Robust importance sampling for error estimation in the context of optimal Bayesian transfer learning
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97 MATHEMATICS AND COMPUTING↗
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nautilus : boosting Bayesian importance nested sampling with deep learning
ABSTRACT We introduce a novel approach to boost the efficiency of the importance nested sampling (INS) technique for Bayesian posterior and evidence estimation using deep learning. Unlike rejection-based sampling methods such as vanilla nested sampling (NS) or Markov chain Monte Carlo (MCMC) algorithms, importance sampling techniques can use all likelihood evaluations for posterior and evidence estimation. However, for efficient importance sampling, one needs proposal distributions that closely mimic the posterior distributions. We show how to combine INS with deep learning via neural network regression to accomplish this task. We also introduce nautilus, a reference open-source python implementation of this technique for Bayesian posterior and evidence estimation. We compare nautilus against popular NS and MCMC packages, including emcee, dynesty, ultranest, and pocomc, on a variety of challenging synthetic problems and real-world applications in exoplanet detection, galaxy SED fitting and cosmology. In all applications, the sampling efficiency of nautilus is substantially higher than that of all other samplers, often by more than an order of magnitude. Simultaneously, nautilus delivers highly accurate results and needs fewer likelihood evaluations than all other samplers tested. We also show that nautilus has good scaling with the dimensionality of the likelihood and is easily parallelizable to many CPUs.
97 MATHEMATICS AND COMPUTING↗
CADIS and FW-CADIS Variance Reduction in Gamma Transport for Predicting Prompt Forensics Signatures
The goal of prompt nuclear forensics is to determine the characteristics of a nuclear detonation based on the signatures available almost immediately after the explosion. An important characteristic is the reaction time history (RTH), a measure of the device’s rate of neutron multiplication. The RTH can be estimated by observation of the gamma radiation emitted from the detonation, which can be detected directly or observed indirectly as Teller light. Gamma transport simulations used to predict these radiation fields are often modeled stochastically using the Monte Carlo N-Particle (MCNP) code, which can be a computationally demanding task due to the number of particle histories needed to achieve statistical convergence. In an attempt to improve the efficiency of these calculations, we evaluate two variance reduction techniques: Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS). These methods use a deterministically calculated adjoint flux to create weight windows and source biasing that guide MCNP sampling. We study the utility of CADIS and FW-CADIS for their use in MCNP gamma transport for nuclear forensics prediction simulations. Furthermore, the results demonstrate that both CADIS and FW-CADIS improve the accuracy for forensics-focused simulations, with CADIS being most beneficial in direct detection and FW-CADIS being ideal for computing a global Teller light source.
CADIS↗
Towards a Robust Sampling Approach: A Computational Review and Design
As pointed out in several other works, the estimation of the reliability of the electrical grid can not be conducted without the estimation of the stochastic phenomena of electicity demand and electricity production by variable renewable sources. Therefore, sampling procedures have become integral in the design of engineering structures and analysis. Commonly referred to as Monte Carlo uncertainty analysis or integration, the general objective of these procedures is to establish specifics about the uncertainty of an output characteristic of such an engineering system, given uncertainty about its input characteristics. These sampling procedures are applied in a context in which establishing such specifics cannot be performed through other means. Variance-reduction techniques are designed to lessen the variability among estimators to estimate statistics of those output uncertainties. Importance-sampling techniques, on the other hand, are designed to reduce the number of samples needed to estimate a particular statistic—e.g., a tail probability. The combination of these approaches can reduce the computational burden considerably for a particular estimator and statistic. Importance sampling—geared and designed as it is toward improving a particular estimator—suffers, unfortunately, from the unintended consequence of reducing the performance of other estimators in terms of their variance. The objective of this paper is to offer an alternative sampling procedure where this variance does not grow unacceptably large for a suite of estimators. Moreover, it is anticipated that, with additional knowledge of how an engineering output characteristic responds to its input characteristics, tuning parameters of the input’s sampling procedure can be set to improve the output characteristic’s estimation. This work proves the effectiveness of the suggested alternative approach. Such positive outcome will lead to a decrease of the computational burden of performing stochastic optimization of integrated energy systems (e.g., components dispatch, and portfolio composition). In particular, capturing the contribution to the overall system cost of rare and unlikely events and patterns of the electricity demand and production will become less computationally expensive. This is due to the fact that the approach demonstrated here will allow the sampling of those rare occurrences more frequently without misrepresenting their probabilistic impacts.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Importance of Sample Handling and Preparation for Surface Analysis: A Summary of ISO Standard 20579 Part 1, Documenting and Reporting the Handling of Specimens Prior to Analysis
Reliable and reproducible analysis of surfaces is critically dependent on how samples have been collected, handled, and prepared before analysis. Although there are important, well-established general guidelines to minimize unintended alteration of the surfaces to be analyzed, specific handling steps depend on the nature of the samples and information desired. Assessments of the validity and reliability of the results require adequate information about sampling, handling, and processing. ISO standard 20579 part 1 describes the information to be recorded and reported for samples that are prepared or submitted for surface analysis. This paper summarizes elements of the standard, which includes annexes that justify and inform the sample handling processes. Also included is a checklist of information that needs to be recorded and reported and an appendix containing an example of a form that might be used to report the information.
