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At least 91 records · Page 5

Uncertainty quantification for nuclear forensics with population analyses

Although neural networks offer cutting-edge predictive power, their deployment in high-consequence nuclear forensic applications is limited, partly because of their black-box nature. Incorporating robust uncertainty quantification methods into the predictive frameworks of neural networks is progress towards their future deployment in such scenarios. This work integrates uncertainty quantification into neural networks for nuclear reactor core-average burnup estimation from simulated environmental samples. We test two regimes (homogeneous and heterogeneous events) on DeepSets and Set Transformer architectures, we find both quantify predictive uncertainty effectively, but Set Transformer excels in partitioning latent events, offering superior predictive power and more informative uncertainty estimates.

Hatton, Conner [ORNL] (ORCID:0009000804970959)↗

Demonstration of TOFFEE: A Response Uncertainty Quantification Tool

A key characteristic in neutron transport is nuclear data. Cross-section uncertainty is not used in MCNP6.3 to propagate response uncertainty without external analysis. Here, the TOol For Fast Error Estimation (TOFFEE) is a Python-based code developed to automate the propagation of cross-section uncertainty for MCNP evaluations. TOFFEE implements the sandwich rule to calculate the uncertainty from cross sections with sensitivity coefficients from MCNP6.3 and ENDF/B covariance data. In this paper, TOFFEE has been tested with benchmark experiments, and it has been compared to the uncertainty quantification capabilities of Sampler and TSUNAMI, within SCALE, to verify the application’s capabilities.

97 MATHEMATICS AND COMPUTING↗

Adjustments and Uncertainty Quantification for SLS Aerodynamic Sectional Loads

This paper presents a method for adjusting sectional loads to match target values for integrated force and moment coefficients. In a typical application, the sectional load profile for one flight condition is calculated from Computational Fluid Dynamics (CFD) while the integrated forces and moments are measured in a wind tunnel experiment. These two methods do not generally result in identical predictions, and this leads to an inherent inconsistency between different data products. This paper aims to provide a procedure to remove that inconsistency. A sectional load profile for a launch vehicle splits the rocket into slices along its length and calculates the aerodynamic loading on each slice, which leads to a one-dimensional aerodynamic load profile that is used for structural analysis. Adjusting sectional loads, also known as line loads, is a nontrivial matter due to several consistency constraints. For example, the adjusted sectional normal force profile must be consistent with both the integrated normal force and pitching moment. To avoid such inconsistency issues, this paper presents a method using a Proper Orthogonal Decomposition (POD) to generate basis functions to adjust the sectional load profiles. As a corollary, this correction method enables the creation of an uncertainty quantification for sectional loads that is consistent with the dispersed integrated force and moment database and its uncertainty quantification. Several extensions to this technique, such as applying the method to the surface pressures, are considered.

Quantification↗

Development Strategies for Uncertainty Quantification to Enable Aircraft Certification by Analysis

Aircraft Certification by Analysis (CbA) is a broad term that describes the process by which engineering analysis tools are used to supplement flight testing to demonstrate compliance with regulatory requirements. For each requirement that is to be met through this process, the analysis tools must be sufficiently accurate to ensure that an equivalent level of safety is obtained as if the aircraft to be certified had been flight tested for the requirement. In recent decades, the ability of analysis tools to accurately predict aircraft performance has improved dramatically, leading to increasing interest and limited early adoption of Certification by Analysis across the aerospace industry. However, rigorously demonstrating the credibility of analysis tools remains a challenge for many types of certification requirements, yet is necessary for widespread adoption of CbA approaches in the future. The field of uncertainty quantification is well-suited to address this problem, but will require substantial advances in order to achieve the ambitious industry goals for Certification by Analysis. The objective of this position paper is to highlight gaps in the current technical and programmatic state of uncertainty quantification. Four main categories – Mindset & Awareness, Tools & Capabilities, Data and Benchmarks for V&V, and Applied Research & Established Processes – will be introduced. Each of these categories contains several shortcomings and impediments which, if overcome, will enable more widespread possibilities for Certification by Analysis in the 2040-2050 timeframe.

Uncertainty Quantification↗

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗

Uncertainty quantification for molecular property predictions with graph neural architecture search

Graph Neural Networks (GNNs) have emerged as a prominent class of data-driven methods for molecular property prediction. However, a key limitation of typical GNN models is their inability to quantify uncertainties in the predictions. This capability is crucial for ensuring the trustworthy use and deployment of models in downstream tasks. To that end, we introduce AutoGNNUQ, an automated uncertainty quantification (UQ) approach for molecular property prediction. AutoGNNUQ leverages architecture search to generate an ensemble of high-performing GNNs, enabling the estimation of predictive uncertainties. Our approach employs variance decomposition to separate data (aleatoric) and model (epistemic) uncertainties, providing valuable insights for reducing them. In our computational experiments, we demonstrate that AutoGNNUQ outperforms existing UQ methods in terms of both prediction accuracy and UQ performance on multiple benchmark datasets, and generalizes well to out-of-distribution datasets. Additionally, we utilize t-SNE visualization to explore correlations between molecular features and uncertainty, offering insight for dataset improvement. AutoGNNUQ has broad applicability in domains such as drug discovery and materials science, where accurate uncertainty quantification is crucial for decision-making.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Uncertainty Quantification for Smooth Functional Data with Application to Material Properties

