Metamodel reports details on the computational algorithm (e.g., ANNs, Support Vector Machines) used to replace the original simulator along with further details on its architecture (i.e., deviations from a hidden layer ANN). The type and number of input and output variables are also reported to infer the dimensionality of the SM and the complexity of the RS to approximate. As for the performance, we report the computational speed-up provided by the metamodel and the fidelity to the original simulation, usually approximated with an accuracy metric. These criteria have been identified as the most relevant ones by previous related studies (Broad et al., 2015; Razavi et al., 2012b). Nevertheless, it is possible to consider other factors, such as development time, robustness and explainability. While assessing these criteria may enrich the analysis, they are not employed in most of the surveyed papers, and they are thus not included in this review.
3 Review – Current status of Machine Learning Surrogate Models in Urban Water networks
The analysis of the surveyed papers show an increase in research activity between 2015 and 2020 with approximately two-thirds of the manuscripts published during this period. In terms of application, most of these papers are related to optimisation. For the case study, there is a noticeable difference between WDSs and UDSs since the latter networks lack the use of benchmark cases. Regarding the metamodel, the most popular algorithm is the fully connected ANN; because of this, we report the details of the used metamodel as deviations from a standard, one hidden layer, fully connected ANN, also referred to as simple Multi-layer perceptron (MLP). Table 2 summarizes the extracted information of the reviewed papers arranged in the previously mentioned categories: purpose, case study, and metamodel.