Liquid Time-Constant Networks for Water Level Forecasting in Urban Drainage: Adaptive Time-Scale Modeling of Hydrological Dynamics

Abstract

Liquid Time-Constant networks (LNNs), recurrent models with adaptive, input-dependent time constants, were evaluated for water level prediction in an urban drainage system. The architecture was assessed on a ten-year measurement dataset from the Bellinge catchment and benchmarked against gated recurrent unit (GRU), long short-term memory (LSTM), temporal convolutional network (TCN), and multilayer perceptron (MLP) baselines. The best-performing LNN variant achieved the highest mean predictive accuracy in the benchmark (Nash–Sutcliffe efficiency, NSE = 0.849), with particularly accurate representation of the continuous response of the gravity-driven part of the network without substantial degradation during flash-flood events. The analysis showed that the adaptive time constants help distinguish system-wide hydraulic processes from local control actions while providing interpretable diagnostics of the model’s internal response scale. The principal challenge for the LNN was the intermittent operation of the pumping station; isolating the pump pathway in the dual-branch DB-LNN variant mitigated this performance degradation while preserving predictive accuracy at the remaining sensors. The ablation analysis indicated that architectural separation of the processing pathways reduced interference between the continuous hydraulic dynamics and the local switching dynamics of the threshold-controlled facility.