Challenge Problem 2: Add Fatigue and Importance Sampling.
Abstract not provided.
Dingreville, Remi Philippe Michel↗
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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↗
Fast simulation of packet loss rates in a shared buffer communications switch
This paper describes an efficient technique for estimating, via simulation, the probability of buffer overflows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity.
Chang, Cheng-Shang↗
Interpretable Machine Learning for Molecular Biosignatures: a Novel Single-Sample Feature Importance Method That Is Sensitive To Statistical Interactions
Isotope ratio mass spectrometry (IRMS) of volatiles (e.g., CO 2 ) promises to be a powerful tool for potential biosignature detection for future missions to ocean worlds (OW) such as Europa and Enceladus. Machine learning (ML) methods for IRMS data could enable science autonomy by onboard prediction of seawater chemistry and biosignature presence. However, ML models are likely to be complex and involve statistical interactions between features (variables), which can make predictions seem opaque and enigmatic. For ML predictions as significant as extraterrestrial biosignatures, we must place extraordinary confidence in models. It is therefore essential that these models make interpretable predictions (i.e., human-understandable) and include false-prediction diagnostics. We achieve high accuracy and interpretability in ML biosignature and seawater chemistry models for OW through a nearest-neighbors feature selection tool that detects statistical interactions between predictors, constructs interaction networks for visualization of selected features working together to make a prediction, and reports single-sample feature importance scores for false-detection diagnostics. Here we develop a novel single-sample nearest-neighbors projected distance regression(ssNPDR) feature selection method that improves upon existing single-sample algorithms through the inclusion of statistical interactions while providing false-prediction diagnostics for ML models.
geochemistry↗
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↗
An Adaptive Bayesian Parameter Estimation of a Synchronous Generator Under Gross Errors
Polynomial-chaos-expansion-based surrogate models have recently been advocated in the literature for power system dynamic parameter estimation. Regarding the estimation of the uncertain generator parameters, a Bayesian inference framework has been proposed based on a polynomial-based reduced-order representation of the synchronous machines using assumed parameter values. Then, the non-Gaussian posterior probability distribution functions (pdfs) of these parameters are recovered through the stochastic sampling approach efficiently. However, facing very large parameter errors, the reliability of the surrogate model decreases, yielding biased estimation results. To overcome this problem, here we develop hierarchical Bayesian inference framework that processes the measurements provided by phasor measurement units, while making use of multifidelity surrogates together with the importance sampling method. The latter allows us to estimate in an efficient manner the posterior pdfs of the uncertain parameters through the normalized weights of the prior samples. To improve the accuracy of the posterior pdfs, an adaptive procedure is further adopted in the importance sampling for the gradual evolution of its proposal functions. The new proposals assist in fine-tuning the sample space and thereby help to construct surrogates with higher fidelity. Through an iterative process, this approach is able to estimate accurately and efficiently non-Gaussian posterior pdfs of the uncertain generator parameters subject to gross errors.
42 ENGINEERING↗
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↗
The Importance of Sample Return in Establishing Chemical Evidence for Life on Mars or Other Solar System Bodies
The search for evidence of life on Mars and elsewhere will continue to be one of the primary goals of NASA s robotic exploration program over the next decade. NASA and ESA are currently planning a series of robotic missions to Mars with the goal of understanding its climate, resources, and potential for harboring past or present life. One key goal will be the search for chemical biomarkers including complex organic compounds important in life on Earth. These include amino acids, the monomer building blocks of proteins and enzymes, nucleobases and sugars which form the backbone of DNA and RNA, and lipids, the structural components of cell membranes. Many of these organic compounds can also be formed abiotically as demonstrated by their prevalence in carbonaceous meteorites [1], though, their molecular characteristics may distinguish a biological source [2]. It is possible that in situ instruments may reveal such characteristics, however, return of the right sample (i.e. one with biosignatures or having a high probability of biosignatures) to Earth would allow for more intensive laboratory studies using a broad array of powerful instrumentation for bulk characterization, molecular detection, isotopic and enantiomeric compositions, and spatially resolved chemistry that may be required for confirmation of extant or extinct Martian life. Here we will discuss the current analytical capabilities and strategies for the detection of organics on the Mars Science Laboratory (MSL) using the Sample Analysis at Mars (SAM) instrument suite and how sample return missions from Mars and other targets of astrobiological interest will help advance our understanding of chemical biosignatures in the solar system.