AES↗
Evaluation of PBR Spent Fuel Criticality and Dose Rate Compliance for Storage and Transportation
Spent tri-structural isotropic (TRISO)–based fuels have a strong track record in storage and transportation without documented incidents. This work seeks to reduce uncertainty to aid in more informed spent fuel management of TRISO-based fuels by modeling both fresh and spent pebble bed reactor (PBR) fuel and comparing the results to the regulatory standards from 10 CFR 71. SCALE was used for all modeling due to it having fast and accurate methods for handling PBR fuel modeling, as well as having an efficient method for shielding calculations in monaco with automated variance reduction using importance calculations (MAVRIC), which utilizes the consistent adjoint-driven importance sampling (CADIS) and the forward-weighted consistent adjoint-driven importance sampling (FW-CADIS) methods. KENO-VI was used for all criticality calculations, TSUNAMI was used for uncertainty quantification on k-effective, TRITON and the Oak Ridge isotope generation code (ORIGEN) were both used for depletion of the fuel, and MAVRIC was used for shielding calculations. For criticality assessments, this study focused on the requirement that the value of the neutron multiplication factor, k-effective (k-eff), would not exceed a peak value of 0.95, including uncertainty, with 95% confidence. Criticality was initially examined by modeling fresh fuel from three different designs—HTR-10 fuel, PBMR-400 fuel, and demonstration fuel representative of a TRISO-fueled modern high-temperature gas reactor (HTGR) design, henceforth referred to as Demo HTGR—and placing them into various sized containers with conditions described in 10 CFR 71 to quantify the peak k-eff state. When the peak value of 0.95 k-eff was exceeded, mitigation methods were examined in those scenarios. Burnup credit, pebble displacement in areas of strong neutron multiplication, and random pebble replacement using pebbles of various compositions and replacement fractions were examined. In summary, the criticality of PBR fuels can be well accounted for by restricting container size, taking credit for burnup, or by displacing/replacing pebbles. Uncertainty of the k-eff due to nuclear data uncertainties was recorded at ~0.6644%Δk/k, or roughly 664% mil (pcm). The nuclear data–induced uncertainty was relatively small and should not require significant modification in the design to be accounted for. Revisions to the evaluated nuclear data file values have been shown to have a larger impact than nuclear data–induced uncertainty. For dose rate aspects, U.S. Nuclear Regulatory Commission regulations require a maximum dose rate of 10 millirem per hour (mrem/h) at 2 meters. In examining the dose rate behavior of spent PBR fuel, the representative Demo HTGR fuel was modeled exclusively due to it possessing the highest target burnup of the examined fuels. Equilibrium cycle modeling methods were used to produce a higher-fidelity discharge isotopic composition than simple assumptions, such as reflected pebbles. The discharge composition was used as a source term in the fixed-source transport shielding calculations, and dose rates were calculated at 2 m for the shortest possible cooling time. The low concentration of fuel material led to dose rates that were in line with regulatory limits, despite the high burnup when compared to traditional light water reactor fuels. In conclusion, the methods employed in this study would require more work to further verify and validate and are limited to the criticality and dose rate analyses performed.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Accelerated statistical failure analysis of multifidelity TRISO fuel models
Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Rare Events via Cross-Entropy Population Monte Carlo
Rare events are events that happen with very low frequency. Estimating rare event probabilities using Monte Carlo techniques is computationally expensive, often to the point of intractability, and special methods are required. Importance sampling (IS) is a well known technique that uses a proposal distribution in place of a target distribution to lower the variance of the estimator. Key to the success of IS methods is the choice of a proposal distribution, or the parameters governing the distribution. Adaptive importance sampling improves the parameters of a family or population of proposal distributions iteratively through trials. We present a novel cross-entropy population Monte Carlo algorithm, which adapts the parameters of proposals through the cross-entropy method. The proposed method stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on rare event examples show that the algorithm can outperform existing resampling based population Monte Carlo methods, especially for higher-dimensional problems. Finally, we also demonstrate efficacy on a conjunction analysis problem.
