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Results for “uncertainty Quantification”

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.

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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A probabilistic graphical model foundation for enabling predictive digital twins at scale

A unifying mathematical formulation is needed to move from one-off digital twins built through custom implementations to robust digital twin implementations at scale. This work proposes a probabilistic graphical model as a formal mathematical representation of a digital twin and its associated physical asset. We create an abstraction of the asset–twin system as a set of coupled dynamical systems, evolving over time through their respective state spaces and interacting via observed data and control inputs. The formal definition of this coupled system as a probabilistic graphical model enables us to draw upon well-established theory and methods from Bayesian statistics, dynamical systems and control theory. The declarative and general nature of the proposed digital twin model make it rigorous yet flexible, enabling its application at scale in a diverse range of application areas. Here, we demonstrate how the model is instantiated to enable a structural digital twin of an unmanned aerial vehicle (UAV). The digital twin is calibrated using experimental data from a physical UAV asset. Its use in dynamic decision-making is then illustrated in a synthetic example where the UAV undergoes an in-flight damage event and the digital twin is dynamically updated using sensor data. The graphical model foundation ensures that the digital twin calibration and updating process is principled, unified and able to scale to an entire fleet of digital twins.

42 ENGINEERING↗
DOE OSTI2026

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

New results in the CTEQ-TEA global analysis of parton distributions in the nucleon

This report summarizes the latest developments in the CTEQ-TEA global analysis of parton distribution functions (PDFs) in the nucleon. The focus is on recent NNLO fits to high-precision LHC data at 8 and 13 TeV, including Drell–Yan, jet, and top-quark pair production, pursued on the way toward the release of the new generation of CTEQ-TEA general-purpose PDFs. The report also discusses advancements in statistical and numerical methods for PDF determination and uncertainty quantification, highlighting the importance of robust and replicable uncertainties for high-stakes observables. Additionally, it covers phenomenological studies related to PDF determination, such as the interplay of experimental constraints, exploration of correlations between high-x nucleon sea and low-energy parity-violating measurements, fitted charm in the nucleon, the photon PDF in the neutron, and simultaneous SMEFT-PDF analyses.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

FY22 Status Report on the ART-GCR CMVB and CNWG International Collaborations

This work presents the numerical model for the high temperature test reactor (HTTR) loss of forced cooling (LOFC) experiment with the INL codes Griffin, BISON, and RELAP-7, based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Promising results were obtained, with the overall behavior of the reactor successfully captured. Changes in the heat transfer coupling, as compared to the fiscal year (FY)-21 model, enabled drastic improvement of the steady-state solution, both in terms of computational time and global energy discrepancies. The former was reduced by a factor of roughly 60, whereas the latter decreased from 11% to less than 2%. Furthermore, the discrepancy in the steady-state multiplication factor was improved from +2,300 and +2,900 pcm (for the 30 and 9 MW cases) to -700 and +1,200 pcm, respectively, and now falls well within the large measurement uncertainties stemming from graphite impurities. Validation of the Monte Carlo model used to generate cross sections was also performed against available measurements. Though significant, the discrepancies remain acceptable overall in light of the large uncertainty. Numerous improvements are still needed to better compare with the experiment involving the 9 MW case and to instill greater confidence in the model’s ability to accurately predict the 30 MW behavior. Specifically, the power levels predicted by the 9 MW transient simulation following re-criticality remain low, pointing to an underestimation of the passive cooling of the core. A key aspect of future work will be to better understand the flow pattern during the LOFC event, particularly to determine if natural or forced convection is occurring inside the reactor pressure vessel (RPV). More generally, additional validation data would be immensely useful for further enhancing the numerical model and better matching the experiments. In addition, a more sophisticated thermal-hydraulics model that simulates all the channels as a single system model should be considered to take into account the rest of the primary loop. Finally, even if the results are in better agreement with the experiments, sensitivity analysis and uncertainty quantification will be necessary to evaluate the model uncertainty.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

