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DOE OSTI2022

Building surrogate models of nuclear density functional theory with Gaussian processes and autoencoders

From the lightest Hydrogen isotopes up to the recently synthesized Oganesson (Z = 118), it is estimated that as many as about 8,000 atomic nuclei could exist in nature. Most of these nuclei are too short-lived to be occurring on Earth, but they play an essential role in astrophysical events such as supernova explosions or neutron star mergers that are presumed to be at the origin of most heavy elements in the Universe. Understanding the structure, reactions, and decays of nuclei across the entire chart of nuclides is an enormous challenge because of the experimental difficulties in measuring properties of interest in such fleeting objects and the theoretical and computational issues of simulating strongly-interacting quantum many-body systems. Nuclear density functional theory (DFT) is a fully microscopic theoretical framework which has the potential of providing such a quantitatively accurate description of nuclear properties for every nucleus in the chart of nuclides. Thanks to high-performance computing facilities, it has already been successfully applied to predict nuclear masses, global patterns of radioactive decay like β or γ decay, and several aspects of the nuclear fission process such as, e.g., spontaneous fission half-lives. Yet, predictive simulations of nuclear spectroscopy—the low-lying excited states and transitions between them—or of nuclear fission, or the quantification of theoretical uncertainties and their propagation to basic or applied nuclear science applications, would require several orders of magnitude more calculations than currently possible. However, most of this computational effort would be spent into generating a suitable basis of DFT wavefunctions. Such a task could potentially be considerably accelerated by borrowing tools from the field of machine learning and artificial intelligence. In this paper, we review different approaches to applying supervised and unsupervised learning techniques to nuclear DFT.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Destructive Analysis of TRISO Particles: Crush/Burn/Leach Followed by Davies-Gray Titration and IDMS

The accurate accounting of nuclear materials is a cornerstone of international nuclear safeguards. One emerging challenge in this domain is the fabrication of TRIstructural ISOtropic (TRISO) particle fuels. Although these innovative fuel forms are critical for advanced reactor applications, their robust refractory ceramics and coating compositions present significant obstacles to destructive analysis (DA) methods. Ensuring full and quantitative recovery from these particles is essential for accurate mass accountancy. The current study was initiated to address these challenges, first by validating a previously established destructive method developed by Oak Ridge National Laboratory (ORNL) for the quantitative recovery of uranium from TRISO particles and then following that process with uranium content determination through isotope dilution mass spectrometry (IDMS) and Davies-Gray titration. This study expands on the scope of a digestive method that was developed under the Advanced Gas Reactor Fuel Development and Qualification program and is currently implemented in both the Coated Particle Fuel Development Laboratory and Irradiated Fuels Examination Laboratory at ORNL. The success of the previous Advanced Gas Reactor work relied on developing a DA method to evaluate the fabrication process and reactor experiments. The methodology described in this report was designed to rigorously investigate the efficacy of the crush/burn/leach sample preparation of TRISO particles; it aims to quantify uranium recovery while also assessing the effects of TRISO constituents (e.g., silicon and zirconium) on analytical precision and accuracy. By comparing the results from the titration method and IDMS, we sought to determine whether existing analytical procedures accepted by the International Atomic Energy Agency (IAEA) could be effectively translated to TRISO fuel forms. The team employed an approach that involved processing replicate TRISO samples, optimizing the milling (i.e., crushing) step and performing serial leaches. The elemental composition of the analytical samples was examined to prepare for interference studies in the second year of this project. The integration of gamma spectrometry to verify residual uranium activity further strengthened the validation. Statistical methods were applied to the collected data to evaluate the uncertainties arising from sampling, sample preparation and uranium quantification. These uncertainties were then compared to the IAEA’s international target values (ITVs). Additional data collected in upcoming project work will strengthen the uncertainty estimates. Ultimately, it is hoped that this project will contribute materially to the body of work related to characterization of TRISO based fuels for the purpose of material accountancy and its applications to international safeguards.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Partial Least Squares, Experimental Design, and Near-Infrared Spectrophotometry for the Remote Quantification of Nitric Acid Concentration and Temperature

