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

Aidan Furlong; Vinicius de Melo Monteiro; Robert Salko; Juliana Pacheco Duarte; Xu Wu

cs.LGSep 18, 2026

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

Authors: Aidan Furlong, Vinicius de Melo Monteiro, Robert Salko, Juliana Pacheco Duarte, Xu Wu

Organizations: Department of Nuclear Engineering, North Carolina State University, Burlington Engineering Laboratories, 2500 Stinson Drive, Raleigh, NC 27695 · Nuclear Engineering & Engineering Physics Department, University of Wisconsin–Madison, Engineering Research Building, 1500 Engineering Drive, Madison, WI 53711 · Nuclear Energy and Fuel Cycle Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830

Abstract

The prediction of critical heat flux (CHF), a key safety-related quantity in nuclear thermal hydraulics, remains an important challenge due to its direct relationship with fuel performance and reactor safety. Recent studies have demonstrated that relative to traditional empirical correlations and lookup tables (LUTs), machine learning (ML) methods can substantially improve CHF prediction accuracy. Most ML-based CHF models, however, have been developed and evaluated using tube databases, leaving their applicability to reactor-relevant rod bundle geometries largely unexplored. This study evaluates ML-based CHF models deployed within the CTF subchannel code using the Electric Power Research Institute (EPRI) rod bundle CHF database. Both pure and hybrid residual correction models are considered in local and semilocal formulations. The tube-trained ML CHF models generally transferred favorably to rod bundle applications and outperformed traditional CHF methods across most geometries and operating conditions. The local hybrid LUT model produced the strongest overall performance, and the semilocal pure ML model remained highly competitive. Comparison against the Bowring correlation, W-3 correlation, and 2006 Groeneveld LUT demonstrated that substantial improvements in rod bundle CHF prediction are possible even when models are trained exclusively on tube data. These findings provide one of the first large-scale assessments of ML-based CHF models in square rod bundles within a production-level subchannel analysis environment and support their broader application in reactor thermal hydraulic analysis.

Figures & tables

Panel of Figure 1 — Figure 1: Bundle characteristics across vendors in the EPRI square lattice subset. WH = Westinghouse Electric Co., GE = General Electric Co., IN = Idaho National Engineering Laboratories, CE = Combustion Engineering Inc., EX = Exxon Nuclear Co., BW = Babcock & Wilcox Co., UN = United Nuclear Corp.

Figure 2: Deployment configuration of a hybrid residual learning ML model.

Method	$\upmu_{\textbf{error}}$ (%)	$\textbf{Med}_{\textbf{error}}$ (%)	$\textbf{Std}_{\textbf{error}}$ (%)	$F_{\epsilon>10\%}$ (%)	$F_{\epsilon>25\%}$ (%)
Traditional methods
Bowring	100.48	32.51	211.38	80.08	57.04
LUT	20.04	11.86	30.20	55.56	21.98
ML-based, local
Pure ML	13.77 $\pm$ 0.48	7.61 $\pm$ 0.32	24.53 $\pm$ 1.06	40.45 $\pm$ 1.34	13.27 $\pm$ 0.64
Hybrid Bowring	14.65 $\pm$ 0.63	7.71 $\pm$ 0.35	28.18 $\pm$ 1.62	41.29 $\pm$ 1.30	14.54 $\pm$ 0.90

Table 1: Test set performance on the NRC tube database. Values for ML-based methods denote the ensemble mean and associated 95% CI across 20 independent training realizations. The W-3 correlation was excluded due to its limited range of validity.

Figure 3: Tube-based CTF models performance on held-out NRC tube database as simulated in CTF. Models are labeled using their CTF identifier values: 1x0 = pure ML, 4x0 = hybrid Bowring, 5x0 = hybrid LUT. Hybrid Biasi model not included due to an open issue on CTF’s Biasi correlation.

Category	Setting/value
CTF version	v4.2-rc7
Flow regime map	Legacy void-based map [ 29 ]
Pressure matrix solver	Direct Gaussian elimination
Thermophysical properties	IAPWS-IF97 steam tables [ 36 ]
Single-phase turbulent mixing †	Rogers and Rosehart correlation [ 27 ]
Two-phase turbulent mixing	Beus multiplier $\Theta=5.0$ [ 2 ]

Table 2: Summary of the CTF baseline modeling configuration used for the rod bundle simulations [ 25 ] .