97 MATHEMATICS AND COMPUTING↗
Clean quartz matters for cosmogenic nuclide analyses: An exploration of the importance of sample purity using the CRONUS-N reference material
We report reference materials are key for assessing inter-laboratory variability and measurement quality, and for placing analytical uncertainty bounds on sample analyses. Here, we investigate four years of data resulting from repeated processing of the CRONUS-N reference material for cosmogenic 10 Be and 26 Al analyses. At University of Vermont, we prepared a CRONUS-N aliquot with most of our sample batches from 2013 to 2017; these reference material samples were then distributed to four different accelerator mass spectrometry facilities, yielding 73 10 Be analyses and 58 26 Al analyses. We determine CRONUS-N 10 Be concentrations of (2.26 ± 0.14) x 10 5 atoms g -1 (n = 73, mean, 1 SD) and 26 Al concentrations of (1.00 ± 0.08) x 10 6 atoms g -1 (n = 58, mean, 1 SD). We find a reproducibility of 6.3% for 10 Be and 7.7% for 26 Al (relative standard deviations). We also document highly variable 27 Al and Mg concentrations and a 10 Be dispersion twice as large as the mean AMS analytic uncertainty. Analyses of the CRONUS-N material with and without density separation demonstrate that non-quartz minerals are present in the material and have a large impact on measured concentrations of 27 Al, 10 Be, and impurities; these non-quartz minerals represent only a very small portion of the total mass (0.6–0.8%) but have a disproportionally large effect on the resulting data. Our results highlight the importance of completely removing all non-quartz mineral phases from samples prior to Be/Al extraction for the determination of in situ cosmogenic 10 Be and 26 Al concentrations.
58 GEOSCIENCES↗
A stochastic covariance shrinkage approach to particle rejuvenation in the ensemble transform particle filter
Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to properly sample the high-probability regions of the state space. Rejuvenation is often implemented in a heuristic manner by the addition of random noise that widens the support of the ensemble. This work aims at improving canonical rejuvenation methodology by the introduction of additional prior information obtained from climatological samples; the dynamical particles used for importance sampling are augmented with samples obtained from stochastic covariance shrinkage. A localized variant of the proposed method is developed. Numerical experiments with the Lorenz '63 model show that modified filters significantly improve the analyses for low dynamical ensemble sizes. Furthermore, localization experiments with the Lorenz '96 model show that the proposed methodology is extendable to larger systems.
54 ENVIRONMENTAL SCIENCES↗
Sequential Bayesian inference of transition rates in the hidden Markov model for multi-state system degradation
The more easily available system performance data and advances in data analytics have provided us with opportunities to optimize maintenance programs for engineered systems, for example nuclear power plants. One key task in maintenance optimization is to obtain an accurate model for system degradation. Here, in this research, we propose a Bayesian method to address this problem. Noting that systems usually exhibit multiple states and that the actual state of a system usually is not directly observable, in the method we first model the system degradation process and the observation process based on a hidden Markov model. Then we develop a sequential Bayesian inference algorithm based on importance sampling and the forward algorithm to infer the posterior distributions of the transition rates in the hidden Markov model based on available observations. The proposed Bayesian method allows us to take advantage of evidence from multiple sources, and also allows us to perform Bayesian inference sequentially, without the need to use the entire history of observations every time new observations are collected. We demonstrate the proposed method using both synthetic data for a nuclear power plant feedwater pump and realistic data for a nuclear power plant chemistry analytical device.
42 ENGINEERING↗
Trepanning Graphite Samples at a Shutdown Magnox Reactor: A US-UK Joint Exercise for Nuclear Verification
In April 2022, a team sponsored by the US DOE Office of Nuclear Verification (ONV) shipped trepanning equipment to the nuclear power station at Trawsfynydd, Wales, UK to collect samples from the graphite moderator of Reactor 1. The sampling campaign to collect 48 graphite samples was completed in five weeks beginning July 11. Half the samples will be analyzed in the US to determine the total energy production of the facility. The other half will be analyzed by Magnox Ltd. to support decisions for options for the ultimate decommissioning path for the facility. This paper provides a description of the equipment and the operations required to trepan, collect, and package the samples while controlling the small amounts of radioactive graphite dust entrained on and within the tool. The most important sample parameter needed is the precise location of the sample, to within ±6 mm in a fuel channel, while the tool is deployed to between 12 and 20 meters below the operations floor; our means of achieving this precision is given.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.
