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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

Perlmutter, M.↗
NASA NTRS1975

Monte Carlo variance reduction study

A mathematical analysis of the transport of nuclear radiation through matter is presented. A computer test bed that was developed is shown, along with flow charts.

Byrn, N. R.↗
DOE OSTI2024

Moment Tensor Inversion Toolkit

The MTINV toolkit (2002-present) is a collection of computer codes and applications written to invert for the moment tensor of a seismic source given the three components of ground motion recorded at regional seismic stations (e.g., Ichinose et al., 2003). The computer codes and workflow are organized to generate moment tensor solutions for a range of source depths and origin times because of the trade-off between these two quantities. The metric used is the variance reduction and variance reduction modulated by the percent double-couple to determine the best-fit moment-tensor solution. We can solve for a deviatoric moment tensor with a constraint added for no isotropic component although this constraint can be lifted for estimating the full moment tensor like mining collapses or explosion sources.

Ichinose, GeneA↗
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Optimizing foreground mitigation for CMB lensing with combined multifrequency and geometric methods

Here, a key challenge for current and upcoming cosmic microwave background lensing measurements is their sensitivity to biases from extragalactic foregrounds, such as Sunyaev-Zel'dovich signals or cosmic infrared background emission. Several methods have been developed to mitigate these lensing foreground biases, dividing broadly into multifrequency cleaning approaches and modifications to the estimator geometry, but how to optimally combine these methods has not yet been explored in detail. In this paper, we examine which combination of lensing foreground mitigation strategies is best able to reduce the impact of foreground contamination for a Simons Observatory-like experiment while preserving maximal signal-to-noise. Although the optimal combination obtained depends on whether bias reduction or variance reduction is prioritized and on whether polarization data is used, generally, we find that combinations involving both geometric (profile hardening, source hardening, or shear) and multifrequency (symmetric cleaning) methods perform best. For lensing power spectrum measurements from temperature (polarization and temperature), our combined estimator methods are able to reduce the bias below σ/4 or 0.3% (0.1%), a factor of 16 (30) lower than the standard quadratic estimator bias, at a modest signal-to-noise cost of only 18% (12%). In contrast, single-method foreground-mitigation approaches struggle to reduce the bias to a negligible level below σ/2 without incurring a large noise penalty. For upcoming and current experiments, our combined methods therefore represent a promising approach for making lensing measurements with negligible foreground bias.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗
DOE OSTI2024

Radiation Dose Modeling for Niowave’s Accelerator Driven Uranium Target Assembly 3

Molybdenum-99 is a high-value radionuclide commonly used for medical purposes within the United States. The National Nuclear Security Administration (NNSA) seeks to reliably produce the radioisotope 99 Mo without the use of highly enriched uranium. NNSA’s Office of Material Management and Minimization (M3) provides funding and government laboratory expertise to private companies to expedite the production process domestically and currently funds designs that use low-enriched uranium or other 99 Mo production pathways. Several production designs are being explored across the industry, including uranium fission and photonuclear conversion of 100 Mo targets. Niowave Inc. seeks to produce 99 Mo via a high-energy electron accelerator that strikes a lead-bismuth eutectic target that ultimately produces a consistent neutron flux. The neutron flux then interacts in a subcritical reactor core configuration to produce fission in low-enriched or natural uranium targets. These fissionable targets are then processed to extract 99 Mo. The purpose of this work is to estimate the neutron and photon dose response across Niowave’s proposed facility for worker safety during operation. Owing to the size of the proposed Niowave facility and necessary shielding, unbiased Monte Carlo radiation transport is impractical, and variance reduction methods are required. This work focuses on the weight window variance reduction method to produce high confidence dose response results within a Monte Carlo radiation transport code. Specifically, an adjoint-informed weight window methodology was created to improve the dose response estimates for accelerator-driven subcritical reactor designs. This adjoint-informed methodology was implemented for Niowave’s proposed design and improved dose results at far-field locations across the facility. Acceptable dose rate contours for the proposed facility were generated across the facility and are presented in this work.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2022

