**4. Conclusions**

For the purpose of proposing accurate data-driven methods for the flow regime classification in PHP systems, three different machine learning algorithms were tested on experimental data from a PHP device, for two different working fluids (namely, ethanol and FC-72). Both datasets were labeled with their corresponding flow regimes, and the most relevant input features were identified and embedded into specific groups of dimensionless numbers that accurately captured the physical phenomena. All three classifiers showed good performance, whereby the classification of the ethanol data was more accurate than that of FC-72, indicating that the process of labeling the data may have been more challenging in the latter case. The use of the multilayer perceptron (MLP) exhibited the highest performance for both working fluids, whereas the random forest algorithm presented the lowest accuracy, although all algorithms performed similarly. The prediction results from the most accurate classifiers were used to build a flow pattern map for each working fluid. In both cases, clear thresholds were identified, where the transition from slug/plug to semi-annular flow took place. These bounds were obtained after scaling the values of the modified Bond number with those of surface tension for both working fluids. The use of a trained and an automatic classifier in this context could provide a more accurate and less demanding classification of flow regimes. Considering a larger set of data with heat fluxes and geometrical parameters, since effective bubble accelerations and

velocities would be dependent variables in this case, this method could effectively offer the chance of overcoming the rough use of Bond numbers to predict confined slug/plug flows in PHPs.

Further extensions of this work include the use of more diverse data, which will improve the robustness of the classification algorithms. In addition, the use of unsupervised learning could be a next step and a significant upgrade. In this way, the labeling process would not be needed, and an appropriate algorithm would identify different clusters of data that may correspond with the flow regimes the clusters belong to. Note that the selection of input features is still of great importance, and the use of the modified Weber, Froude, and Bond numbers can be validated from the results of the clustering.

The use of accurate classifiers in this context allows for a more straightforward identification of flow regimes. This enables the correct selection of models to be used for design, simulation, and optimization of PHP systems. Additionally, regression algorithms can be integrated to the current framework to estimate thermal resistance, which would provide a substantial input for estimating the thermal performance of PHP devices. The results can reveal a clear and robust path to define operational regimes in PHP devices. Moreover, the use of more data from other experiments with different geometries, fluids, and materials can provide a useful resource to improve the applicability of classifiers.

**Author Contributions:** Conceptualization, J.L.-F., L.P., M.M. and F.C.; methodology, J.L.-F. and F.C.; software, J.L.-F.; data curation, L.P. and J.L.-F.; writing—original draft preparation, L.P. and J.L.-F.; writing—review and editing, L.P., J.L.-F., M.M. and F.C.; supervision, M.M. and F.C.; funding acquisition, M.M. and F.C. All authors read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EPSRC grant HyHP (EP/P013112/1), the European Space Agency MAP projects TOPDESS and Hexxcell Ltd.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