A probabilistic inverse prediction method for predicting plutonium processing conditions

In the past decade, nuclear chemists and physicists have been conducting studies to investigate the signatures associated with the production of special nuclear material (SNM). In particular, these studies aim to determine how various processing parameters impact the physical, chemical, and morphological properties of the resulting special nuclear material. By better understanding how these properties relate to the processing parameters, scientists can better contribute to nuclear forensics investigations by quantifying their results and ultimately shortening the forensic timeline. This paper aims to statistically analyze and quantify the relationships that exist between the processing conditions used in these experiments and the various properties of the nuclear end-product by invoking inverse methods. In particular, these methods make use of Bayesian Adaptive Spline Surface models in conjunction with Bayesian model calibration techniques to probabilistically determine processing conditions as an inverse function of morphological characteristics. Not only does the model presented in this paper allow for providing point estimates of a sample of special nuclear material, but it also incorporates uncertainty into these predictions. This model proves sufficient for predicting processing conditions within a standard deviation of the observed processing conditions, on average, provides a solid foundation for future work in predicting processing conditions of particles of special nuclear material using only their observed morphological characteristics, and is generalizable to the field of chemometrics for applicability across different materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Learning thermodynamically constrained equations of state with uncertainty

Numerical simulations of high energy-density experiments require equation of state (EOS) models that relate a material’s thermodynamic state variables—specifically pressure, volume/density, energy, and temperature. EOS models are typically constructed using a semi-empirical parametric methodology, which assumes a physics-informed functional form with many tunable parameters calibrated using experimental/simulation data. Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in EOS predictions. Model uncertainty is challenging for UQ studies since it requires exploring the space of all possible physically consistent functional forms. Thus, it is often neglected in favor of parametric uncertainty, which is easier to quantify without violating thermodynamic laws. This work presents a data-driven machine learning approach to constructing EOS models that naturally captures model uncertainty while satisfying the necessary thermodynamic consistency and stability constraints. We propose a novel framework based on physics-informed Gaussian process regression (GPR) that automatically captures total uncertainty in the EOS and can be jointly trained on both simulation and experimental data sources. A GPR model for the shock Hugoniot is derived, and its uncertainties are quantified using the proposed framework. We apply the proposed model to learn the EOS for the diamond solid state of carbon using both density functional theory data and experimental shock Hugoniot data to train the model and show that the prediction uncertainty is reduced by considering thermodynamic constraints.

Sharma, Himanshu (ORCID:000900050235718X)↗
DOE OSTI2025

Toward shell model interactions with credible uncertainties

Background: The nuclear shell model is a powerful framework for predicting nuclear structure observables, but relies on interaction matrix elements fit to experimental data as its inputs. Extending the shell model's applicability, particularly toward dripline nuclei, requires efficient fitting methods and credible uncertainty quantification. Traditional approaches face computational challenges and may underestimate uncertainties. Purpose: We develop and test a framework combining eigenvector continuation and Markov chain Monte Carlo to efficiently fit shell model interaction matrix elements and quantify their uncertainties. Methods: Eigenvector continuation is used to emulate shell model calculations, reducing computational costs. The emulator enables Markov chain Monte Carlo sampling to optimize interaction matrix elements and rigorously assess parametric uncertainties. Here, the framework is benchmarked using the USDB interaction in the 𝑠⁢𝑑 shell. Results: The emulator reproduces the USDB interaction with negligible error, validating its use in shell model fitting applications. However, we find that to obtain credible predictive intervals, the model defect of the shell model itself, rather than experimental or emulator error, must be taken into account in order to obtain credible uncertainties. Conclusions: The proposed framework provides an efficient and rigorous approach for fitting shell model interactions and quantifying uncertainties. Further, the normality assumption used in the past appears sufficient to describe the distribution of interaction matrix elements. However, it is crucial to account for model correlations to avoid underestimating uncertainties.

