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At least 253 records · Page 14

Probabilistic Nanomagnetic Memories for Uncertain and Robust Machine Learning

This project evaluated the use of emerging spintronic memory devices for robust and efficient variational inference schemes. Variational inference (VI) schemes, which constrain the distribution for each weight to be a Gaussian distribution with a mean and standard deviation, are a tractable method for calculating posterior distributions of weights in a Bayesian neural network such that this neural network can also be trained using the powerful backpropagation algorithm. Our project focuses on domain-wall magnetic tunnel junctions (DW-MTJs), a powerful multi-functional spintronic synapse design that can achieve low power switching while also opening the pathway towards repeatable, analog operation using fabricated notches. Our initial efforts to employ DW-MTJs as an all-in-one stochastic synapse with both a mean and standard deviation didn’t end up meeting the quality metrics for hardware-friendly VI. In the future, new device stacks and methods for expressive anisotropy modification may make this idea still possible. However, as a fall back that immediately satisfies our requirements, we invented and detailed how the combination of a DW-MTJ synapse encoding the mean and a probabilistic Bayes-MTJ device, programmed via a ferroelectric or ionically modifiable layer, can robustly and expressively implement VI. This design includes a physics-informed small circuit model, that was scaled up to perform and demonstrate rigorous uncertainty quantification applications, up to and including small convolutional networks on a grayscale image classification task, and larger (Residual) networks implementing multi-channel image classification. Lastly, as these results and ideas all depend upon the idea of an inference application where weights (spintronic memory states) remain non-volatile, the retention of these synapses for the notched case was further interrogated. These investigations revealed and emphasized the importance of both notch geometry and anisotropy modification in order to further enhance the endurance of written spintronic states. In the near future, these results will be mapped to effective predictions for room temperature and elevated operation DW-MTJ memory retention, and experimentally verified when devices become available.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

An Approach to Dependence Assessment in Human Reliability Analysis: Application of Lag and Linger Effects

Dependence assessment refers to an approach used in human reliability analysis (HRA) to adjust a human error probability (HEP) for the following action by considering the impact of the preceding action. It has been known to significantly affect the overall results of probabilistic safety assessment (PSA). If the dependence assessment is not adequate, the result could be unconvincing for explaining the operator failures in the context of PSA. To date, several methods and some recent research have identified suggestions for treating dependence issues in HRA; however, these are still exclusively based on the intrinsic approach of the Technique for Human Error Rate Prediction (THERP), an HRA method. THERP inevitably has a challenge with the subjectivity of expert evaluation as well as the requirement for PSA and HRA expertise with resource-intensive and time-consuming processes. This paper suggests an approach to dependence assessment that could not only minimize the influence of expert judgment, but also saves time to perform the analysis with reasonable manpower. It modifies existing HRA methods with considering lag and linger effects to apply dependence effects for them. Based on a representative HRA method, i.e., Standardized Plant Analysis Risk - HRA (SPAR-H), guidance for how to apply lag and linger effects for the HRA method is suggested. Then, an investigation is carried out to compare quantification results of the revised HRA method with that of the original approach based on experimental data.

99 GENERAL AND MISCELLANEOUS↗

Weight function procedure for reduced order fracture analysis of arbitrary flaws in cylindrical pressure vessels

Fracture mechanics calculations using the finite element method can be computationally expensive, which makes them challenging to use in engineering evaluations of flaws in pressure vessels. The weight function (WF) technique is a reduced order fracture modeling method that is widely used to greatly reduce these computational costs. Its computational efficiency is essential for use in probabilistic fracture mechanics evaluations of embrittled nuclear reactor pressure vessels (RPVs), due to the large number of sampled flaws that must be evaluated. Although the WF technique is general, it is typically used only for axis-aligned flaws. Recent discoveries of off-axis flaws in operating nuclear reactors have necessitated detailed simulations of such flaws and the interactions between neighboring flaws. This paper presents a generalized WF approach applicable for analyzing arbitrary flaw geometries in thick-walled cylindrical vessels, including surface-breaking and subsurface flaws, which can either axis-aligned or off-axis, and can account for interactions with other flaws. Herein, this approach is demonstrated on representative simulations of multiple flaw geometries in a RPV subjected to transient loading conditions. In all cases, the WF technique gives good comparison with benchmark results from direct simulation with greatly reduced computational effort.

