SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
UQ is traditionally defined as quantitative characterization and estimation of uncertainties in both computational and real-world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
The Workshop for Applied Nuclear Data Activities (WANDA) is designed to increase communication among nuclear data (ND) users in multidisciplinary federal programs, ND producers, ND funders, and other ND experts. It also presents an opportunity to cross-pollinate ideas as well as introduce ND gaps identified by federal programs to ND experts and ND capabilities to the various federal ND users. WANDA 2024 included five technical sessions, three of which focused on Fusion Energy Sciences (FES)—FES Fusion Neutronics, FES Tritium Production, and FES Material Damage—and two stand-alone sessions—Isotopes and Targetry for Nuclear Data and Uncertainty Quantification. The FES sessions successfully brought new voices to the WANDA discussions, expanding the application space in which nuclear data are critical. FES programs need accurate nuclear data with realistic uncertainty quantification to properly estimate, for example, shielding, activation, tritium production, helium production, structural material integrity, and superconducting magnet operation. This includes a variety of projectile (neutrons, photons, charged particles) and target atoms. One of the action items common to all the FES sessions was a need to perform sensitivity studies to identify the prioritization of nuclear data needs. The Isotopes and Targetry session highlighted the many capabilities available to produce high-quality targets for nuclear data measurements, including 3D printing with spherical powders, combustion synthesis coupled with spin coating & electrospraying, inkjet printing, and isotopic doping. These new methods open doors for more accurate measurement, but it was also stressed that sample characterization following any method of fabrication is of the highest importance to accurately interpret nuclear data measurement results that used that sample. The Uncertainty Quantification (UQ) session was broken into two categories: nuclear data uncertainty quantification and the use of that uncertainty quantification. Thematic to the UQ session was the loss of information when going from nuclear data measurement, to evaluation, to evaluated file, and finally to neutron transport calculations. Current evaluated ND libraries typically only contain covariances, which assume that the probability distributions are Gaussian. Beyond being a simplified assumption for many evaluations, this can lead to negative values on many observables when attempting to sample the covariance. The covariance format, however, is very efficient in that a simple set of linear equations can transform uncertainty from parameters or cross sections to the application of interest. Focused collaboration is needed between nuclear data evaluators and nuclear data users to ensure that needs are being met.
Small-angle X-ray scattering (SAXS) is a powerful high-throughput characterization tool for probing nanoscale structure in native sample environments, providing real-time morphological information such as nanoparticle size and shape during synthesis. However, automated SAXS data analysis for extracting meaningful structural parameters is non-trivial and remains a bottleneck in closed-loop experimentation towards autonomous materials discovery, which demands fast, reliable, and uncertainty-aware data analysis. Here, we develop a machine-learning approach for automated SAXS analysis tailored to closed-loop nanoparticle synthesis. A Random Forest (RF) regression model is trained on 100,000 synthetic SAXS curves generated from polydisperse spherical nanoparticles with realistic background contributions. Using normalized one-dimensional SAXS intensity profiles as input, the RF model directly predicts nanoparticle radius, size polydispersity, and background parameters, while the ensemble standard deviation across trees provides built-in uncertainty quantification (UQ). On synthetic data, we show that combining fit-quality metrics (R 2 , MAE) with thresholds on prediction uncertainty reliably identifies accurate parameter estimates without access to ground truth. We then apply the trained model to 365 experimental SAXS profiles of citrate-reduced gold nanoparticles synthesized using an automated droplet-flow microreactor with in situ SAXS at a synchrotron beamline, classifying the results into high- and low-confidence subsets based on UQ metrics. Finally, we integrate RF-based SAXS analysis into a simulated closed-loop optimization campaign using Gaussian process Bayesian optimization to minimize nanoparticle polydispersity, benchmarking against conventional automated Levenberg–Marquardt fitting. The RF-guided campaign exhibits substantially faster convergence and lower relative opportunity cost (∼0.07 vs ∼0.3), demonstrating that uncertainty-aware machine-learning SAXS analysis significantly enhances the efficiency and robustness of autonomous nanomaterials synthesis workflows.
To date, while the use of CFD for aerospace vehicle design and development is prevalent, the documentation of uncertainties associated with the simulations are rare. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the research and engineering design community, test and evaluation community, and ultimately certification for flight. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. These factors have prevented the adoption of UQ methods in the engineering design and development cycle. This presentation will outline a credible approach to UQ using Probability Boxes that is straightforward to apply, and can readily be automated using existing UQ tool sets such as the DAKOTA packaged developed at Sandia. The added expense incurred when moving away from a deterministic CFD process to a stochastic one that captures uncertainties to enable risk-informed decision making will be discussed, as well as effective ways to reduce the computational costs.