Panel of Figure 4 — Figure 4: Sensitivity of CTF simulation DNBR and channel equilibrium quality values to choice of $\beta_{\mathrm{SP}}$ in a representative CE $5\times 5$ geometry using the Groeneveld LUT as the CHF model [ 8 ] . The calibrated value for the shown testbed is 0.0044 [ 32 ] .

Figure 5: Marginal distributions of key input features in tube (training) and rod bundle (testing) datasets, measured with respect to the experimental CHF locations.

Metric	Local	Semilocal
Domain coverage
Min–max coverage (%)	67.0	67.0
Convex hull coverage (%)	48.7	35.6
Bundle-to-training distances
Median distance	0.692	0.845
95th percentile distance	2.125	2.234

Table 3: Comparison of rod bundle deployment domain states to the tube training domain for the local and semilocal feature formulations. Min–max coverage denotes the fraction of bundle states lying within the tube training bounds for all inputs simultaneously. Convex hull coverage denotes the fraction of bundle states residing within the multivariate tube training domain estimated using a Delaunay triangulation of a subset of tube observations. Nearest-neighbor distances were computed in tube-standardized feature space.

Method	$\upmu_{\textbf{error}}$ (%)	$\textbf{Med}_{\textbf{error}}$ (%)	$\textbf{Std}_{\textbf{error}}$ (%)	$F_{\epsilon>10\%}$ (%)	$F_{\epsilon>25\%}$ (%)
Traditional methods
W-3	31.69	24.50	36.34	79.40	48.96
Bowring	54.09	36.89	68.66	86.04	64.57
LUT	28.63	23.47	36.57	80.24	45.71
ML-based, local
Pure ML	25.86	20.24	30.65	75.16	38.70

Table 4: Aggregate CHF predictive performance on the entire square rod bundle evaluation dataset, organized by CHF model type. Grey cells denote those with the most favorable error metrics.

Figure 6: Tube-based CTF model performance on the EPRI square bundle database subset as simulated in CTF. Models are labeled using their CTF identifier values: 1x0 = pure ML, 4x0 = hybrid Bowring, 5x0 = hybrid LUT.

Figure 7: Visualization of the CHF models’ signed relative error distributions.

Method	$\mathbf{3\times 3}$	$\mathbf{4\times 4}$	$\mathbf{5\times 5}$
	$n=176$	$n=2291$	$n=2396$
Traditional methods
W-3	29.05 / 56.82	24.55 / 51.42	22.08 / 46.04
Bowring	40.87 / 71.02	38.28 / 68.79	30.46 / 60.06
LUT	25.55 / 52.27	25.42 / 53.56	19.84 / 37.73
ML-based, local

Table 5: CHF predictive performance by bundle geometry. Entries are reported as

\text{Med}_{\text{error}}

(%) /

F_{\epsilon>25\%}

(%).

Figure 8: Visualization of the CHF models’ performance by lattice size.

Method	Uniform	Nonuniform
	$n=3396$	$n=1467$
Traditional methods
W-3	21.40 / 45.64	27.94 / 56.65
Bowring	33.07 / 64.69	37.90 / 64.28
LUT	21.44 / 43.55	25.00 / 50.72
ML-based, local

Table 6: CHF predictive performance by axial power shapes. Entries are reported as

\text{Med}_{\text{error}}

(%) /

F_{\epsilon>25\%}

(%). Two nonuniform column entries are highlighted, as they each have one of two metrics outperforming all other models.

Figure 9: Visualization of the CHF models’ performance by axial power profile.

Panel of Figure 10 — Figure 10: Traditional model baselines compared to the best local (hybrid LUT) and semilocal (pure) ML-based models across local thermal hydraulic conditions at the experimental CHF locations. The curves indicate median relative error values in each method’s 12 statistical bins, with the actual points behind.

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Learning Complex Physical Regimes via Coverage-oriented Uncertainty Quantification: An application to the Critical Heat Flux

Michele Cazzola, Alberto Ghione, Lucia Sargentini, Julien Nespoulous+1

Université Paris Saclay, Cea, Service Thermo-hydraulique et Mécanique des Fluides (Stmf), Gif-sur-Yvette, F-91191, France · Université Paris Saclay, Cea, Service de Génie Logiciel pour la Simulation (Sgls), Gif-sur-Yvette, F-91191, France

Uncertainty Quantification Heteroscedastic Regression Conformal Prediction

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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.

Abstract

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