42 ENGINEERING↗

Twisty-puzzle-inspired approach to Clifford synthesis

The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's cube twisty puzzle, here we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than the decomposition methods used in the Qiskit decomposition protocol, which uses a combination of several well-known Clifford decomposition schemes. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may be incorporated, thus allowing for the approach to be tailored to a specific device.

97 MATHEMATICS AND COMPUTING↗

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

97 MATHEMATICS AND COMPUTING↗

Radioisotope Identification with List-Mode Gamma-Ray Data

This work explores the potential of utilizing temporal data from gamma-ray detectors, known as list-mode data, to enhance radioisotope identification. Traditional identification methods, which rely on full gamma-ray spectrum analysis, often require long dwell times and struggle with spectra containing similarly spaced spectral peaks. We hypothesize that by leveraging the probabilistic nature of nuclear decay and the time-encoded information from decay sequences and interactions with surrounding materials, we can improve classification accuracy over static spectral analysis. This research examines the temporal content of list-mode data through exploratory data analysis via correlation discovery and qualitative distribution analysis. Additionally, we propose a probabilistic classification model that can utilize spectral data, temporal data, or both to determine if the incorporation of temporal information improves radioisotope identification. Our findings suggest that the temporal information present in list-mode gamma-ray data has merit and should be further investigated to develop more robust and optimal methods for utilizing this temporal information in applications requiring radioisotope identification.

List-mode data↗

MASTODON: An Open-Source Software for Seismic Analysis and Risk Assessment of Critical Infrastructure

Seismic analysis and risk assessment of safety-critical infrastructure like hospitals, nuclear power plants, dams, and facilities handling radioactive materials involve computationally intensive numerical models and coupled multiphysics scenarios. They are also performed in a strict regulatory environment that requires high software quality assurance standards, and in the case of safety-related nuclear facilities, a conformance to the American Society of Mechanical Engineers Nuclear Quality Assurance (NQA-1) standard. This paper introduces the open-source finite-element software, MASTODON (Multi-hazard Analysis of Stochastic Time-Domain Phenomena), which implements state-of-the-art seismic analysis and risk assessment tools in a quality-controlled environment. MASTODON is built on MOOSE (Multi-physics Object-Oriented Simulation Environment), which is a highly parallelizable, NQA-1 conforming, coupled multiphysics, finite-element framework developed at Idaho National Laboratory. MASTODON is capable of fault rupture and source-to-site wave propagation using the domain reduction method, nonlinear site response, and soil-structure interaction analysis, implicit and explicit time integration, automated stochastic simulations, and seismic probabilistic risk assessment. When coupled with other MOOSE applications, MASTODON can also solve strongly and weakly coupled multiphysics problems. This paper presents a summary of the capabilities of MASTODON and some demonstrative examples.

42 ENGINEERING↗

Uniformly decaying subspaces for error-mitigated quantum computation

Here, we present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error-mitigated quantum computation. The expectation values of dynamics encoded in such subspaces are unbiased estimators of noise-free expectation values. In analogy to the decoherence free subspaces which are left invariant by the action of Lindblad operators, we show that the uniformly decaying subspaces are left invariant (up to orthogonal terms) by the action of the dissipative part of the Lindblad equation. We apply our theory to a system of qubits and qudits undergoing relaxation with varying decay rates and show that such subspaces can be used to eliminate bias up to first-order variations in the decay rates without requiring full knowledge of noise. Since such a bias cannot be corrected through standard symmetry verification, our method can improve error mitigation in dual-rail qubits and, given partial knowledge of noise, can perform better than probabilistic error cancellation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty

