“…However, industrial and environmental applications often deal with complex inputs or outputs, which can be spatial, temporal, spatio-temporal i.e., functional in a more general way. As a motivating real case example, the coastal flood early warning system (FEWS) developed at Gâvres, France (Idier et al 2021) predicts scalar output indicators of flooding (like total flooded area, maximum volume of water entering the territory, maximum water depth at a given location, etc. ), based on inputs which are multiple scalar and time-varying maritime conditions (e.g., mean sea level, tide, atmospheric storm surge, and wave conditions), i.e., multiple time series (that are here sampled regularly over time).…”