SCALE 6.2.4 Validation: Radiation Shielding

For safe and reliable use of computer codes by the community, accuracy must be clearly evaluated. In particular, the nuclear reactor engineering and licensing field needs accurate tools for radiation shielding modeling. Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) is one such tool, with built-in variance reduction methods distributed within the SCALE code, and its validity is demonstrated in this report for the released version 6.2.4. Representative benchmarks corresponding to shielding analysis are selected for the validation study. Typical experimental results analyzed from those benchmarks include neutron fluxes, detector count rates, detector energy response functions, neutron and gamma doses, foil neutron activation rates and activities, neutron leakage fluxes, and skyshine dose rates. Thousands of points of comparison between experiment and calculation are presented in this work. Other than rare outliers typically explained by either a lack of information or large uncertainties in the experiment conditions, material, or dimensions, MAVRIC agrees well with the experiment results. MAVRIC is also compared to Monte Carlo N-Particle (MCNP) calculations when available, and both codes generally produce good agreements within estimated uncertainties. The selected benchmarks are obtained from reliable sources such as the International Criticality Safety Benchmark Evaluation Project Handbook (ICSBEP Handbook), the Shielding Integral Benchmark Archive & Database (SINBAD), and other shielding validation work found in the literature. Additional datapoints and benchmarks will be added to future versions of this report to incrementally expand the shielding validation suite incrementally.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

SCALE 6.3 Validation: Radiation Shielding

Safe and reliable use of scientific and engineering computer codes requires validation for the types of applications in which they will be used. An example in the nuclear reactor engineering and licensing field is radiation transport employed in shielding analyses. The validity of computer codes for shielding applications is demonstrated in this report for SCALE version 6.3.0. Representative benchmarks corresponding to shielding analyses are selected for the validation study. Typical measurement results analyzed from these benchmarks include neutron fluxes, detector count rates, detector energy response functions, neutron and gamma dose rates, neutron activation rates and activities, neutron leakage fluxes, and skyshine dose rates. Thousands of points of comparison between measurement and calculation are presented in this work. Other than rare outliers typically explained by either a lack of information or large uncertainties in the experiment conditions, material, or dimensions, the Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) radiation transport computer code with built-in variance reduction methods distributed with the SCALE computer code system agrees well with the measurement results. In selected benchmarks, MAVRIC is also compared to Monte Carlo N- Particle® (MCNP® ) 1 calculations. Both computer codes generally agree well within the estimated uncertainties. With the release of SCALE 6.3.0, Shift was integrated as an alternative transport solver in MAVRIC, denoted MAVRIC-Shift. Although the traditional MAVRIC using Monaco was used primarily in this validation study, many results have also been generated using MAVRIC-Shift. Agreement between MAVRIC-Monaco and MAVRIC-Shift is generally very good. The benchmarks presented in this report were obtained from reliable sources such as the International Criticality Safety Benchmark Evaluation Project Handbook, the Shielding Integral Benchmark Archive & Database, and other shielding validation work found in the literature. Additional datapoints and benchmarks will be added to future versions of this report to expand the shielding validation suite.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS2007

Dynamic and Regression Modeling of Ocean Variability in the Tide-Gauge Record at Seasonal and Longer Periods

Comparison of monthly mean tide-gauge time series to corresponding model time series based on a static inverted barometer (IB) for pressure-driven fluctuations and a ocean general circulation model (OM) reveals that the combined model successfully reproduces seasonal and interannual changes in relative sea level at many stations. Removal of the OM and IB from the tide-gauge record produces residual time series with a mean global variance reduction of 53%. The OM is mis-scaled for certain regions, and 68% of the residual time series contain a significant seasonal variability after removal of the OM and IB from the tide-gauge data. Including OM admittance parameters and seasonal coefficients in a regression model for each station, with IB also removed, produces residual time series with mean global variance reduction of 71%. Examination of the regional improvement in variance caused by scaling the OM, including seasonal terms, or both, indicates weakness in the model at predicting sea-level variation for constricted ocean regions. The model is particularly effective at reproducing sea-level variation for stations in North America, Europe, and Japan. The RMS residual for many stations in these areas is 25-35 mm. The production of "cleaner" tide-gauge time series, with oceanographic variability removed, is important for future analysis of nonsecular and regionally differing sea-level variations. Understanding the ocean model's strengths and weaknesses will allow for future improvements of the model.