Glavin, D. P.↗
Rate constants in spatially inhomogeneous systems
Here, we introduce a theory and accompanying importance sampling method for computing rate constants in spatially inhomogeneous systems. Using the relationship between rate constants and path space partition functions, we illustrate that the relative change in the rate of a rare event through space is isomorphic to the calculation of a free energy difference, albeit in a trajectory ensemble. Like equilibrium free energies, relative rate constants can be estimated by importance sampling. An extension to transition path sampling is proposed that combines biased path ensembles and weighted histogram analysis to accomplish this estimate. We demonstrate that rate constants can also be decomposed into different contributions, including relative changes in stability, barrier height, and flux. This decomposition provides a means of interpretation and insight into rare processes in complex environments. We confirm these ideas with a simple model of diffusion with spatially varying diffusivity and illustrate their utility in a model of ion pair dissociation near an electrochemical interface.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Importance of sample preparation on reliable surface characterisation of nano-objects: ISO Standard 20579-4
The international ISO Standard 20579-4, dealing with the history and preparation of nano-objects for surface analysis, has been developed to help address some of the replication and reproducibility issues caused by the fundamental nature of nano-objects. Although all types of samples requiring surface analysis need thoughtful preparation, nano-objects, for which many properties are controlled by their surfaces, present additional challenges in order to avoid variations and artefacts due to the handling and preparation of materials prior to analysis. This international standard is part of a series of standards related to preparation of samples for surface chemical analysis. Parts 1 and 2 of ISO Standard series 20579 address general issues that apply to many samples. Part 4 specifically considers issues that arise due to the inherent nature of nano-objects. Because of sensitivity to their environment, the standard indicates the minimum information that needs to be reported about the handling and preparation of nano-objects prior to surface analysis. This information should become part of sample provenance information that helps assure the reliability and usefulness of data obtained from surface-analysis in the context of the synthesis, processing and analysis history of a batch of material. Application of this standard can help address reproducibility and traceability issues associated with synthesis, processing, and characterization of nano-objects in research and commercial applications.
nano-object characterization, surface analysis, sa↗
An adaptive least-squares global sensitivity method and application to a plasma-coupled combustion prediction with parametric correlation
We introduce an efficient non-intrusive surrogate-based methodology for global sensitivity analysis and uncertainty quantification. Modified covariance-based sensitivity indices (mCov-SI) are defined for outputs that reflect correlated effects. The overall approach is applied to simulations of a complex plasma-coupled combustion system with disparate uncertain parameters in sub-models for chemical kinetics and a laser-induced breakdown ignition seed. The surrogate is based on an Analysis of Variance (ANOVA) expansion, such as widely used in statistics, with orthogonal polynomials representing the ANOVA subspaces and a polynomial dimensional decomposition (PDD) representing its multi-dimensional components. The coefficients of the PDD expansion are obtained using a least-squares regression, which both avoids the direct computation of high-dimensional integrals and affords an attractive flexibility in choosing sampling points. This facilitates importance sampling using a Bayesian calibrated posterior distribution, which is fast and thus particularly advantageous in common practical cases, such as our large-scale demonstration, for which the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense. Effort, instead, is focused on efficient finite-resolution sampling. Standard covariance-based sensitivity indices (Cov-SI) are employed to account for correlation of the uncertain parameters. Magnitude of Cov-SI is unfortunately unbounded, which can produce extremely large indices that limit their utility. Alternatively, mCov-SI are then proposed in order to bound this magnitude $\in$ [0, 1]. The polynomial expansion is coupled with an adaptive ANOVA strategy to provide an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational cost of a high-dimensional expansion. It is also adaptively simplified according to the relative contribution of the different polynomials to the total variance. Finally, the approach is demonstrated for a laser-induced turbulent combustion simulation model, which includes parameters with correlated effects.
42 ENGINEERING↗
GeoLab Concept: The Importance of Sample Selection During Long Duration Human Exploration Mission
In the future when humans explore planetary surfaces on the Moon, Mars, and asteroids or beyond, the return of geologic samples to Earth will be a high priority for human spaceflight operations. All future sample return missions will have strict down-mass and volume requirements; methods for in-situ sample assessment and prioritization will be critical for selecting the best samples for return-to-Earth.
Calaway, M. J.↗