Acronymns: Small (S), Medium (M), Intermediate (I), Large (L); Correlation coefficient (CC). Mean squared error (MSE). Nash Sutcliff Efficiency (NSE). Root mean squared error (RMSE). Mean absolute error (MAE). Squared sum of error (SSE).
3.1 Metamodel Purpose
Figure 1 shows that the two main application categories for metamodels are optimisation (48%) and real-time applications (32%), with several examples for both WDSs and UDSs. Metamodels have been also used, although to a lesser extent, for conducting uncertainty analyses, system state estimation, and to complement LFPB surrogates. The last one refers to the use of an RS method (e.g., linear approximations, polynomials, ANNs) to complement an LFPB metamodel by replacing a slow component or fine-tuning the outputs for better accuracy, e.g., surrogating water exchange between sub-catchments with ANNs (Wolfs & Willems, 2017), or correcting the predictions of a hydrodynamic model of wastewater flows (Vojinovic et al., 2003). In all cases, metamodels are used to reduce the computational efforts required for the hydraulic simulation of these complex systems, which may severely compromise the feasibility of the applications.