2.1 Search methodology
We reviewed journal papers published in the last two decades (2001-2021)
that use MLSMs for WDSs and UDSs. We established two main search
criteria: surrogate modelling and water networks. Since both topics have
a multiplicity of names, each of them was represented by a set of
keywords. For surrogate modelling, the search terms were: “Surrogate
model*”, “Metamodel*”, “Response surface”, “model emulation”, and
“hybrid model”. In the case of water networks, the search terms
referred to both water distribution and drainage systems along with
popular software for their analysis, “Water distribution”, “Water
supply”, “Drinking water”, “Urban drainage”, “Wastewater”,
“Sewer”, “Sewerage”, “EPANET”, “WaterCAD”, “SWMM”, “SOBEK”,
and “Urban water”.
For the search, we employed the SCOPUS database. By intersecting the
search terms, we identified an initial set of 64 papers that were
further filtered to only include ML applications, yielding a total of 31
papers to review. Next, we searched through the citations of the
selected set of papers and other relevant papers in the field (i.e.,
Maier et al., 2014; Maier & Dandy, 2000; Razavi et al., 2012b) for
further references. However, the original set already contained the
cited papers. Therefore, the results are equivalent to the keyword
search. This validates the thoroughness of the original search and makes
the methodology more replicable by avoiding arbitrarily selected papers.
This list of papers may not be totally inclusive since some studies do
not use the formal terminology of surrogate modelling, as indicated by
Razavi et al. (2012b). Nevertheless, the purpose of this paper is to
depict the recent state-of-the-art, identify gaps in knowledge and
propose future research directions. We believe that the selected set of
papers is sufficient to achieve this goal.