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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

ROBUST ONLINE MONITORING FOR CALIBRATION ASSESSMENT OF TRANSMITTERS AND INSTRUMENTATION

Robust online monitoring (OLM) technologies are expected to enable the extension or elimination of periodic sensor calibration intervals in operating and new reactors. Specifically, the next generation of OLM technology is expected to include newly developed advanced algorithms that improve monitoring of sensor/system performance and enable the use of plant data to derive information that currently cannot be measured. These advances in OLM technologies will improve the safety and reliability of current and planned nuclear power systems through improved accuracy and increased reliability of sensors used to monitor key parameters. In this paper, we discuss an overview of research being performed within the Nuclear Energy Enabling Technologies (NEET)/Advanced Sensors and Instrumentation (ASI) program, for the development of OLM algorithms to use sensor outputs and, in combination with other available information, 1) determine whether one or more sensors are out of calibration or failing and 2) replace a failing sensor with reliable, accurate sensor outputs. Algorithm development is focused on the following OLM functions: • Signal validation – fault detection and selection of acceptance criteria • Virtual sensing – signal value prediction and acceptance criteria • Response-time assessment – fault detection and acceptance criteria selection A GP-based uncertainty quantification (UQ) method previously developed for UQ in OLM, was adapted for use in sensor-fault detection and virtual sensing. For signal validation, the various components to the OLM residual (which is computed using an AAKR model) were explicitly defined and modeled using a GP. Evaluation was conducted using flow loop data from multiple sources. Results using experimental data from laboratory-scale flow loops indicate that the approach, while capable of detecting sensor drift, may be incapable of discriminating between sensor drift and model inadequacy. This may be due to a simplification applied in the initial modeling, where the sensor degradation is assumed to be stationary. In the case of virtual sensors, the GP model was used in a predictive mode to estimate the correct sensor reading for sensors that may have failed. Results have indicated the viability of using this approach for virtual sensing. However, the GP model has proven to be computationally expensive, and so alternative algorithms for virtual sensing are being evaluated. Finally, automated approaches to performing noise analysis for extracting sensor response time were developed. Evaluation of this technique using laboratory-scale data indicates that it compares well with manual techniques previously used for noise analysis. Moreover, the automated and manual approaches for noise analysis also compare well with the current “gold standard”, hydraulic ramp testing, for response time monitoring. Ongoing research in this project is focused on further evaluation of the algorithms, optimization for accuracy and computational efficiency, and integration into a suite of tools for robust OLM that are applicable to monitoring sensor calibration state in nuclear power plants.

calibration interval extension↗
DOE OSTI2023

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
DOE OSTI2016

RAVEN User Manual, Revision 4

RAVEN is a generic software framework to perform parametric and probabilistic analysis based on the response of complex system codes. The initial development was aimed to provide dynamic risk analysis capabilities to the Thermo-Hydraulic code RELAP-7, currently under development at the Idaho National Laboratory (INL). Although the initial goal has been fully accomplished, RAVEN is now a multi-purpose probabilistic and uncertainty quantification platform, capable to agnostically communicate with any system code. This agnosticism includes providing Application Programming Interfaces (APIs). These APIs are used to allow RAVEN to interact with any code as long as all the parameters that need to be perturbed are accessible by inputs files or via python interfaces. RAVEN is capable of investigating the system response, and investigating the input space using Monte Carlo, Grid, or Latin Hyper Cube sampling schemes, but its strength is focused to- ward system feature discovery, such as limit surfaces, separating regions of the input space leading to system failure, using dynamic supervised learning techniques. The development of RAVEN has started in 2012, when, within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the need to provide a modern risk evaluation framework became stronger. RAVEN principal assignment is to provide the necessary software and algorithms in order to employ the concept developed by the Risk Informed Safety Margin Characterization (RISMC) program. RISMC is one of the pathways defined within the Light Water Reactor Sustainability (LWRS) program. In the RISMC approach, the goal is not just the individuation of the frequency of an event potentially leading to a system failure, but the closeness (or not) to key safety-related events. Hence, the approach is interested in identifying and increasing the safety margins related to those events. A safety margin is a numerical value quantifying the probability that a safety metric (e.g. for an important process such as peak pressure in a pipe) is exceeded under certain conditions. The initial development of RAVEN has been focused on providing dynamic risk assess- ment capability to RELAP-7, currently under development at the INL and, likely, future replacement of the RELAP5-3D code. Most the capabilities that have been implemented having RELAP-7 as principal focus are easily deployable for other system codes. For this reason, several side activates are currently ongoing for coupling RAVEN with soft- ware such as RELAP5-3D, etc. The aim of this document is the explanation of the input requirements, focalizing on the input structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