This work focuses on visualizing uncertainty of local divergence of two-dimensional vector fields. Divergence is one of the fundamental attributes of fluid flows, as it can help domain scientists analyze potential positions of sources (positive divergence) and sinks (negative divergence) in the flow. However, uncertainty inherent in vector field data can lead to erroneous divergence computations, adversely impacting downstream analysis. While Monte Carlo (MC) sampling is a classical approach for estimating divergence uncertainty, it suffers from slow convergence and poor scalability with increasing data size and sample counts. Thus, we present a two-fold contribution that tackles the challenges of slow convergence and limited scalability of the MC approach. (1) We derive a closed-form approach for highly efficient and accurate uncertainty visualization of local divergence, assuming independently Gaussian-distributed vector uncertainties. (2) We further integrate our approach into Viskores, a platform-portable parallel library, to accelerate uncertainty visualization. In our results, we demonstrate significantly enhanced efficiency and accuracy of our serial analytical (speed-up up to 1946×) and parallel Viskores (speed-up up to 19698×) algorithms over the classical serial MC approach. We also demonstrate qualitative improvements of our probabilistic divergence visualizations over traditional mean-field visualization, which disregards uncertainty. We validate the accuracy and efficiency of our methods on wind forecast and ocean simulation datasets.

Ouermi, Timbwaoga [University of Utah]↗

CV4Quantum

CV4Quantum is a statistical technique for reducing the sampling overhead in probabilistic error cancellation, which is an error mitigation technique used in quantum computing. CV4Quantum is based on the control variates method, which is a Monte Carlo variance reduction technique. This repository contains the code and data associated with a demonstration of CV4Quantum using simulation experiments.

Shyamsundar, Prasanth [Fermi National Accelerator ↗

Internship Final Report on the unsupervised learning sensor fusion (ULSF) approach

This paper describes a summer internship project undertaken at Sandia National Labs (SNL), both current status and future work. The project was to explore various machine learning approaches for use on turbulent flow data. Specifically, unsupervised classification of turbulent flow data was explored. First, the usage of models in this field is discussed, and several issues in the common usage of the models are identified. Solutions to these issues are then proposed, in the form of a Bayesian filtering approach which probabilistically incorporates multiple sources of data to improve confidence in a result. Several types of sensors are suggested for this method, the incorporation of which range from semi-supervised learning approaches to fully unsupervised. These approaches are then tested on several turbulent flow cases.

97 MATHEMATICS AND COMPUTING↗

Probabilistic Power Flow Based on a Gaussian Process Emulator

In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator has allowed us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method.

42 ENGINEERING↗

Probabilistic Evaluation of Geomechanical Risks in CO2 Storage: An Exploration of Caprock Integrity Metrics Using a Multilaminate Model

The probabilistic uncertainty assessment of geomechanical risk—specifically, caprock failure—attributable to CO2 injection, as presented in a simplified hypothetical geological model, was the focus of this study. Our approach amalgamates the implementation of a multilaminate model, the creation of a response surface model in conjunction with the Box–Behnken sampling design, the execution of associated numerical modeling experiments, and the utilization of Monte Carlo simulations. Probability distributions to encapsulate the inherent variability (elastic and mechanical properties of the caprock and reservoir) and uncertainty in prediction estimates (vertical displacement, total strain, and F value) were employed. Our findings reveal that the Young modulus of the caprock is a key factor controlling equivalent total strain but is insufficient as a stand-alone indicator of caprock integrity. It is confirmed that the caprock can accommodate significant deformation without failure, if it possesses a low Young’s modulus and high mechanical strength properties, such as the friction angle and uniaxial compressive strength. Similarly, vertical displacement was found to be an unreliable indicator for caprock integrity, as caprock failure can occur across a broad spectrum of vertical displacements, particularly when both the Young modulus and mechanical strength properties have wide ranges. This study introduces the F value as the most dependable indicator for caprock failure, although it is a theoretical attribute (the shortest distance between the Mohr circle and the nearest failure envelope used to measure the sensitivity to failure) and not physically measurable in the field. Deviatoric stress levels were found to vary based on stress regimes, with the maximum levels observed under extensive and compressive stress regimes. In conjunction with the use of the response surface method, this study demonstrates the efficacy of the multilaminate framework and the Mohr–Coulomb constitutive model in providing a simplified, yet effective, probabilistic model of the mechanical behavior of caprock failure, reducing mathematical and computational complexities.