Nuclear forces↗
DOE OSTI2025

Quantifying uncertainty in machine learning for nuclear binding energy

Techniques from artificial intelligence and machine learning are increasingly employed in nuclear theory; however, the uncertainties that arise from the complex parameter manifold encoded by the neural networks are often overlooked. Epistemic uncertainties arising from training the same network multiple times for an ensemble of initial weight sets offer a first insight into the confidence of machine learning predictions, but they often come with a high computational cost. Instead, we apply a single-model uncertainty quantification method called Δ-UQ that gives epistemic uncertainties with one-time training. Here, we demonstrate our approach on a two-feature model of nuclear binding energies per nucleon with proton and neutron number pairs as inputs. We show that Δ-UQ can produce reliable and self-consistent epistemic uncertainty estimates and can be used to assess the degree of confidence in predictions made with deep neural networks.

Huang, Mengyao [Lawrence Livermore National Labora↗
DOE OSTI2020

CheKiPEUQ Intro 2: Harnessing Uncertainties from Data Sets, Bayesian Design of Experiments in Chemical Kinetics**

When choosing experimental conditions, Bayesian statistical tools can predict the experimental choices which will yield the highest information gain. Experimental choices could be temperature, pressure, reaction time, number of measurements, reactor volume, etc.. Three example analyses are presented here, each using the software Chemical Kinetics Parameter Estimation and Uncertainty Quantification (CheKiPEUQ). Information gain is a measure of reduction of uncertainty in a model's parameters. The three chemical system examples presented each illustrate Bayesian Design of Experiments using information gain. In the first chemical example, temperature selection impacts the information gain for the free energy of reaction in a two-component equilibrium reaction. In the second example, temperature and pressure are explored for a competitive adsorption Langmuir replacement reaction system. Finally, the third example is a catalytic membrane reactor which is a culmination of the previous examples. The catalytic membrane reactor has a complex and nonlinear response in the observables which is solved by numerical evaluation. In the three examples, the experimental conditions are treated as design variables for maximizing information gain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Improved nuclear-structure corrections to the hyperfine splitting of electronic and muonic deuterium

We calculate the nuclear-structure correction to the hyperfine splitting in both electronic and muonic deuterium using interactions from chiral effective field theory. We explore the sensitivity to different parameterizations of the nucleon-nucleon force, study the convergence pattern in the order-by-order chiral expansion, and estimate remaining uncertainties. Our results are consistent with earlier calculations from pionless effective field theory, offering new insights for a robust uncertainty quantification. Thanks to the order-of-magnitude reduction in uncertainty achieved with chiral effective field theory, the two-photon exchange contribution in electronic deuterium agrees with experimental extractions within 0.5σ, in contrast to the 2.6σ discrepancy observed in muonic deuterium. This study lays the groundwork for extending TPE calculations to HFS in heavier atomic systems.

Chiral effective field theory↗
DOE OSTI2025

Enhancing generative molecular design via uncertainty-guided fine-tuning of variational autoencoders

In recent years, deep generative models have been successfully applied to various molecular design tasks, particularly in the life and materials sciences. One critical challenge for pre-trained generative molecular design (GMD) models is to fine-tune them to be better suited for downstream design tasks that aim at optimizing specific molecular properties. However, redesigning and training an existing effective generative model from scratch for each new design task are impractical. Furthermore, the black-box nature of typical downstream tasks that involve property prediction makes it nontrivial to optimize the generative model in a task-specific manner. In this work, we propose an uncertainty-guided fine-tuning strategy that can effectively enhance a pre-trained variational autoencoder (VAE) for GMD through performance feedback in an active learning setting. The strategy begins by quantifying the model uncertainty of the generative model using an efficient active subspace-based UQ (uncertainty quantification) scheme. Next, the decoder diversity within the characterized model uncertainty class is explored to expand the viable space of molecular generation. The low-dimensionality of the active subspace makes this exploration tractable using a black-box optimization scheme, which in turn enables us to identify and leverage a diverse set of high-performing models to generate enhanced molecules. Empirical results across six target molecular properties using multiple VAE-based generative models demonstrate that our uncertainty-guided fine-tuning strategy consistently leads to improved models that outperform the original pre-trained models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Characterization of uncertainties in electron-argon collision cross sections