This document outlines a method for processing functional output (i.e., curves) for the ultimate purpose of sampling curves under specified input conditions for use in modeling and simulation uncertainty quantification (UQ) studies. A set of benchmark curves sufficiently representative of the relevant scenario(s) being simulated are provided to the process and formatted as described in Section 1. Principal Component Analysis (PCA) is utilized to discover the components of uncertainty in the benchmark curves and is outlined in Section 2. Section 3 describes the application of uncertainty quantification to the PCA results for the purpose of sampling curves to be used in UQ analysis. Section 4 applies these techniques to an example benchmark dataset. Concluding remarks are provided in the final section.

36 MATERIALS SCIENCE↗

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

Uncertainty quantification and propagation in lithium-ion battery electrodes using bayesian convolutional neural networks

The complex nature of manufacturing processes stipulates electrodes to possess high variability with increased heterogeneity during production. X-ray computed tomography imaging has proved to be critical in visualizing the complicated stochastic particle distribution of as-manufactured electrodes in lithium-ion batteries. However, accurate prediction of their electrochemical performance necessitates precise evaluation of kinetic and transport properties from real electrodes. Image segmentation that characterizes voxels to particle/pore phase is often meticulous and fraught with subjectivity owing to a myriad of unconstrained choices and filter algorithms. Here we utilize a Bayesian convolutional neural network to tackle segmentation subjectivity and quantify its pertinent uncertainties. Otsu inter-variance and Blind/Referenceless Imaging Spatial Quality Evaluator are used to assess the relative image quality of grayscale tomograms, thus evaluating the uncertainty in the derived microstructural attributes. We analyze how image uncertainty is correlated with the uncertainties and magnitude of kinetic and transport properties of an electrode, further identifying pathways of uncertainty propagation within microstructural attributes. The coupled effect of spatial heterogeneity and microstructural anisotropy on the uncertainty quantification of transport parameters is also understood. This work demonstrates a novel methodology to extract microstructural descriptors from real electrode images through quantification of associated uncertainties and discerning the relative strength of their propagation, thus facilitating feedback to manufacturing processes from accurate image based electrochemical simulations.

25 ENERGY STORAGE↗

Uncertainty Quantification for Component Modeling Using the Discrete-Direct Approach

Threaded fastener behavior can be an important aspect of complex component and system behavior, but there is no one-size-fits-all finite element analysis technique. Proper modeling of threaded fastener joints requires careful consideration of many details, from test setup and data acquisition to constitutive modeling and uncertainty quantification approaches. This report details analysis of a “mini-radax” bolted-joint exemplar where a Discrete-Direct uncertainty quantification approach is employed to evaluate margin of the component. The mini-radax geometry is tested to failure on a drop table, and single-coupon tests of individual fasteners serve as foundational data for the analysis. Analysis predictions complement the test data well and provide additional context for engineering decision-making.

42 ENGINEERING↗

UQpy v4.1: Uncertainty quantification with Python

This paper presents the latest improvements introduced in Version 4 of the UQpy, Uncertainty Quantification with Python, library. In the latest version, the code was restructured to conform with the latest Python coding conventions, refactored to simplify previous tightly coupled features, and improve its extensibility and modularity. To improve the robustness of UQpy, software engineering best practices were adopted. A new software development workflow significantly improved collaboration between team members, and continuous integration and automated testing ensured the robustness and reliability of software performance. Continuous deployment of UQpy allowed its automated packaging and distribution in system agnostic format via multiple channels, while a Docker image enables the use of the toolbox regardless of operating system limitations.

97 MATHEMATICS AND COMPUTING↗

Uncertainty quantification for equations of state: copper as an example

Equations of state are essential for providing a fundamental description of materials properties in thermodynamic equilibrium and are used to provide closure relations for hydrodynamics simulations. Generally, equations of state rely on simple physics-based parameterized materials models to inform on the free energy of a material through out a given thermodynamic state space. Historically the parameters of these models have been tuned by hand to fit various experimental data. However, modern optimization and uncertainty quantification techniques allow us to quickly test thousands of parameter combinations and obtain meaningful uncertainty estimates on the parameters, opening opportunities for assessing systematic uncertainties in experiments, assessing model adequacy, and more. In this report, we use Bayesian inference to fit the solid (fcc) equation of state of copper. We focus on fitting five different experimental datasets, including the isobaric density, isobaric heat capacity, room temperature isotherm, principal isentrope, and principal Hugoniot. We fit all five data types simultaneously, and then explore the extent to which combinations of 2 subsets of the 5 datasets can constrain the EOS parameters, as compared to the fit to all 5. This information is useful for investigating the extent to which different datasets can con strain EOS models and thereby help guide experimental investigations in order to best constrain the EOS. We also discuss ways that the methodologies can be used to investigate systematic discrepancies between experiments, as well as how the methods can be used to assess model uncertainty. The framework we develop is general, in that it can be used with a variety of optimization or uncertainty quantification techniques and with a variety of data sources, including both experimental and ab-inito data.

