Hydraulic informed multi-layer perceptron for estimating discharge coefficient of labyrinth weir

Data science techniques (DST) are the most popular approaches for estimating the discharge coefficient (Cd) of labyrinth weirs (LW). This study proposes a hydraulic-informed multi-layer perceptron (HI-MLP) by incorporating the effects of hydraulic phenomena on Cd, which were previously neglected due to their immeasurability. The HI-MLP is not a black box and selects its internal parameters considering the nape behavior attributes. HI-MLP is trained using Levenberg–Marquardt and Genetic algorithms, resulting in HI-MLP-LM and HI-MLP-GA, which are compared against adaptive neuro-fuzzy inference systems (ANFIS), support vector regression (SVR), and standard MLP. Evaluating the models through randomly selected testing data shows that HI-MLP-GA is the most accurate, with an MAEP of 0.732%, while all techniques also had acceptable performances. Conversely, when estimating Cd for LWs with excluded intermediate and extrapolated geometries, only HI-MLP-LM and HI-MLP-GA could predict accurate values with average MAEP of 1.94% and 0.62%, respectively. This value in ANFIS and SVR was equivalent to 27.01% and 6.47%, respectively. Furthermore, hydraulic-informed techniques could be trained with at least a 25% smaller dataset, while the robustness analysis indicated that they are less prone to overfitting. HI-MLP-GA has the highest computational effort and is almost five times slower than HI-MLP-LM. Nevertheless, due to the disappearance of the vanishing gradient and considering the higher generalizability of HI-MLP-GA, GA is still a more desirable learning algorithm than LM.