By virtually representing a physical object and process, a digital twin (DT) enables optimal autonomous operations by combining classical and novel frameworks in sensors, state predictions, and multi-input/multi-output systems. A DT’s values depend on how well models estimate quantities of interest and on how uncertainty is handled. Moreover, DTs often combine physics-based and data-driven models with mixed fidelities, where classical uncertainty quantification (UQ) struggles with many sources of uncertainty and real-time constraints. Here, this work presents a UQ-based discrepancy checking and diagnosis tool for a DT-based supervisory control system. The tool is developed using metadata from an automated DT development process to learn correlations between sources of uncertainties and outcomes. During operation, it compares predictions with measurements, attributes discrepancies to dominant sources, and recommends parameter and configuration updates. We verify the workflow on a synthetic temperature-control problem and deploy it on a virtual Thermal Energy Delivery System, reducing mismatch and improving control robustness.
Defined as a virtual representation of a physical object, process, or service, and used to support real-world decision-making, a digital twin (DT) can be utilized to combine classical and novel frameworks in sensors, state predictions, and multi-input/multi-output systems, and to enable optimal autonomous operations. However, a DT’s usefulness largely depends on its ability to adequately mirror the state of its physical counterpart, and this adequacy should be reflected by the level of uncertainty in the underlying simulation models when estimating and predicting quantities of interest (QOIs). Moreover, simulation models in a DT may involve multiple fidelities of representations—ranging from physics-based models to data-driven ones—but classical uncertainty quantification (UQ) methods struggle to handle numerous uncertainty sources, nor are they designed for real-time applications. This work presents a UQ-based discrepancy checking and diagnosis tool for a DT-based supervisory control system applied to a thermal energy delivery system (TEDS) at Idaho National Laboratory. The discrepancy checker was developed using metadata from an automated DT development process, and these metadata included different combinations of physical model forms and model parameters, training data and hyperparameters for surrogate models, and design parameters for supervisory control systems. Next, correlations between the uncertainty results and the metadata were established and then applied to the DT operations. The discrepancy checker evaluates the discrepancies between model predictions from virtual and sensor measurements and backtraces them to the corresponding major sources of uncertainty. The discrepancy checker showed reasonable performance in detecting discrepancies and diagnosing sources of uncertainty in testing scenarios.
Uncertainty quantification (UQ) has become more critical in aerospace engineering due to the growing dependence on computational tools for design optimization and performance analyses of aerospace vehicles. Even though the significance of UQ in assessing the credibility of computational analyses is well recognized, its costs and complexity impede its integration into standard practices, particularly in computational fluid dynamics (CFD) and other fluid analyses. This paper presents a UQ study for low-fidelity computational aerodynamics analyses with XFOIL and mfoil (i.e., the MATLAB version of XFOIL with several implementation modifications); these tools are utilized widely in both research and education. The main contributions of this paper are as follows: 1) improved precision in quantifying the uncertainty of the baseline Monte Carlo results used to benchmark surrogate modeling techniques for UQ, 2) quantification of the effect of the implementation differences between XFOIL and mfoil on solution quantities of interest (QoIs), such as lift and pitching moment coefficients, and 3) development of an open-source UQ library for use with XFOIL and mfoil, which has educational values and helps promote UQ for fluid analyses with aerospace applications. Results and discussions revolve around cases 1-4 of the challenge problem posed by the AIAA Fluid Dynamics Technical Committee’s Uncertainty Quantification Discussion Group (UQDG). In case 3, this work employs CFDverify, an open-source solution verification software, to quantify the discretization error and evaluate the extrapolated QoIs based on the grid convergence index (GCI). This UQ study differentiates itself from previous studies in the rigor of handling baseline Monte Carlo uncertainty and in including mfoil, which is a more accessible alternative to XFOIL. Finally, despite the growing computing power, low-fidelity computational tools remain valuable, such as for aerodynamic shape optimization at Mach numbers below 0.65 and low-to-mid Reynolds numbers.
The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.
There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.
For multi-scale multi-physics applications e.g., the turbulent combustion code Pele, robust and accurate dimensionality reduction is crucial to solving problems at exascale and beyond. A recently developed technique, Co-Kurtosis based Principal Component Analysis (CoK-PCA) which leverages principal vectors of co-kurtosis, is a promising alternative to traditional PCA for complex chemical systems. To improve the effectiveness of this approach, we employ Artificial Neural Networks for reconstructing thermo-chemical scalars, species production rates, and overall heat release rates corresponding to the full state space. Our focus is on bolstering confidence in this deep learning based non-linear reconstruction through Uncertainty Quantification (UQ) and Sensitivity Analysis (SA). UQ involves quantifying uncertainties in inputs and outputs, while SA identifies influential inputs. One of the noteworthy challenges is the computational expense inherent in both endeavors. To address this, we employ the Monte Carlo methods to effectively quantify and propagate uncertainties in our reduced spaces while managing computational demands. Our research carries profound implications not only for the realm of combustion modeling but also for a broader audience in UQ. By showcasing the reliability and robustness of CoK-PCA in dimensionality reduction and deep learning predictions, we empower researchers and decision-makers to navigate complex combustion systems with greater confidence.
