the canonical, isobaric-isothermal (including constant stress for solids), grand-canonical, semi-grand, and Gibbs (NVT, NPT, and more than two simulation boxes) ensembles. It uses the configurational-bias Monte Carlo method to efficiently sample phase space for linear, branched and cyclic chain molecules, the adiabatic nuclear and electronic sampling Monte Carlo method to treat many-body polarization effects, and the aggregation-volume-bias Monte Carlo algorithm to efficiently sample the spatial distribution of associating molecules. MCCCS-MN employs a molecular representation of the system where force fields contain bonded and non-bonded terms. Funding for the development of MCCCS-MN through grants from the National Science Foundation (simulation of fluid phase equilibria and chromatography) and the Department of Energy (simulation of adsorption equilibria) is gratefully acknowledged.

Siepmann, J.Ilja [University of Minnesota - Twin C↗

DOE OSTI2026

Renovating Monte Carlo Methods and Codebases with Generative Models

The code will implement a standardized interface for Monte Carlo sampling methods, including conventional techniques, and going beyond current available packages to also incorporate generative model-enabled Monte Carlo sampling to provide a unified framewor

Garcia-Cardona, Cristina↗

DOE OSTI2019

Analytical Approach to Evaluate Uncertainty in Discharged Inventory Estimates at the Hanford Site - 19012

Many waste sites (>400) located within the Central Plateau portion of the Hanford Site received liquid discharges during the nuclear weapons material production mission (1944-1988). The Hanford Soil Inventory Model (SIM) is developed to quantitatively evaluate the discharged inventory for important radionuclides and chemicals at a given waste site to support fate and transport modeling of contaminants. An analytic approach was developed to estimate inventory and associated uncertainty. The approach was implemented for SIM and compared to a prior stochastic implementation applying a Monte-Carlo sampling approach. The analytic approach provides exact mean and variance results and the run times are much faster compared to the Monte-Carlo sampling approach. With the improved solution method using the analytical approach, it is feasible to run inventory updates and reduce associated uncertainty ranges. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2015

Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

RESOLVE AND ECO: THE HALO MASS-DEPENDENT SHAPE OF GALAXY STELLAR AND BARYONIC MASS FUNCTIONS

In this work, we present galaxy stellar and baryonic (stars plus cold gas) mass functions (SMF and BMF) and their halo mass dependence for two volume-limited data sets. The first, RESOLVE-B, coincides with the Stripe 82 footprint and is extremely complete down to baryonic mass M {sub bary} ∼ 10{sup 9.1} M {sub ⊙}, probing the gas-rich dwarf regime below M {sub bary} ∼ 10{sup 10} M {sub ⊙}. The second, ECO, covers a ∼40× larger volume (containing RESOLVE-A) and is complete to M {sub bary} ∼ 10{sup 9.4} M {sub ⊙}. To construct the SMF and BMF we implement a new “cross-bin sampling” technique with Monte Carlo sampling from the full likelihood distributions of stellar or baryonic mass. Our SMFs exhibit the “plateau” feature starting below M {sub star} ∼ 10{sup 10} M {sub ⊙} that has been described in prior work. However, the BMF fills in this feature and rises as a straight power law below ∼10{sup 10} M {sub ⊙}, as gas-dominated galaxies become the majority of the population. Nonetheless, the low-mass slope of the BMF is not as steep as that of the theoretical dark matter halo MF. Moreover, we assign group halo masses by abundance matching, finding that the SMF and BMF, separated into four physically motivated halo mass regimes, reveal complex structure underlying the simple shape of the overall MFs. In particular, the satellite MFs are depressed below the central galaxy MF “humps” in groups with mass <10{sup 13.5} M {sub ⊙} yet rise steeply in clusters. Our results suggest that satellite destruction and stripping are active from the point of nascent group formation. We show that the key role of groups in shaping MFs enables reconstruction of a given survey’s SMF or BMF based on its group halo mass distribution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Denoising Autoencoder for Reconstructing Sensor Observation Data and Predicting Evapotranspiration: Noisy and Missing Values Repair and Uncertainty Quantification

Abstract Machine learning (ML) methods applied in scientific research often deal with interrelated features in high‐dimensional data. Reducing data noise and redundancy is needed to increase prediction accuracy and efficiency especially when dealing with data from field sensors. We explored an unsupervised learning method, the denoising autoencoder (DAE), to extract the underlying data structure from noisy raw data in the context of predicting hydrologic quantities from multiple field sensors. These sensors have intrinsic instrumental noise and occasional malfunctions that cause missing values. Our DAE neural network reconstructed meteorological sensor data containing noise and missing values to predict evapotranspiration in a mountainous watershed. The DAE reconstructed the sensor variables with a mean coefficient of determination value of 0.77 across 15 dimensions representing individual sensors. It reduced variance and bias uncertainties compared to a classical autoencoder model. The reconstruction quality varied across dimensions depending on their cross‐correlation and alignment with the underlying data structure. Uncertainties arising from the model structure were overall higher than those resulting from data corruption. We attached the DAE structure to a downstream ET‐prediction neural network in three formats and achieved reasonably accurate ET predictions . The use of the DAE notably reduced variance uncertainty in ET prediction. However, excessive variance reduction may be accompanied by an increase in bias due to the intrinsic bias‐variance tradeoff. Our method of evaluating and reducing uncertainties in aggregated data from different sources can be used to improve predictive models, process understanding, and uncertainty quantification for better water resource management. Plain Language Summary We present a machine learning method, namely the denoising autoencoder, which reduces the effects of data noise and missing values typically present in scientific data sets collected through sensor measurements. This method selects the most relevant information from noisy raw data collected by the instruments and fills in missing values. To demonstrate the effectiveness of our method, we applied it to predict evapotranspiration, a hydrologic variable that represents the water moved from the land surface to the atmosphere through a combination of evaporation and plant water use (transpiration). We also used a random sampling technique (the Monte Carlo method) to compare the uncertainty in the predictions when using the raw and noisy data versus the reconstructed data. The denoising process produced more accurate predictions of evapotranspiration with less uncertainty. Improved predictions of evapotranspiration can lead to a better understanding and accounting of water budgets. This ML approach is broadly suitable for a wide variety of applications that involve noisy sensor data with missing values. Key Points We used a denoising autoencoder (DAE) neural network to reduce noise in meteorological and soil sensor observations by on average We used Monte Carlo sampling to estimate the bias and variance of all model outputs, including uncertainty sources from data and the model We attached the DAE component to a downstream neural network to predict ET with the variance reduced by , compared to that without the DAE

