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.