97 MATHEMATICS AND COMPUTING↗
Persistent Sampling: Enhancing the Efficiency of Sequential Monte Carlo
Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an extension of SMC that systematically retains and reuses particles from all prior iterations to construct a growing, weighted ensemble. By leveraging multiple importance sampling and resampling from a mixture of historical distributions, PS mitigates the need for excessively large particle counts, directly addressing key limitations of SMC such as particle impoverishment and mode collapse. Crucially, PS achieves this without additional likelihood evaluations-weights for persistent particles are computed using cached likelihood values. This framework not only yields more accurate posterior approximations but also produces marginal likelihood estimates with significantly lower variance, enhancing reliability in model comparison. Furthermore, the persistent ensemble enables efficient adaptation of transition kernels by leveraging a larger, decorrelated particle pool. Experiments on high-dimensional Gaussian mixtures, hierarchical models, and non-convex targets demonstrate that PS consistently outperforms standard SMC and related variants, including recycled and waste-free SMC, achieving substantial reductions in mean squared error for posterior expectations and evidence estimates, all at reduced computational cost. PS thus establishes itself as a robust, scalable, and efficient alternative for complex Bayesian inference tasks.
Karamanis, Minas↗
Assessment of Contaminant Bioaccumulation in Aquatic Biota on and Adjacent to the Oak Ridge Reservation—2020
This report provides information on contaminant concentrations in multiple wildlife prey species inhabiting or associated with water bodies on and downstream from the Oak Ridge Reservation (ORR), including regional reference sites. This information can be used to understand the nature and extent of contaminant exposure and transfer through the food web and to provide a baseline for evaluating temporal trends in contaminant exposure and accumulation. This information was gathered as part of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) Five-Year Review (FYR) process, and it also addresses regulator comments on the annual Remediation Effectiveness Report (RER). This report summarizes the results of biological sampling completed in the spring and summer of 2020, prior to the 2021 FYR. Sampled locations included key sites upstream from the point sources of contaminants, along with watershed integration points on and off the ORR. Integration points are spatially the most important sampling sites because they capture biological responses to upstream contaminant inputs from both aqueous and groundwater sources, as well as responses to various remedial actions. These sites are most often located at a watershed administration unit boundary and may have regulatory significance for performance measures. In many cases, there are long-term biological and other monitoring data associated with these sites; these data generally fall within the areas of exposure and effects.
54 ENVIRONMENTAL SCIENCES↗
Leverage Score Sampling for Parametric PDEs (Final Technical Report)
This final technical report summarizes the accomplishments of work performed under DOE Office of Science Award DE-SC0022266, which is titled “Leverage Score Sampling for Parametric PDEs”. The goal of the project was to extend methods from Randomized Numerical Linear Algebra (RandNLA) to tackle central computational challenges in model order reduction and uncertainty quantification (UQ) for parametric partial differential equations (PDEs). In particular, we sought to use importance sampling methods originally developed for RandNLA to develop sample efficient active learning algorithms for approximating high-dimensional scalar functions, e.g. by polynomials, Gaussian process models, and simple neural networks. Such methods can be immediately applied to developing surrogate models or to approximating quantity of interest (QoI) surfaces. In the context of PDEs, each sample used for learning equates to the solution of the differential equation for a particular set of parameters, so sample efficiency translates to improved computational efficiency for a variety of downstream tasks.
97 MATHEMATICS AND COMPUTING↗
Adaptive, Active Learning, and Multifidelity Monte Carlo Methods in the MOOSE Stochastic Tools Module
MOOSE is an open-source computational platform for constructing multi-physics models and executing them in a massively parallel fashion. It has a stochastic tools module (STM) for forward/inverse uncertainty quantification (UQ) and surrogate modeling. This presentation details some recent developments to the STM with respect to the implementation of adaptive, active learning, and multifidelity Monte Carlo methods for forward UQ of computational models. Specifically, the adaptive Monte Carlo methods include Markov Chain Monte Carlo (MCMC)-driven algorithms like adaptive importance sampling and parallelized subset simulation for statistical QoI estimation, rare events analysis, and stochastic gradient-free optimization. The active learning methods include Gaussian Process (GP) surrogates and their training via Adam optimization, design of acquisition functions, and integration with samplers like Monte Carlo, adaptive importance, and parallelized subset simulation. These active learning methods are also designed to work in a batch mode, wherein, the required calls to the full computational model are executed in parallel whenever a user-specified batch size is met. The multifidelity methods in STM are broadly divided into two categories: hierarchical, where a defined hierarchy exists among the low-fidelity models, and peer, where all the low-fidelity models are treated equally. A GP surrogate is used to learn the differences between the low- and high-fidelity models in both multifidelity categories, and acquisition functions from the active learning classes are used to decide whether to rely on a low-fidelity model or call the expensive high-fidelity model. Alongside the software description and usage, applications are also presented to nuclear engineering computational models including a TRISO nuclear fuel particle, a reactor pressure vessel, and a heat-pipe microreactor.
97 MATHEMATICS AND COMPUTING↗