Hill, Emma M.↗
DOE OSTI2022

GANISP: A GAN-Assisted Importance Splitting Probability Estimator

Designing manufacturing processes with high yield and strong reliability relies on effective methods for rare event estimation. Genealogical importance splitting reduces the variance of rare event probability estimators by iteratively selecting and replicating realizations that are headed towards a rare event. The replication step is difficult when applied to deterministic systems where the initial conditions of the offspring realizations need to be modified. Typically, a random perturbation is applied to the offspring to differentiate their trajectory from the parent realization. However, this random perturbation strategy may be effective for some systems while failing for others, preventing variance reduction in the probability estimate. This work seeks to address this limitation using a generative model such as a Generative Adversarial Network (GAN) to generate perturbations that are consistent with the attractor of the dynamical system. The proposed GAN-assisted Importance SPlitting method (GANISP) improves the variance reduction for the system targeted. An implementation of the method is available in a companion repository (https://github.com/NREL/GANISP).

generative adversarial network↗
DOE OSTI2022

GANISP: A GAN-Assisted Importance Splitting Probability Estimator: Preprint

To reduce the variance of rare event probability estimator, genealogical importance splitting marches towards a rare event by iteratively selecting and replicating realizations that are headed towards a rare event. The replication step is made difficult when applied to deterministic systems as the initial conditions of the offspring realizations need to be modified. Typically, a random perturbation is applied to the offspring to differentiate their trajectory from the parent realization. It is shown that a random perturbation strategy may be effective for some systems but may also fail for others, thereby preventing variance reduction in the probability estimate. To address this limitation, it is proposed to use a generative model such as a Generative Adversarial Network (GAN) to generate perturbations that are consistent with the attractor of the dynamical system. The GAN-assisted Importance SPlitting method (GANISP) improves the variance reduction for the system targeted. An implementation of the method is available in a companion repository (https://github.com/NREL/GANISP).

generative adversarial network↗
NASA NTRS2020

Multi Model Monte Carlo with Python (MXMCPy)

Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.

Geoffrey F Bomarito↗
NASA NTRS2020

Algorithm Performance Dataset from NASA Open-Source Software

NASA Langley Research Center has recently developed and released the open-source software Multi Model Monte Carlo with Python (MXMCPy- LAR-19756-1) as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Given a fixed computational budget and a collection of models with varying cost/accuracy, multi model Monte Carlo (MC) seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. MXMCPy is a versatile tool that enables convenient access to many existing multi-model MC approaches (over a dozen algorithms available) within one modular and extensible package [1]. With MXMCPy, users can easily compare existing methods to determine the best choice for their particular problem,while developers have a basis for implementing and sharing new variance reduction approaches. However,there is currently very little understanding about which algorithm will perform best for a given problem (defined by the correlation between and relative cost of the available models) without a brute force search.

Geoffrey F Bomarito↗
DOE OSTI2022

Accelerated radiation transport modeling techniques for pencil beam computed tomography using gamma rays

Monte Carlo radiation transport modeling studies were performed for a compact, and high-resolution gamma-ray computed tomography system designed for imaging irradiated nuclear fuel. The system comprises a 60 Co source – chosen for its highly penetrating 1173 keV and 1332 keV gamma rays – a pair of high-aspect-ratio pencil beam collimators, and an inorganic scintillator detector. Here two acceleration methods are proposed to rapidly model a transmission type gamma-ray tomography system. The first, a variance reduction technique, is based on performing Monte Carlo simulations with a monodirectionally-biased source, sampled from a characteristic sub-volume of the full source volume. The second acceleration method is based on the deterministic calculations using the Beer–Lambert law and detector response characteristics. Comparison of simulations using acceleration approaches with analog simulations of the fully isotropic, full-volume equivalent, show that the Monte Carlo variance reduction technique gives quantitatively accurate predictions for large collimator aspect ratios while the deterministic calculations are semi-quantitative but converge close to the correct result as the collimator aspect ratio increases. As such, these techniques can be used to reduce the computational cost in generating simulated radiographs and tomographs by several orders of magnitude. Experimental validation efforts are currently underway and will be demonstrated in future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

FedOSAA: Improving Federated Learning with One-Step Anderson Acceleration

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly those incorporating variance reduction techniques, are the most widely used FL algorithms due to their simple implementation and stable performance. However, these methods tend to be slow and require a large number of communication rounds to reach the global minimizer. We propose FedOSAA, a novel approach that preserves the simplicity of first-order methods while achieving the rapid convergence typically associated with second-order methods. Our approach applies one Anderson acceleration (AA) step following classical local updates based on first-order methods with variance reduction, such as FedSVRG and SCAFFOLD, during local training. This AA step is able to leverage curvature information from the history points and gives a new update that approximates the Newton-GMRES direction, thereby significantly improving the convergence. We establish a local linear convergence rate to the global minimizer of FedOSAA for smooth and strongly convex loss functions. Numerical comparisons show that FedOSAA substantially improves the communication and computation efficiency of the original first-order methods, achieving performance comparable to second-order methods like GIANT.

Feng, Xue [University of California, Davis]↗