We define the notions of verification, validation, and uncertainty quantification (VVUQ), and place them in the context of retrievals of Earth science data. Uncertainty quantification (UQ) is the process of characterizing the uncertainty of a measurement system relative to the true, physical quantity it measures. UQ is needed when measurements are used for scientific inference, assimilated into models with other data, and used for decision-making and risk analysis. Many measurements come with measures of standard error and bias, but these uncertainty measures are often inaccurate, due to the operational need to assume crisp values for parameters which are in fact uncertain, as well as the failure of technical assumptions needed by operational error-estimation approaches. UQ provides a way to study which assumptions fail to hold, and a tool to improve the measurement. We describe a particular, broadly-applicable UQ setup that has been successful for JPL retrievals including OCO-2, and provide recommendations for furthering the UQ state of the practice at JPL.
Joule heating (JH) is an energy-efficient and sustainable technique for heating materials. Its application for industrial heating, particularly, has been gaining attention due to its potential for increasing the yield of various chemical products. The process involves the use of heating elements (materials that are highly conductive electrically and thermally) to heat up other materials or substances. These conductors, however, can exhbit varying degrees of uncertainty due to non-linearities in their temperature-dependent properties, which could result in variable material behavior. In this work, we carry out uncertainty quantification (UQ) at the pore scale to describe the uncertainty of such materials. In so doing, we applied the non-intrusive polynomial chaos expansion (PCE) technique to quantify the uncertainty within the system. The steady state Joule heating equation was solved numerically at the pore scale mimicking conditions within a heating chamber for propane dehydrogenation, and various electro-thermal profiles were obtained. We also examined the effect of the number of sampling points (20 – 100) and order of the PCE coefficients (2 – 5) on the accuracy of the temperature evaluations. The results were then benchmarked with the standard Monte Carlo (MC) method. The average temperature of the 4th-order global PCE showed good agreement with the MC results (which were positively skewed). Orders greater than 4 gave an underestimation of the temperatures while predictions for the peak temperature improved as the number of sampling points increased.
The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.
To date, while the use of CFD is prevalent, very few efforts have been undertaken that truly attempt to document all (or even most) of the sources of uncertainty in the simulations. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the design research and engineering community, test and evaluation community, and ultimately certification for flight. This is especially true for hypersonic air-breathing propulsion systems due to the environment, scale, and duration limitations of ground test facilities. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. Hence, a major obstacle that has prevented the adoption of UQ methods for engineering design and development work is the lack of a tool set to automate most (if not all) of the UQ workflow. Towards this end, the SANDIA package DAKOTA (which has been developed to drive both UQ and optimization processes) will be tightly wrapped around the VULCAN-CFD code to automate the uncertainty quantification process. The automated process will be applied to an isolator turbulence model validation exercise that has previously been documented using a manual approach to the UQ process. Hence, the focus of this paper will be documenting the level to which automation can hide the UQ process details from the CFD practitioner rather than the UQ method itself.
Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret exactly. We systematically compare aleatoric uncertainty measured by two UQ techniques, Deep Ensembles (DE) and Deep Evidential Regression (DER). Our method focuses on both zero-dimensional (0D) and two-dimensional (2D) data, to explore how the UQ methods function for different data dimensionalities. We investigate uncertainty injected on the input and output variables and include a method to propagate uncertainty in the case of input uncertainty so that we can compare the predicted aleatoric uncertainty to the known values. We experiment with three levels of noise. The aleatoric uncertainty predicted across all models and experiments scales with the injected noise level. However, the predicted uncertainty is miscalibrated to $\rm{std}(\sigma_{\rm al})$ with the true uncertainty for half of the DE experiments and almost all of the DER experiments. The predicted uncertainty is the least accurate for both UQ methods for the 2D input uncertainty experiment and the high-noise level. While these results do not apply to more complex data, they highlight that further research on post-facto calibration for these methods would be beneficial, particularly for high-noise and high-dimensional settings.
Uncertainty quantification (UQ) provides statistical bounds on prediction accuracy based on finite element model (FEM) uncertainty. An alternate method for UQ, called the Hybrid Parametric Variation (HPV) combines a parametric variation of the Hurty/Craig-Bampton (HCB) fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method. This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available.