97 MATHEMATICS AND COMPUTING↗

Eucalyptus – An Analysis Suite for Fault Trees with Uncertainty Quantification

Eucalyptus is a novel code developed at Lawrence Livermore National Laboratory to incorporate uncertainty quantification into Fault Tree Analysis (FTA). This tool addresses the challenge of imperfect knowledge in “grey-box” systems by allowing analysts to incorporate and propagate uncertainty from component-level assessments to system-level effects. Eucalyptus facilitates a consistent evaluation of the impact of subject matter expert judgment and knowledge gaps on overall system response by Monte Carlo generation of possible system fault trees, sampling probabilities of the existence of subsystems and components. Here, the code supports the specification of fault trees through text and allows export to various formats, including auto-generated images, easing analysis and reducing errors. It has undergone extensive verification testing, demonstrating its reliability and readiness for deployment, and leverages on-node parallelism for rapid analysis. Example analyses are shown that include the identification of system failure paths and quantification of the value of further information about system components.

Fault Tree Analysis↗

Development of the uncertainty quantification toolkit's python interface and surrogate construction tutorial

The uncertainty quantification toolkit (UQTk) is a collection of c++ libraries that assess the confidence of numerical models. Surrogate approximations, often polynomial chaos expansions (PCEs), lessen the computational cost of these assessments. I developed a Python interface in UQTk for regression and Bayesian compressive sensing to add to the existing Galerkin projection method. These methods receive an object containing the polynomial basis information and NumPy arrays of sample points, call c++ methods, and return the PCE coefficients in a NumPy array. To demonstrate these methods, I wrote a tutorial in which I use them to construct surrogates for Genz functions and calculate the resulting error.

97 MATHEMATICS AND COMPUTING↗

UQ4QM: Uncertainty Quantification for Quantum Materials (Chemical Dynamics Initiative Final Report)

The Uncertainty Quantification for Quantum Materials (UQ4QM) LDRD project focused on developing solutions for strategic two project areas the Chemical Dynamics Initiative (CDi) Use Case 3. This included data-driven approaches toward understanding heterogeneous data, such as multi-fidelity data or data with unknown spatial or temporal perturbations. The applications were varied but the project aims pursued solutions which were amenable to common UQ approaches in order to maximize impact.

36 MATERIALS SCIENCE↗

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. In conclusion, we demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

97 MATHEMATICS AND COMPUTING↗

An Uncertainty Quantification Framework for Autonomous Flight System Tracking and Health Monitoring

This work proposes a perspective towards establishing a framework for uncertainty quantification of autonomous system tracking and health monitoring. The approach leverages the use of a predictive process structure, which maps uncertainty sources and their interaction according to the quantity of interest and the goal of the predictive estimation. It is systematic and uses basic elements that are system agnostic, and therefore needs to be tailored according to the specificity of the application. This work is motivated by the interest in low-altitude unmanned aerial vehicle operations, where awareness of vehicle and airspace state becomes more relevant as the density of autonomous operations grows rapidly. Predicted scenarios in the area of small vehicle operations and urban air mobility have no precedent, and holistic frameworks to perform prognostics and health management (PHM) at the system- and airspace-level are missing formal approaches to account for uncertainty. At the end of the paper, two case studies demonstrate implementation framework of trajectory tracking and health diagnosis for a small unmanned aerial vehicle. This work has been accepted for publication at the International Journal of Prognostics and Health Management Jan 2021. Minor edits have been incorporated to this original submission to incorporate complete overview and software integration.

Uncertainty Quantification↗

UQTools: The Uncertainty Quantification Toolbox - Introduction and Tutorial

UQTools is the short name for the Uncertainty Quantification Toolbox, a software package designed to efficiently quantify the impact of parametric uncertainty on engineering systems. UQTools is a MATLAB-based software package and was designed to be discipline independent, employing very generic representations of the system models and uncertainty. Specifically, UQTools accepts linear and nonlinear system models and permits arbitrary functional dependencies between the system s measures of interest and the probabilistic or non-probabilistic parametric uncertainty. One of the most significant features incorporated into UQTools is the theoretical development centered on homothetic deformations and their application to set bounding and approximating failure probabilities. Beyond the set bounding technique, UQTools provides a wide range of probabilistic and uncertainty-based tools to solve key problems in science and engineering.

Kenny, Sean P.↗