RAVEN User Manual

RAVEN is a generic software framework to perform parametric and probabilistic analysis based on the response of complex system codes. The initial development was aimed to provide dynamic risk analysis capabilities to the Thermo-Hydraulic code RELAP-7, currently under development at the Idaho National Laboratory (INL). Although the initial goal has been fully accomplished, RAVEN is now a multi-purpose probabilistic and uncertainty quantification platform, capable to agnostically communicate with any system code. This agnosticism includes providing Application Programming Interfaces (APIs). These APIs are used to allow RAVEN to interact with any code as long as all the parameters that need to be perturbed are accessible by inputs files or via python interfaces. RAVEN is capable of investigating the system response, and investigating the input space using Monte Carlo, Grid, or Latin Hyper Cube sampling schemes, but its strength is focused to- ward system feature discovery, such as limit surfaces, separating regions of the input space leading to system failure, using dynamic supervised learning techniques. The development of RAVEN has started in 2012, when, within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the need to provide a modern risk evaluation framework became stronger. RAVEN principal assignment is to provide the necessary software and algorithms in order to employ the concept developed by the Risk Informed Safety Margin Characterization (RISMC) program. RISMC is one of the pathways defined within the Light Water Reactor Sustainability (LWRS) program. In the RISMC approach, the goal is not just the individuation of the frequency of an event potentially leading to a system failure, but the closeness (or not) to key safety-related events. Hence, the approach is interested in identifying and increasing the safety margins related to those events. A safety margin is a numerical value quantifying the probability that a safety metric (e.g. for an important process such as peak pressure in a pipe) is exceeded under certain conditions. The initial development of RAVEN has been focused on providing dynamic risk assessment capability to RELAP-7, currently under development at the INL and, likely, future replacement of the RELAP5-3D code. Most the capabilities that have been implemented having RELAP-7 as principal focus are easily deployable for other system codes. For this reason, several side activates are currently ongoing for coupling RAVEN with soft- ware such as RELAP5-3D, etc. The aim of this document is the explanation of the input requirements, focalizing on the input structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Motivations for early high-profile FRIB experiments

This white paper is the result of a collaboration by many of those that attended a workshop at the facility for rare isotope beams (FRIB), organized by the FRIB Theory Alliance (FRIB-TA), on ‘Theoretical Justifications and Motivations for Early High-Profile FRIB Experiments’. It covers a wide range of topics related to the science that will be explored at FRIB. After a brief introduction, the sections address: section 2: Overview of theoretical methods, section 3: Experimental capabilities, section 4: Structure, section 5: Near-threshold Physics, section 6: Reaction mechanisms, section 7: Nuclear equations of state, section 8: Nuclear astrophysics, section 9: Fundamental symmetries, and section 10: Experimental design and uncertainty quantification.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Accounting for uncertainty in complex alluvial aquifer modeling by Bayesian multi-model approach

Alluvial aquifers by nature are complex caused by varied depositional environments. Developing a reliable groundwater model to represent an alluvial aquifer is non-trivial. Also, relying on a single best calibrated model may not be sufficient because of an inadequate choice of model parameter values. To better understand groundwater dynamics and improve model prediction reliability, this study presents a Bayesian multi-model uncertainty quantification (BMMUQ) framework to account for model parameter uncertainty in complex alluvial groundwater modeling. The methodology was applied to the agriculturally intensive Mississippi River alluvial aquifer (MRAA), Northeast Louisiana. An aquifer architecture was first constructed using 7,259 well logs in the MRAA area which covers three fluvial deposits (alluvium, braided-stream terrace, and braided-stream terrace-loess). A 12-layer MODFLOW model was then developed to address the alluvial aquifer complexity and well calibrated through a genetic algorithm. This study quantified model parameter uncertainty in hydraulic conductivity and specific storage of sand facies. Bayesian model averaging (BMA) with the Expectation Maximization (EM) algorithm was adopted to derive posterior model weights and head variances of 50 alternative conceptual groundwater flow models, and thereby obtains BMA ensemble model predictions instead of only relying on the best calibrated conceptual model. Overall, results show that an estimated around 950 million m3 of groundwater storage loss occurs in 2015 with respect to the beginning of 2004, due to high groundwater demand for irrigation in the MRAA area. Explicitly quantifying model uncertainty can produce more reliable groundwater level predictions from BMA ensemble model. The presented groundwater modeling framework improves our understanding of the MRAA and provides a valuable tool to assist agricultural water management.

