HydEquivNet

Abstract

Traditional data-driven Deep Learning (DL) hydrological models often suffer from poor physical consistency and weak extrapolation robustness. To address this, we propose HydEquivNet (HEN), a novel architecture that introduces Lie group equivariance into hydrological modeling. By employing steerable Hermite basis convolutions, HEN embeds scale-equivariant physical priors into feature extraction, drawing on classical unit hydrograph theory and mass-consistency considerations to form learnable routing priors. The model utilizes a hybrid structure, integrating equivariant layers for physical feature extraction with Long Short-Term Memory (LSTM) networks for nonlinear residual compensation. Extensive validation on 531 Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) catchments shows that HEN achieves a median Nash-Sutcliffe Efficiency (NSE) of 0.724 and avoids negative NSE values in the evaluated catchments. Controlled precipitation-scaling experiments further indicate improved equivariance-guided proportional-response robustness under synthetic out-of-distribution input amplification. Furthermore, model-derived routing diagnostics show interpretable unit-hydrograph-like response patterns, including a 0.94 bin-averaged correlation between extracted Peak Lag Time (Tp) and a physically motivated concentration-time factor (CTF). HEN thus offers a parameter-efficient and transparent route toward more physically informed rainfall-runoff modeling under changing hydroclimatic conditions.