denoising autoencoder↗

DOE OSTI2016

An Atomic Mix Closure for Stochastic Media Transport Problems

The accurate modeling of stochastic media in radiation transport calculations remains on ongoing research challenge. The Levermore-Pomraning (LP) closure for the statistical transport equation is simple and inexpensive, but it is often inaccurate. More accurate closures have been proposed, but they can be prohibitively expensive. In this work we present a relatively inexpensive closure that we have observed to be more accurate than LP in almost all cases studied. Obtaining solutions to stochastic transport problems can be quite difficult. Transport calculations on an ensemble of explicit realizations generated by Monte Carlo sampling can be prohibitively expensive. Atomic mix or LP calculations are relatively inexpensive, but they can be inaccurate. The present work illustrates an approach that is less expensive than Monte Carlo sampling yet more accurate than atomic mix or LP approximations. We still need to analyze the reasons why the atomic mix closures derived for thicker problems lead to source iteration instabilities. It is not clear if the closure itself induces an ill-posed problem or if it is merely the iterative process that is problematic. We hope to examine alternative source terms to drive the subsidiary calculations. We also want to extend the work to multigroup and multidimensional problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Conditional Point Sampling: A Monte Carlo Method for Radiation Transport in Stochastic Media.

Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2025

Progress in Normalizing Flows for 4d Gauge Theories

Normalizing flows have arisen as a tool to accelerate Monte Carlo sampling for lattice field theories. This work reviews recent progress in applying normalizing flows to 4-dimensional nonabelian gauge theories, focusing on two advancements: an architectural improvement referred to as learned active loops, and the application of correlated ensemble methods to QCD with N f = 2 dynamical fermions.

Abbott, Ryan [Massachusetts Institute of Technolog↗

DOE OSTI2017

Determination of critical experiment correlations for experiments involving arrays of low-enriched fuel rods

Quantifying correlations among critical experiments has become a topic of interest over the last 10-15 years. Correlations arise from the shared use of fissile material, non-fissile materials, fixtures, and procedures in multiple experiments or multiple experiment series. A Monte-Carlo sampling technique proposed as a viable technical method to evaluate these correlations has been implemented in the SCALE 6.2 Sampler sequence. This paper presents an investigation of the use of this new tool and technique for low-enriched uranium pin array experiments with a thermal neutron energy spectrum. The Nuclear Energy Agency's Expert Group on Uncertainty Analyses for Criticality Safety Assessments has been examining methods of calculating the correlation coefficients among experiments from the LCT-007 and LCT-039 series. Results for two scenarios are presented to demonstrate the impact of pin pitch uncertainty modeling on the correlation coefficients. The convergence of the correlation coefficients is also investigated. Additional studies examine the impact of the stochastic uncertainty and the use of continuous-energy Monte-Carlo for individual realizations on the correlation coefficients. Correlation coefficients are also determined for the LCT-042 experiment series. This experiment series differs from other experiments because unique poison panels and fuel array separation distances may reduce correlation of the individual experiments within the series. The effects of pin pitch uncertainty and stochastic uncertainty are also examined for this series. Comparing the results of the two sets of experiments shows potential conclusions that can be drawn regarding viability of the Monte-Carlo sampling technique for determining critical experiment correlations. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2015

Determination of critical experiment correlations using the sampler sequence within scale 6.2 - 14602

The validation of neutron transport methods used in nuclear criticality safety analyses is required by consensus American National Standards Institute/American Nuclear Society (ANSI/ANS) standards. In the last decade, there has been an increased interest in correlations among critical experiments used in validation that have shared physical attributes and which impact the independence of each measurement. The statistical methods included in many of the frequently cited guidance documents on performing validation calculations incorporate the assumption that all individual measurements are independent, so little guidance is available to practitioners on the topic. Typical guidance includes recommendations to select experiments from multiple facilities and experiment series in an attempt to minimize the impact of correlations or common-cause errors in experiments. Recent efforts have been made both to determine the magnitude of such correlations between experiments and to develop and apply methods for adjusting the bias and bias uncertainty to account for the correlations. This paper describes recent work performed at Oak Ridge National Laboratory using the Sampler sequence from the SCALE code system to develop experimental correlations using a Monte Carlo sampling technique. Sampler will be available for the first time with the release of SCALE 6.2, and a brief introduction to the methods used to calculate experiment correlations within this new sequence is presented in this paper. Techniques to utilize these correlations in the establishment of upper subcritical limits are the subject of a companion paper and will not be discussed here. Example experimental uncertainties and correlation coefficients are presented for a variety of low-enriched uranium water-moderated lattice experiments selected for use in a benchmark exercise by the Working Party on Nuclear Criticality Safety Subgroup on Uncertainty Analysis in Criticality Safety Analyses. The results include studies on the effect of fuel rod pitch on the correlations, and some observations are also made regarding difficulties in determining experimental correlations using the Monte Carlo sampling technique. (authors)

42 ENGINEERING↗