Data assimilation of post-irradiation examination data for fission yields from GEF

Siefman, Daniel; Hursin, Mathieu; Sjöstrand, Henrik; Schnabel, Georg; Rochman, D.; Pautz, Andreas

doi:10.1051/epjn/2020015

Cited by 9 publications

(6 citation statements)

References 42 publications

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“…At some point in the future, templates of measurement uncertainties [96,97] may be used for the specification of default priors on the experimental errors associated with different measurement types, and also to check the compatibility of the posterior estimates with sensible ranges given by a template. The Bayesian network framework is also compatible with the procedures described in [14,22,98,99] for the automated determination of missing or misspecified uncertainties. As the relations between experiments in nuclear databases, such as EXFOR [100], can also be represented as a graph [101,102], with links established by common features, Bayesian networks may be used for the automatic correction of experimental datasets and also outlier detection there.…”

Section: Discussionmentioning

confidence: 99%

Nuclear data evaluation with Bayesian networks

Schnabel¹,

Capote²,

Koning³

et al. 2021

Preprint

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Bayesian networks are graphical models to represent the deterministic and probabilistic relationships between variables within the Bayesian framework. The knowledge of all variables can be updated using new information about some of the variables. The Bayesian Generalized Linear Least Squares method can be regarded as an inference method for Bayesian networks of variables with multivariate normal priors and linear relationships between them. We show that relying explicitly on the Bayesian network interpretation enables large scale inference and gives more flexibility in incorporating prior assumptions and constraints into the nuclear data evaluation process, such as the constraints that some cross sections equal linear combinations of other cross sections and that all cross sections must be non-negative. The latter constraint is accounted for by a nonlinear transformation and therefore we also discuss inference in Bayesian networks with non-linear relationships between variables. Using Bayesian networks, the evaluation process yields more detailed information, such as posterior estimates and uncertainties of all statistical and systematic errors associated with the experiments. We further elaborate on a sparse Gaussian process construction that can be well integrated into the Bayesian network framework and applied to, e.g., the modeling of energy-dependent model parameters, model deficiencies of the physics model or energy-dependent systematic errors of experiments. We present three proof-of-concept examples that emerged in the context of the neutron data standards project and in the ongoing international evaluation efforts of 56 Fe. In the first example we demonstrate the modelization and explicit estimation of relative energy-dependent error components associated with experimental datasets. Then we show that Bayesian networks in combination with the outlined Gaussian process construction may be applied to an evaluation of 56 Fe in the energy range between one and two MeV, where it is difficult to obtain satisfactory evaluations by R-Matrix and nuclear model fits. Finally, we present a model-based evaluation of 56 Fe between 5 MeV and 30 MeV with a consistent and statistically sound treatment of model deficiencies. The R scripts to reproduce the Bayesian network examples and the nucdataBaynet package for Bayesian network modeling and inference have been made publicly available.

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Section: Discussionmentioning

confidence: 99%

Nuclear data evaluation with Bayesian networks

Schnabel¹,

Capote²,

Koning³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is worth noticing that the effects of thermal scattering and decay data are not included in this study. For fission yields, the approach presented in references [12,16,17] is applied (sampling based on uncertainties from the evaluated libraries, plus a number of mass and charge normalizations).…”

Section: Uncertainty Propagationmentioning

confidence: 99%

Analysis for the ARIANE GU3 sample: nuclide inventory and decay heat

Rochman

Vasiliev

Ferroukhi

et al. 2021

EPJ Nuclear Sci. Technol.

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This study presents an analysis of the ARIANE GU3 sample, in terms of nuclide inventory, as well as sample rod and assembly decay heat. The validation of a number of CASMO5 and library versions are performed with regards to the measured nuclide inventory, taking into account two dimensional lattice simulations. Uncertainties due to various sources (nuclear data, operating conditions and manufacturing tolerances) are also provided, and are combined with biases into expanded uncertainties. This study is similar to a previous one on the GU1 sample and fit in the framework of code validation, as well as in the estimation of code predictive power for spent fuel characterization.

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“…Ignoring these effects in a Bayesian evaluation using integral data bears the risk of adjusting differential data too much in an attempt to compensate for the unaccounted errors due to approximations during processing. First attempts to account for such effects are presented in [80,81] using the MLO approach. The long runtime of neutron transport codes for certain benchmark experiments is another obstacle to the inclusion of integral data in Bayesian methods for nuclear data evaluation.…”

Section: The Nuclear Data Evaluation Pipelinementioning

confidence: 99%

Conception and software implementation of a nuclear data evaluation pipeline

Schnabel,

Sjöstrand,

Hansson

et al. 2020

Preprint

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B. LINEAR ALGEBRA IDENTITIES TO SPEED UP COMPUTATIONS 37 1. Derivative of an inverse matrix 37 2. Derivative of a logarithmized determinant 37 3. Matrix determinant lemma 37 4. Woodbury identity 38 5. Products involving the inverse of sparse covariance or other positive-definite matrices 38 C. BAYESIAN INFERENCE 38 1. Details on modified Levenberg-Marquardt algorithm 38 2. Prior on second-derivative as smoothness prior 39 3. Necessity of second-order Taylor approximation of posterior pdf 40 4. Computation of the posterior covariance matrix 41 5. Computation of the posterior expectation of insensitive paramaters 42 D. DOWNLOADING THE PIPELINE AND PACKAGES 42 1. About identification strings 43 2. Catalogue of pipeline modules 43

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Data assimilation of post-irradiation examination data for fission yields from GEF

Cited by 9 publications

References 42 publications

Nuclear data evaluation with Bayesian networks

Nuclear data evaluation with Bayesian networks

Analysis for the ARIANE GU3 sample: nuclide inventory and decay heat

Conception and software implementation of a nuclear data evaluation pipeline

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