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Fuel performance codes, such as Transuranus, predict fuel behavior and are used to ensure the safe operation of nuclear reactors. These codes are moderately time-consuming and affordable in many applications but may be limited in others, primarily when many fuel rods must be evaluated simultaneously. This work presents how the temporal neural network techniques, Temporal Convolutional Networks, and a Fourier Neural Operator can be combined to form a deep heterogeneous joint architecture as a surrogate model for fuel performance modeling in time-critical situations. We train the model using realistic power histories and corresponding outputs generated using the fuel performance code Transuranus. The ultimate result is a surrogate model for use in time-critical situations that take milliseconds to evaluate for thousands of fuel rods and have a mean test error of unseen data around a few percent.

Nuclear power is a key electricity source, with light water reactors being the most common type. Their fuel typically consists of uranium dioxide pellets stacked in zirconium alloy cladding tubes. The purpose of the fuel is to produce heat and act as a barrier against releasing radioactive material. During operation, heat and radiation cause thermomechanical changes that can lead to fuel failure if not controlled. Thus, the nuclear industry needs efficient fuel performance codes with well-quantified uncertainties to predict fuel rod behavior. This thesis focuses on improving inverse uncertainty quantification and surrogate modeling for efficient fuel performance predictions.

Inverse uncertainty quantification is essential because fuel performance codes require calibrated model parameters to ensure that predictions match measurements. However, standard calibration methods often underestimate uncertainties due to unaccounted-for uncertainty sources, such as model inadequacy. Therefore, this thesis presents how unknown sources of uncertainty can be accounted for in calibration using Markov Chain Monte Carlo (MCMC) by assuming a variability in the calibration parameters. Two methods are presented, and both are based on MCMC, requiring numerous samples to converge. Hence, Gaussian Process (GP) surrogate modeling is used in place of the code to provide the calibration methods with inexpensive estimates of code responses. The first method is derivative-based, relying on differentiated GPs. While it effectively calibrates cladding oxidation, it struggles with fission gas release. Consequently, a more accurate method based on MH-within-Gibbs sampling is presented that successfully calibrates fission gas release.

The presented calibration methods use GP surrogate models to efficiently calibrate model parameters with inexpensive scalar estimates of code predictions. Beyond calibration, surrogate modeling is also essential when time-dependent predictions are needed for numerous fuel rod irradiations simultaneously. For example, if time-dependent predictions of fuel rod behavior are required in core optimization or core monitoring, calculation time can become a limiting factor. Therefore, this work also investigates neural network architectures for temporal data based on Temporal Convolutional Neural Networks (TCNs) and Fourier Neural Operators (FNOs) designed to model numerous fuel rods with varying irradiation histories. These networks accurately predict the behavior of thousands of fuel rods within seconds, significantly improving computational efficiency.

The ratio of branching fractions between B-0 -> J/psi pi(0) and B+ -> J/psi K*+ decays is measured with proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb(-1). The measured value is B-B(0) -> -> J/psi pi(0)/B+ -> J/psi K*+ = (1.153 +/- 0.053 +/- 0.048) x 10-2, where the first uncertainty is statistical and the second is systematic. The branching fraction for B-0 -> J/psi pi(0) decays is determined using the branching fraction of the normalisation channel, resulting in B-B(0) -> J/psi pi(0) = (1.670 +/- 0.077 +/- 0.069 +/- 0.095) x 10-5, where the last uncertainty corresponds to that of the external input. This result is consistent with the current world average value and competitive with the most precise single measurement to date.

Fuel performance codes are used to forecast fuel behavior and ensure safe operation. These analyses must typically include prediction uncertainties, and fuel performance models need calibration. Consequently, code calibration must derive the best estimates and corresponding uncertainties of model parameters for subsequent propagation.

Bayesian calibration is popular for generating the probability distribution of model parameters. However, model inadequacy disrupts these techniques, typically resulting in underestimated uncertainties. Earlier research showcased the incorporation of model inadequacy by model parameter inflation. The method demands cheap code predictions and derivatives, which required further research to develop differentiated Gaussian process surrogates.

This work combines those techniques into a complete methodology. We demonstrate it by calibrating Transuranus against fission gas release and cladding oxidation data. The result is model parameter uncertainties that primarily explain the discrepancies between the predictions and corresponding measurements, except when the output behaves highly non-linearly.