Assessment of Machine Learning-Based Critical Heat Flux Models in the CTF Subchannel Code for Square Rod Bundle Prediction

A central challenge in scientific machine learning (ML) is the correct representation of physical systems governed by multi-regime behaviours. In these scenarios, standard data analysis techniques often fail to capture the nature of the data, as the system's response varies significantly across the state space due to its stochasticity and the different physical regimes. Uncertainty quantification (UQ) should thus not be viewed merely as a safety assessment, but as a support to the learning task itself, guiding the model to internalise the behaviour of the data. We address this by focusing on the Critical Heat Flux (CHF) benchmark and dataset presented by the OECD/NEA Expert Group on Reactor Systems Multi-Physics. This case study represents a test for scientific ML due to the non-linear dependence of CHF on the inputs and the existence of distinct microscopic physical regimes. These regimes exhibit diverse statistical profiles, a complexity that requires UQ techniques to internalise the data behaviour and ensure reliable predictions. In this work, we conduct a comparative analysis of UQ methodologies to determine their impact on physical representation. We contrast post-hoc methods, specifically conformal prediction, against end-to-end coverage-oriented pipelines, including (Bayesian) heteroscedastic regression and quality-driven losses. These approaches treat uncertainty not as a final metric, but as an active component of the optimisation process, modelling the prediction and its behaviour simultaneously. We show that while post-hoc methods ensure statistical calibration, coverage-oriented learning effectively reshapes the model's representation to match the complex physical regimes. The result is a model that delivers not only high predictive accuracy but also a physically consistent uncertainty estimation that adapts dynamically to the intrinsic variability of the CHF.

The demand for clean energy is ever increasing, with new nuclear technologies presenting a complementary solution to renewable energies. However, designing and operating these systems is exceptionally difficult, given the complexity of the physical phenomena that interact to form the system dynamics. While high-fidelity simulations help to understand the non-linear, multi-physics interactions within a reactor, they are computationally expensive and rarely suitable for real-time applications. Furthermore, model-based approaches are inherently sensitive to simplifying assumptions required to derive their governing equations and parameters, leading to inevitable discrepancies with real-world measurements. In contrast, Machine Learning (ML) methods have the potential to generate reliable surrogate models which may be able to quickly predict the system's behaviour. However, the number of data-driven methods that can potentially be used for this task is large and diverse. In a safety-critical setting such as nuclear engineering, a fair comparison of different ML methods, and a clear understanding of their advantages and limitations, is of paramount importance. To address this, we introduce a Common Task Framework (CTF) for ML in nuclear engineering, building upon previous efforts in dynamical systems and seismology. This CTF considers a curated set of datasets from different nuclear and nuclear-adjacent systems. The CTF evaluates the performance of a method on 12 established metrics, alongside a new paradigm focused on system monitoring from sparse measurements only. We illustrate the framework by benchmarking standard ML baselines against these datasets, revealing current method limitations. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigour and reproducibility in scientific ML for the nuclear industry.

High-fidelity computational fluid dynamics (CFD) simulations are widely used to analyze nuclear reactor transients, but are computationally expensive when exploring large parameter spaces. Multifidelity surrogate models offer an approach to reduce cost by combining information from simulations of varying resolution. In this work, several multifidelity machine learning methods were evaluated for predicting the time to onset of natural circulation (ONC) and the temperature after ONC for a high-temperature gas reactor (HTGR) depressurized loss of forced cooling transient. A CFD model was developed in Ansys Fluent to generate 1000 simulation samples at each fidelity level, with low and medium-fidelity datasets produced by systematically coarsening the high-fidelity mesh. Multiple surrogate approaches were investigated, including multifidelity Gaussian processes and several neural network architectures, and validated on analytical benchmark functions before application to the ONC dataset. The results show that performance depends strongly on the informativeness of the input variables and the relationship between fidelity levels. Models trained using dominant inputs identified through prior sensitivity analysis consistently outperformed models trained on the full input set. The low- and high-fidelity pairing produced stronger performance than configurations involving medium-fidelity data, and two-fidelity configurations generally matched or exceeded three-fidelity counterparts at equivalent computational cost. Among the methods evaluated, multifidelity GP provided the most robust performance across input configurations, achieving excellent metrics for both time to ONC and temperature after ONC, while neural network approaches achieved comparable accuracy with substantially lower training times.