This study presents a comparative analysis of regression techniques for modeling few-group cross-section libraries as a function of state parameters, with prediction targets that include both mean values and covariance matrices to represent aleatoric uncertainty from nuclear data perturbations. Beyond absolute accuracy, the primary focus is convergence performance: whether the prediction error decreases monotonically as the number of unique training samples Nbranch increases. The results show that the convergence behavior differs substantially across the methods. In particular, the transformed neural network model exhibits inconsistent, nonmonotonic convergence with respect to Nbranch, indicating limited robustness. In contrast, the transformed polynomial regression (tp-PR) model shows stable convergence and achieves the best performance at the largest training set (Nbranch = 1024) with a kinf error of 0.015%. A comparison of the predicted and reference keff distributions further shows that the tp-PR model was able to reproduce uncertainty induced by nuclear data uncertainty.

Accurate prediction of nuclide composition evolution during fuel depletion typically requires computationally intensive transport calculations to determine 1-group cross sections for all transmutation reactions in the reaction network. These cross sections are influenced by the neutron energy spectrum, which varies with both depletion and changing state parameters, such as fuel and moderator temperatures. This study investigates the feasibility of a machine learning-based model designed to predict nuclide composition directly from power history and state parameters, bypassing the need to calculate group cross sections and solve the Bateman equation. Model testing on an unseen power and state parameter history showed a mean absolute relative error of 0.471% for 235U. Due to its rapid inference speed, this approach is well suited to applications where traditional transport calculations are prohibitively expensive.

Nodal few-group cross-section representation models are used to generate estimates of cross-section parameters for nodal codes as a function of various state parameters. In this work we present a feasibility study for constructing representational models which provide mean and covariance estimates of these parameters. We consider two sources of uncertainty in the model predictions, namely the uncertainty due to randomized nuclear data during the lattice calculation and the uncertainty in the model parameters. To handle these uncertainties, we investigate the use of parametric polynomial regression models and parametric Bayesian polynomial regression models. These methods are tested on a typical training set of cross-section parameters for pressurized water reactor analysis.

To compute few-group nodal cross sections, lattice codes must first generate multi-group cross sections using continuous energy cross-section libraries for each material in each fuel cell. Since the processing cost is significant, we propose representing the multi-group cross sections during lattice calculations using a pre-trained deep-learning-based model. The model utilizes a combination of Principal Component Analysis (PCA) and fully connected Neural Networks (NN). The model is specifically designed to manage extensive multi-group cross-section data sets, which contain data for several dozen nuclides and encompass more than 50 energy groups. Our testing of the trained model on a PWR assembly with a realistic boron letdown curve revealed an average relative error of around 0.1% for both fission and total macroscopic cross sections. The average time required for the model to generate the cross sections was approximately 0.01% of the time needed to execute the cross-section processing module.

A deep neural network model is proposed to predict assembly node cross section libraries based on fuel pellet nuclide concentrations and instantaneous state parameters.We tested the impact of two different factors on model p erformance.The first factor is the impact of averaging fuel pellet nuclide compositions and the second factor is the use of a single large DNN model versus the use of multiple DNNs for different cross section p arameters.The combination of the two factors result in four variations of the model architecture.All four architectures are rigourously tested and statistically compared using the Nemenyi posthoc test.The pair-wise Nemenyi results indicates that the averaging of fuel pellet nuclide concentrations had no impact on model performance.However, the results show a clear improvement of the representational model when a single large DNN model is used compared with multiple smaller DNN models.The selected best model with averaged fuel pellet compositions and a single large DNN model was tested on previously unseen data.The model was shown to have high accuracy with less than 1% mean relative error for the fission and total cross section values.

To compute few-group nodal data, lattice codes first need to generate multi-group cross-sections for each constituent material within the lattice model. This generation process utilizes continuous-energy cross-section libraries, which is expensive in terms of the computing cost. Moreover, any alteration in the nuclide compositions or other state parameters necessitates the repetition of this process. To reduce the computational demands, we propose the application of a pre-trained representational model. This model, which integrates Deep Neural Networks (DNN) and Principal Component Analysis (PCA) modules, is particularly beneficial in scenarios that require repeated multi-group data processing by the lattice code. In our previous research, we established that such a model could accurately generate multi-group data for fuel pellet materials. In the present study, we have broadened the scope of the model to encompass a more extensive range of materials typically found in pressurized water reactors, including zirc-alloy cladding and borated water moderators. We also show that the model can be trained on a wide spectrum of fuel enrichments. When integrated into lattice calculations, the errors introduced by the deep-learning-based representational model result in less than 1% deviation in the k eff and pin-power distribution. We have further refined the model to assess also the neutron fluxes in the fuel pellet and borated water. This refined model was subsequently employed to perform a flux-weighted collapse and generate few-group cross-section libraries for lattice calculation. The few-group libraries generated in this manner exhibited high accuracy and gave a low average k eff error and minimal errors in pin power distribution.

Monte Carlo criticality calculations of large, loosely-coupled problems are long known to suffer from slow convergence of the tally errors due to cycle-to-cycle fission source correlations. In several recent studies, it was suggested that these correlations could be possibly attributed to the neutron clustering phenomenon that is visible in calculations with a small number of neutrons per iteration cycle (batch size). Nevertheless, other studies have also shown the error convergence rate in such loosely-coupled problems to be batch size-independent during active criticality cycles. Here, we aim to address this inconsistency by studying the error convergence in a large number of test calculations, varying the neutron batch size from small to large. In our tests, we have observed that the presence of visible neutron clusters does not increase the cycle-to-cycle fission source correlations and does not worsen the convergence rate of the tally errors.

Until recently, reactor transient problems were exclusively solved by approximate deterministic methods. The increase in available computing power made it feasible to approach the transient analyses with time-dependent Monte Carlo methods. These methods offer the first-principle solution to the space-time evolution of reactor power by explicitly tracking prompt neutrons, precursors of delayed neutrons and delayed neutrons in time and space. Nevertheless, a very significant computing cost is associated with such methods. The general benefits of the Monte Carlo approach may be retained at a reduced computing cost by applying a hybrid stochastic-deterministic computing scheme. Among such schemes are those based on the fission matrix and the response matrix formalisms. These schemes aim at estimating a variant of the Greens function during a Monte Carlo transport calculation, which is later used to formulate a deterministic approach to solving a space-time dependent problem. In this contribution, we provide an overview of the time-dependent response matrix method, which describes a system by a set of response functions. We have recently suggested an approach where the functions are determined during a Monte Carlo criticality calculation and are then used to deterministically solve the space-time behaviour of the system. Here, we compare the time-dependent response matrix solution with the transient fission matrix and the time-dependent Monte Carlo solutions for a control rod movement problem in a mini-core reactor geometry. The response matrix formalism results in a set of loosely connected equations which offers favourable scaling properties compared to the methods based on the fission matrix formalism.

Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.

We show here that computing efficiency of Monte Carlo burnup simulations depends on chosen values of certain free parameters, such as the length of the time steps and the number of neutron histories simulated at each Monte Carlo criticality run. The efficiency can thus be improved by optimising these parameters. We have set up a simple numerical model that made it possible for us to test a large number of combinations of the free parameters, and suggest a way to optimise their selection.