Machine Learning CHF Models Trained on Tubes Work in Rod Bundles, and That Matters for Nuclear Safety
Critical heat flux is the point where heat transfer in a boiling system rapidly deteriorates. In a nuclear reactor, which operates under heat-flux-controlled conditions, crossing this threshold causes cladding temperature to spike and fuel safety margins to vanish. Many operating reactors are ultimately limited by CHF, and it affects both their operational flexibility and fuel utilization. Predicting CHF accurately is therefore not an academic exercise. It is a safety requirement that directly constrains how hard you can push a reactor.
The prediction problem has been studied for over half a century. The traditional approach relies on empirical correlations and lookup tables (LUTs) developed from experimental measurements. Most of those measurements come from uniformly heated tubes, which are the simplest geometry to instrument and control. The Biasi correlation, the Bowring correlation, and the 2006 Groeneveld LUT are the workhorses of the field. But reactor fuel assemblies are not tubes. They are rod bundles, and rod bundles introduce additional physics: turbulent mixing between subchannels, crossflow, spacer grid effects, and nonuniform radial power distributions. A method trained on tube data is not guaranteed to work in a bundle, and the degree to which it does has been an open question.
Recent work has shown that machine learning methods can substantially improve CHF prediction accuracy on tube databases. Deep neural networks, tree-based models, ensemble methods, and hybrid physics-informed approaches all beat the traditional correlations on held-out tube test sets. But almost all of that work stays within the tube geometry. The paper by Furlong, Monteiro, Salko, Duarte, and Wu from North Carolina State University, University of Wisconsin-Madison, and Oak Ridge National Laboratory asks what happens when you take those tube-trained models and deploy them in rod bundles inside a production subchannel analysis code.
What the Models Are and How They Are Deployed
Six ML-based CHF models are included in the current CTF subchannel code distribution. They come in two flavors: pure ML and hybrid residual correction. The pure ML models are deep neural networks trained to predict CHF directly from input features. The hybrid models couple an established CHF methodology (Bowring correlation or Groeneveld LUT) with an ML correction term that learns the residual between the base prediction and the experimental value. The hybrid approach is attractive because it simplifies what the ML component must learn and provides a physically interpretable prediction process.
Each flavor comes in two input feature formulations. The semilocal formulation uses diameter, heated length, pressure, mass flux, and equilibrium quality at the evaluation point. The fully local formulation drops heated length, using only diameter, pressure, mass flux, and equilibrium quality. The local formulation avoids dependencies on experimental assumptions like uniform heating or inlet conditions, which makes it theoretically more transferable between geometries, but it also loses upstream information that influences CHF. The inlet condition-based formulation, which depends entirely on tube inlet parameters, is excluded because its strong dependence on tube-specific inlet-outlet relationships is not expected to hold in rod bundle subchannels.
All models were trained on the NRC public CHF database, which contains 24,320 tube measurements after cleaning. The training data were shuffled, split 90/5/5 into training, validation, and testing, and standardized. Each model configuration was trained 20 times with different random initializations to establish confidence intervals. The final models were frozen, exported, and loaded into CTF v4.2-rc7 using a TensorFlow-Fortran bridge.
The evaluation uses the EPRI rod bundle CHF database, one of the largest publicly available rod bundle datasets with 11,077 measurements from 235 test sections. The study focuses on the square lattice subset: 3x3, 4x4, and 5x5 bundles, covering 4,935 cases. Of these, 72 (about 1.5%) failed CTF convergence, concentrated in the low mass flux regime below 500 kg/m2/s where subchannel solvers are known to struggle. All nine methods (three traditional plus six ML) are evaluated over the identical 4,863 converged cases, so any performance difference reflects the CHF formulation itself.
The Domain Shift Is Real but Manageable
Before looking at prediction accuracy, the paper quantifies how different the rod bundle deployment domain is from the tube training domain. This is the central tension: can a model trained on one geometry generalize to another?
The min-max coverage, measuring the fraction of rod bundle states that fall within the tube training bounds for all input variables simultaneously, is 67.0% for both formulations. But min-max coverage is a loose metric. The convex hull coverage, which measures the fraction of rod bundle states inside the multivariate tube training domain estimated by Delaunay triangulation, drops to 48.7% for the local formulation and 35.6% for the semilocal formulation. Many rod bundle conditions occupy combinations of variables not represented in the tube training data, even though each individual variable stays within the tube range.
The nearest-neighbor distances make this concrete. In the standardized feature space, the median distance from a rod bundle state to its nearest tube training sample is 0.692 for the local formulation and 0.845 for the semilocal formulation. The median distance between tube training points is only 0.024 and 0.033, respectively. Rod bundle states are roughly 30 times farther from the training data than tube points are from each other. The dominant contributor is heated equivalent diameter, which accounts for 48% of the average squared bundle-to-training distance. About 33% of rod bundle states exceed the maximum diameter in the tube training data. This is not purely a statistical artifact: the physical meaning of heated equivalent diameter changes between the two geometries. In a tube it equals the tube diameter; in a rod bundle it characterizes the subchannel geometry.
Adding heated length to the semilocal formulation reduces overlap further. The convex hull coverage drops from 48.7% to 35.6%, and all distance metrics increase. Heated length introduces an additional source of distributional shift despite all rod bundle states remaining within the tube heated length range.
