Intelligent Modeling of Critical Heat Flux via Interpretable Symbolic Regression

Critical heat flux (CHF) is an important thermal-hydraulic parameter for the design and safety analysis of water-cooled nuclear reactors. For departure from nucleate boiling (DNB)-type CHF, an accurate prediction model is needed to evaluate heat transfer limits and maintain adequate thermal margin. Empirical CHF correlations have been widely used in engineering applications, but their accuracy is often limited by the experimental range from which they are derived. Data-driven methods can describe complex nonlinear relationships between thermal-hydraulic parameters and CHF, but many deep learning models provide limited information on the mathematical form of the learned relationship. This lack of transparency makes it difficult to examine the physical consistency of the model and restricts its use in safety-related analysis. This study aims to develop an interpretable data-driven modeling method for DNB-type CHF prediction by combining the nonlinear approximation ability of the Kolmogorov-Arnold network (KAN) with symbolic regression. A publicly available uniformly heated round-tube CHF database was used in this study. The input variables included major thermal-hydraulic and geometric parameters associated with DNB-type CHF, such as pressure, mass flux, tube diameter, inlet subcooling, and equilibrium quality. Before model development, the database was preprocessed to remove abnormal samples and to ensure consistency of variable formats. Feature importance analysis was then carried out to identify the dominant input parameters and reduce variable redundancy. Based on the selected feature set, a KAN model was constructed to predict CHF from the input parameters. To evaluate its predictive performance, multilayer perceptron, long short-term memory network, and Transformer models were also established as comparison models. All models were trained and tested using the same data partition and evaluation procedure. After the KAN model was trained, symbolic regression was applied to the learned univariate functions in the KAN structure. Candidate symbolic expressions were selected according to prediction accuracy, structural simplicity, and numerical stability. The selected functions were further combined to obtain an explicit algebraic expression for CHF prediction. The results show that feature importance analysis reduces input redundancy while retaining the main information required for CHF prediction. The KAN model gives lower prediction errors than the comparison models under the same dataset and evaluation conditions. It also shows better performance on test samples, indicating that the KAN structure is suitable for representing the nonlinear dependence of CHF on key thermal-hydraulic parameters. In addition to prediction accuracy, the main advantage of the proposed method lies in its ability to provide an explicit mathematical expression. The extracted expression preserves the major predictive capability of the trained KAN model and presents the CHF relationship in a form that is easier to inspect, implement, and compare with existing empirical correlations. This study shows that KAN combined with symbolic regression can be used as an interpretable modeling tool for CHF prediction. Compared with conventional black-box deep learning models, the proposed method provides both numerical prediction results and a readable algebraic correlation. This approach offers a practical way to improve the transparency of data-driven CHF models and can support the development of interpretable thermal-hydraulic prediction methods for nuclear reactor engineering.