Near-infrared spectrophotometry and partial least squares regression (PLSR) were evaluated to create a pleasantly simple yet effective approach for measuring HNO3 concentration with varying temperature levels. A training set, which covered HNO3 concentrations (0.1–8 M) and temperature (10–40 °C), was selected using a D-optimal design to minimize the number of samples required in the calibration set for PLSR analysis. The top D-optimal-selected PLSR models had root mean squared error of prediction values of 1.4% for HNO 3 and 4.0% for temperature. The PLSR models built from spectra collected on static samples were validated against flow tests including HNO 3 concentration and temperature gradients to test abnormal conditions (e.g., bubbles) and the model performance between sample points in the factor space. Based on cross-validation and prediction modeling statistics, the designed near-infrared absorption approach can provide remote, quantitative analysis of HNO 3 concentration and temperature for production-oriented applications in facilities where laser safety challenges would inhibit the implementation of other optical techniques (e.g., Raman spectroscopy) and in which space, time, and/or resources are constrained. The experimental design approach effectively minimized the number of samples in the training set and maintained or improved PLSR model performance, which makes the described chemometric approach more amenable to nuclear field applications.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2024

Analytical capabilities for iodine detection: Review of possibilities for different applications

This Review summarizes a range of analytical techniques that can be used to detect, quantify, and/or distinguish between isotopes of iodine (e.g., long-lived 129 I, short-lived 131 I, stable 127 I). One reason this is of interest is that understanding potential radioiodine release from nuclear processes is crucial to prevent environmental contamination and to protect human health as it can incorporate into the thyroid leading to cancer. It is also of interest for evaluating iodine retention performances of next-generation iodine off-gas capture materials and long-term waste forms for immobilizing radioiodine for disposal in geologic repositories. Depending upon the form of iodine (e.g., molecules, elemental, and ionic) and the matter state (i.e., solid, liquid, and gaseous), the available options can vary. In addition, several other key parameters vary between the methods discussed herein, including the destructive vs nondestructive nature of the measurement process (including in situ vs ex situ measurement options), the analytical data collection times, and the amount of sample required for analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Risk Informed, Performance-Based, Technology-Inclusive Regulatory Infrastructure: Technology-Inclusive Determination of Mechanistic Source Terms for Offsite Dose-Related Assessments for Advanced Nuclear Reactor Facilities

This report summarizes a risk informed, performance-based and technology-inclusive approach to determine source terms for dose related assessments at advanced nuclear facilities. This approach uses a graded process which allows both the non-mechanistic source terms calculation methods, which adopt conservative approaches and assumptions based on known physical and chemical principles, and more importantly the mechanistic source term calculation methods, which consider design-specific scenarios and use best estimate models with uncertainty quantification for a range of licensing basis events (LBEs), to be used for the design and licensing of advanced nuclear technologies. The source terms developed with this graded approach, and radionuclide inventories elsewhere in the facility that are determined during source term analysis, can be used to address licensing issues to support the application processes of 10 CFR Part 50 for a construction permit and operating license or 10 CFR Part 52 for a Combined Operating License (COL), Standard Design Certification, Early Site Permit, Standard Design Approval or Manufacturing License. They can also be used for other purposes including equipment environmental qualification, control room habitability analyses, and assessments of severe accident risks in environmental impact statements. There are many advanced reactor concepts being developed including high temperature gas-cooled reactor (HGTR), sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), molten salt reactor (MSR), micro-reactor, etc. The graded approach presented in this report for source terms determination is, to the extent possible, generic to any of these reactor designs and to future reactor designs. This report provides information on the review of the regulatory foundation for use of conservative bounding source terms as well as event-specific mechanistic source terms for advanced nuclear reactor designs.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