Energy & Fuels↗

Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

97 MATHEMATICS AND COMPUTING↗

Revisiting a Drag Partition Model For Canopy-Like Roughness Elements

Turbulent flows over a large surface area (S) covered by n obstacles experience an overall drag due to the presence of the ground and the protruding obstacles into the flow. The drag partition between the roughness obstacles and the ground is analyzed using an analytical model proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992) and is hereafter referred to as R92. The R92 is based on the premise that the wake behind an isolated roughness element can be described by a shelter area A and a shelter volume V. The individual sizes of A and V without any interference from other obstacles can be determined from scaling analysis for the spread of wakes. To upscale from an individual roughness element to n/S elements where wakes may interact, R92 adopted a background stress re-normalizing instead of reducing A or V with each element addition. This work demonstrates that R92’s approach results in a linear background stress reduction in A and V only when the ratio of n/S is small, due to a low probability of wake interactions. This probabilistic nature suggests that up-scaling from individual to multiple roughness elements can be re-formulated using stochastic averaging methods proposed here. The two approaches are shown to recover R92 under plausible conditions. An alternative scaling for the shelter volume is also proposed here using thermodynamic arguments of work and dissipation though the final outcome remains similar to R92. Comparisons between R92 and available data spanning more than two decades after R92 on blocks and vegetation-like roughness elements confirm the practical utility of R92. The agreement between R92 and this updated databases of experiments and simulations confirm the potential use of R92 in large-scale models provided that the relevant parameters accommodate certain features of the roughness element type (cube versus vegetation-like) and, to a lesser extent, their configuration throughout S. Last, a comparison between R92 and models based on first-order closure principles with constant mixing length suggests that R92 can outperform such models when evaluated across a wide range of roughness densities.

canopy turbulence↗

Analyzing Hardware and Software Common Cause Failures in Digital Instrumentation and Control Systems using Dual Error Propagation Method

This paper develops a methodology for quantifying software common cause failures (CCFs) in digital instrumentation and control (I&C) systems of nuclear power plants. To support the transition of analog I&C systems to digital in nuclear power plants, probabilistic risk assessment (PRA) techniques are used. The hardware components of the I&C systems have reliability databases that can be used in the PRA studies. However, the failure data for redundant software components of the systems is sparse. Failure of components constitutes a CCF, wherein two or more components or systems fail due to a single shared cause and coupling mechanism. This paper proposes a quantification approach that can simultaneously model hardware and software components, incorporate the CCFs of software systems in the models, and bridge the gap between the failure quantification of models and the development of CCF parametric databases. We demonstrate the dual error propagation method (DEPM) by developing I&C systems failure models for a representative digital reactor trip system. The DEPM models are built to simulate the control and data flows within the systems and can accommodate failure states. By expanding DEPM to software CCFs, we generated alpha factor parameter estimates for each of the modeled error propagation mechanisms.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗

Machine Learning Emulation of Spatial Deposition from a Multi-Physics Ensemble of Weather and Atmospheric Transport Models

In the event of an accidental or intentional hazardous material release in the atmosphere, researchers often run physics-based atmospheric transport and dispersion models to predict the extent and variation of the contaminant spread. These predictions are imperfect due to propagated uncertainty from atmospheric model physics (or parameterizations) and weather data initial conditions. Ensembles of simulations can be used to estimate uncertainty, but running large ensembles is often very time consuming and resource intensive, even using large supercomputers. In this paper, we present a machine-learning-based method which can be used to quickly emulate spatial deposition patterns from a multi-physics ensemble of dispersion simulations. We use a hybrid linear and logistic regression method that can predict deposition in more than 100,000 grid cells with as few as fifty training examples. Logistic regression provides probabilistic predictions of the presence or absence of hazardous materials, while linear regression predicts the quantity of hazardous materials. The coefficients of the linear regressions also open avenues of exploration regarding interpretability—the presented model can be used to find which physics schemes are most important over different spatial areas. A single regression prediction is on the order of 10,000 times faster than running a weather and dispersion simulation. However, considering the number of weather and dispersion simulations needed to train the regressions, the speed-up achieved when considering the whole ensemble is about 24 times. Ultimately, this work will allow atmospheric researchers to produce potential contamination scenarios with uncertainty estimates faster than previously possible, aiding public servants and first responders.

97 MATHEMATICS AND COMPUTING↗