54 ENVIRONMENTAL SCIENCES↗
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 OSTI2017

Carbon Capture Multidisciplinary Simulation Center Trilab Support Team (TST) Fall Meeting 2016 Report

The theme of this year’s meeting was “Predictivity: Now and in the Future”. After welcoming remarks, Erik Draeger gave a talk on the NNSA Labs’ history of predictive simulation and the new challenges faced by upcoming architecture changes. He described an example where the volume of analysis data produced by a set of inertial confinement fusion (ICF) simulations on the Trinity machine was too large to store or transfer, and the steps needed to reduce it to a manageable size. He also described the software re-engineering plan for LLNL’s suite of multiphysics codes and physics packages with a new push toward common components, making collaboration with teams like the CCMSC who already have experience trying to architect complex multiphysics code infrastructure on next-generation architectures all the more important. Phil Smith then gave an overview outlining the goals of the project, namely to accelerate development of new technology in the form of high efficiency carbon capture pulverized coal power generation as well as further optimize existing state of the art designs. He then presented a summary of the Center’s top-down uncertainty quantification approach, in which ultimate target predictivity informs uncertainty targets for lower-level components, and gave data on how close all the different components currently are to their targets. Most components still need an approximately two-fold reduction in uncertainty to hit the ultimate predictivity target, but the current accuracy is already rather impressive.

01 COAL, LIGNITE, AND PEAT↗
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 OSTI2019

ATF material model development and validation for priority cladding concepts

Development, implementation, and validation of material and behavior models for accident tolerant fuel (ATF) concepts in the Bison fuel performance code began in 2014 in response to the events that occurred at the Fukushima Daichii nuclear power plant in March 2011. Early on the focus was on U 3 Si 2 fuel and FeCrAl cladding as part of a high impact problem through the Nuclear Energy and Advanced Modeling Simulation (NEAMS) program. Then, developments for Cr 2 O 3 -doped UO 2 fuel, and SiC-SiC and Cr-coated zirconium-based claddings began based upon industry interests. In late fiscal year 2018 the Consortium for Advanced Simulation of Light Water Reactors (CASL) took over further ATF work in Bison in support of the Nuclear Regulatory Commission (NRC) engagement. Discussions with the NRC identified their list of priority fuel and cladding concepts, which included Cr 2 O 3 -doped UO 2 and U 3 Si 2 fuels, and Cr-coated zirconium-based and FeCrAl claddings. In particular, the NRC suggested that reports similar in form to NUREG/CR-7024 that was developed for traditional LWR materials UO 2 and zirconium-based claddings (i.e., Zircaloy-4, M5 ® , ZIRLO TM ) be created for the priority ATF concepts. The approach to ATF capability development in Bison since the beginning has been two-fold: (1) empirical correlations and (2) multiscale model development. Both approaches have uncertainty inherent to them. Uncertainty in empirical correlations is bounded by the experimental data upon which with the correlation was developed. Models developed through a multiscale approach have uncertainty associated with the lower length scale calculations and input parameters that must be propagated to the engineering scale model in Bison. In this report, the recommended models, their range of applicability (e.g., temperature, fluence), and associated uncertainty for the NRC priority clad concepts Cr-coated zirconium based clad and FeCrAl are presented in a manner similar to the aforementioned NUREG. In addition, in the absence of experimental data for validation, demonstration cases are presented that investigate the ballooning and burst behavior of Cr-coated and FeCrAl clads as well as tritium permeation in FeCrAl. A portion of the study by Gamble et al. on FeCrAl failure is also revisited with the latest updated models. First, the nominal results are shown using the as implemented models. Then a sensitivity analysis and uncertainty quantification is performed to assess the impact of the uncertainties in the models on the parameters of interest. For the Cr-clad ballooning case the parameter of interest is the time to burst. For the revisited FeCrAl study, the parameter of interest is the pressure at burst.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