Abstract The predictive capability of a plasma discharge model depends on accurate representations of electron-impact collision cross sections, which determine the corresponding reaction rates and electron transport properties. The values of cross sections can be known only approximately either through experiments or simulations and are thus subject to uncertainties. Quantifying the uncertainties in plasma simulations allows us to assess the reliability of simulations and to provide a basis for interpreting discrepancies between simulations and experiments. For such uncertainty quantification of plasma simulations, it is essential to quantify the uncertainties of the underlying cross sections. Although much effort has been committed to calibrate the cross section values, their uncertainties are not well investigated. We characterize uncertainties in electron-argon atom collision cross sections using a Bayesian framework. Six collision processes—elastic momentum transfer, ionization, and four excitations—are characterized with semi-empirical models, which effectively capture the features important to the macroscopic properties of the plasma. A probability model for the uncertain parameters of these semi-empirical models is developed. Specifically, a Gaussian-process likelihood model is proposed to capture discrepancies among data sets, as well as the model-form inadequacies of the semi-empirical models. Two other likelihood models are compared with the proposed Gaussian-process model, to illustrate the importance of the choice of the likelihood model. The cross section models are calibrated using the electron-beam experiments and ab-inito quantum simulations. The resulting calibrated uncertainties capture well the scattering among the data sets. The calibrated cross section models are further validated against swarm-parameter experiments and zero-dimensional Boltzmann equation simulations of widely used cross section datasets.

Chung, Seung Whan (ORCID:0000000302501549)↗
DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Data Generation for Machine Learning Interatomic Potentials and Beyond

The field of data-driven chemistry is undergoing an evolution, driven by innovations in machine learning models for predicting molecular properties and behavior. Recent strides in ML-based interatomic potentials have paved the way for accurate modeling of diverse chemical and structural properties at the atomic level. The key determinant defining MLIP reliability remains the quality of the training data. A paramount challenge lies in constructing training sets that capture specific domains in the vast chemical and structural space. This Review navigates the intricate landscape of essential components and integrity of training data that ensure the extensibility and transferability of the resulting models. We delve into the details of active learning, discussing its various facets and implementations. We outline different types of uncertainty quantification applied to atomistic data acquisition and the correlations between estimated uncertainty and true error. The role of atomistic data samplers in generating diverse and informative structures is highlighted. Furthermore, we discuss data acquisition via modified and surrogate potential energy surfaces as an innovative approach to diversify training data. The Review also provides a list of publicly available data sets that cover essential domains of chemical space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A theoretical study on quasifission and fusion–fission processes in heavy-ion collisions

Despite recent advances and focus on rigorous uncertainty quantification for microscopic models of quantum many-body systems, the uncertainty on the dynamics of those systems has been underexplored. To address this, we have used time-dependent Hartree-Fock to examine the model uncertainty for a collection of low-energy, heavy-ion fusion reactions. Fusion reactions at near-barrier energies represent a rich test-bed for the dynamics of quantum many-body systems owing to the complex interplay of collective excitation, transfer, and static effects that determine the fusion probability of a given system. The model uncertainty is sizable for many of the systems studied and the primary contribution arises from static properties that are ill-constrained, such as the neutron radius of neutron-rich nuclei. These large uncertainties motivate the use of information from reactions to better constrain existing models and to infer static properties from reaction data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

DeepUQ: Assessing the Aleatoric Uncertainties from two Deep Learning Methods

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.

Nevin, Rebecca↗
DOE OSTI2024

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