This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open AccessArticle Investigating Machine Learning Surrogates for the Design of a Solar Thermal DHW System with a Heat Pump Auxiliary 1 Department of Mechanical Engineering and Aeronautics, University of Patras, 26504 Rio, Greece 2 Department of Mechanical Engineering, University of Western Macedonia, 50132 Kozani, Greece 3 School of Mechanical Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 4 Department of Electrical and Computer Engineering, University of Western Macedonia, 50132 Kozani, Greece * Author to whom correspondence should be addressed. Energies 2026, 19(12), 2740; https://doi.org/10.3390/en19122740 (registering DOI) Submission received: 27 April 2026 / Revised: 3 June 2026 / Accepted: 5 June 2026 / Published: 6 June 2026 Accurate design and performance assessment of solar thermal domestic hot water systems coupled with a heat pump auxiliary typically requires transient simulation, as the system’s behavior depends on multiple interactions among collector characteristics, storage stratification, control logic, weather, and draw-off timing. Monthly methods such as the f-chart are useful for first-pass estimates, but they do not resolve stratification, thermostat operation, or demand timing, and they may become inaccurate for stratified thermostat-controlled systems. Direct comparisons of locally inspectable symbolic and black-box surrogate families for this system class remain limited. A 10,982-case development dataset was generated from minute-resolved annual MATLAB simulations, parameterized by collector area, optical efficiency, and first- and second-order loss coefficients. Three surrogate families were benchmarked under a unified protocol, random forest-assisted shape-constrained symbolic regression (SR), feed-forward artificial neural network (ANN) models, and Automatic Learning of Algebraic Models for Optimization (ALAMO), with the f-chart used as a monthly reference method. The targets were the 12 monthly solar fractions under the direct solar heat definition and the corresponding annual mean solar fraction, evaluated on the same independent 991-case test set. SR achieved the lowest average error (mean absolute percentage error, MAPE = 0.82%; root mean square error, RMSE = 0.006), followed by the ANN (MAPE = 2.07%, RMSE = 0.028) and ALAMO (MAPE = 3.67%, RMSE = 0.060), with Nash–Sutcliffe efficiency (NSE) values above 0.98 for all models. Evaluation times were 0.0026–0.124 s per target, compared with about 1000 s for one full-year simulation. These results define the study as a common protocol benchmark within the studied simulator-defined envelope. SR gives the strongest accuracy with local symbolic inspectability, the ANN remains the flexible retrainable option, and ALAMO provides compact algebraic evaluation with the shortest learned model runtime. Keywords: Share and Cite MDPI and ACS Style Sourgoutsidis, M.; Zouloumis, L.; Kilis, V.; Giama, E.; Vouros, A.P.; Souliotis, M.; Ploskas, N.; Panaras, G. Investigating Machine Learning Surrogates for the Design of a Solar Thermal DHW System with a Heat Pump Auxiliary. Energies 2026, 19, 2740. https://doi.org/10.3390/en19122740 AMA Style Sourgoutsidis M, Zouloumis L, Kilis V, Giama E, Vouros AP, Souliotis M, Ploskas N, Panaras G. Investigating Machine Learning Surrogates for the Design of a Solar Thermal DHW System with a Heat Pump Auxiliary. Energies. 2026; 19(12):2740. https://doi.org/10.3390/en19122740 Chicago/Turabian Style Sourgoutsidis, Michalis, Leonidas Zouloumis, Vasileios Kilis, Effrosyni Giama, Andreas P. Vouros, Manolis Souliotis, Nikolaos Ploskas, and Giorgos Panaras. 2026. "Investigating Machine Learning Surrogates for the Design of a Solar Thermal DHW System with a Heat Pump Auxiliary" Energies 19, no. 12: 2740. https://doi.org/10.3390/en19122740 APA Style Sourgoutsidis, M., Zouloumis, L., Kilis, V., Giama, E., Vouros, A. P., Souliotis, M., Ploskas, N., & Panaras, G. (2026). Investigating Machine Learning Surrogates for the Design of a Solar Thermal DHW System with a Heat Pump Auxiliary. Energies, 19(12), 2740. https://doi.org/10.3390/en19122740 Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here. Article Metrics Article metric data becomes available approximately 24 hours after publication online.
Investigating Machine Learning Surrogates for the Design of a Solar Thermal DHW System with a Heat Pump Auxiliary