Tube-Trained Models Outperform Traditional Methods
Despite the domain shift, the tube-trained ML models generally transfer favorably to rod bundles and outperform traditional CHF methods across most geometries and operating conditions. The aggregate results on all 4,863 square rod bundle cases:
- Local hybrid LUT: median error 15.46%, fraction above 25% error 29.10%
- Semilocal pure ML: median error 18.33%, mean error 21.78% (lowest of any method)
- Groeneveld LUT: median error 23.47%, fraction above 25% error 45.71%
- W-3 correlation: median error 24.50%, fraction above 25% error 48.96%
- Bowring correlation: median error 36.89%, fraction above 25% error 64.57%
The local hybrid LUT achieves approximately a 34% reduction in median error and a 36% reduction in the fraction of predictions exceeding 25% error compared to the Groeneveld LUT. The semilocal pure ML model has the lowest mean error and the lowest error standard deviation (25.14%) and remains highly competitive across all other metrics.
Hybrid modeling does not universally improve performance. The local hybrid Bowring model retains much of the error behavior of the underlying Bowring correlation and is the only ML-based model that does not consistently outperform traditional methods. The semilocal hybrid LUT is noticeably worse than its pure ML counterpart. The effectiveness of residual learning depends on both the base model quality and the feature formulation.
All methods exhibit negative median relative errors, indicating systematic underprediction of CHF. The local hybrid LUT shows the smallest bias, with the most balanced distribution of positive and negative error values. Underprediction is conservative from a safety perspective (the real CHF is higher than predicted, so the safety margin is larger than calculated), but systematic bias complicates uncertainty quantification.
Performance Breaks Down by Geometry and Operating Condition
No single model is uniformly dominant across all bundle geometries. On the 3x3 bundles (176 cases), the local hybrid LUT wins with a median error of 18.19% versus 25.55% for the Groeneveld LUT. On the 4x4 bundles (2,291 cases), the local hybrid LUT dominates at 13.40% median error versus 25.42% for the LUT, with the fraction above 25% error dropping from 53.56% to 21.65%. On the 5x5 bundles (2,396 cases), the semilocal pure ML model takes the lead at 15.35% median error versus 19.84% for the LUT.
Under nonuniform axial power profiles, most ML-based models maintain similar or improved performance compared to uniform heating, while traditional methods generally exhibit larger errors. The local hybrid LUT produces the lowest median error for both uniform (14.62%) and nonuniform (14.91%) conditions. The semilocal hybrid Bowring achieves the lowest median error under nonuniform conditions at 14.63%, a narrow margin over the local hybrid LUT.
Examining performance across operating condition bins, the local hybrid LUT keeps median errors within 10% across nearly all bins of equilibrium quality, mass flux, pressure, and coolant temperature. The Bowring correlation is highly sensitive to all four variables, with error increasing at both ends of each range. The W-3 correlation drifts toward more negative relative error at higher mass fluxes, pressures, and temperatures. Both ML-based models generally avoid the pronounced degradation at operational ranges' extrema that plagues traditional methods.
The Turbulent Mixing Question
A practical complication in subchannel CHF analysis is the choice of turbulent mixing coefficient. The EPRI report recommends a constant value of 0.02 for all bundle geometries, but this value was obtained by calibrating against a specific CHF correlation. The sensitivity is significant: varying the single-phase mixing coefficient causes the departure from nucleate boiling ratio to vary by more than 45%, with subchannel enthalpy gain varying by up to 60% and local mass flux by up to 30%.
The authors adopt the Rogers and Rosehart correlation for single-phase turbulent mixing with the Beus two-phase multiplier, a classical experimentally derived model that avoids calibrating the mixing coefficient against CHF prediction performance. This choice does not uniquely identify the true physical parameter, but it provides a consistent thermal hydraulic treatment that does not bias the CHF method comparison.
What This Means for Nuclear Thermal Hydraulics
The practical finding is that tube-trained ML CHF models can transfer to rod bundle applications without retraining, and they outperform the traditional methods they are compared against. This is not obvious a priori. The domain shift is real: a third of rod bundle states exceed the tube training diameter range, and the multivariate convex hull coverage is below 50%. But the ML models generalize well enough to deliver meaningful improvements.
The local hybrid LUT is the strongest overall performer, combining the physical grounding of the Groeneveld lookup table with an ML correction that reduces both bias and variance. The semilocal pure ML model is the second choice, especially when error standard deviation matters. The Bowring-based hybrid is the weakest ML option and should be avoided.
These findings provide one of the first large-scale assessments of tube-trained ML-based CHF models in square rod bundles within a production-level subchannel analysis environment. The CTF code is used by national laboratories and commercial vendors for fuel performance and safety analysis. Demonstrating that ML models can improve CHF prediction in this setting, without retraining on bundle-specific data, supports their broader application in reactor thermal hydraulic analysis.
The remaining limitation is that the evaluation covers square lattice bundles only. Triangular-pitch configurations, which appear in some operating reactor designs, are present in the EPRI database but excluded from this study. The generalization to those geometries, and to bundles with complex spacer grid designs or significant flow blockage, remains to be tested. But for the standard square fuel assemblies that dominate the current LWR fleet, the tube-to-bundle transfer works, and the improvement over traditional methods is substantial.