A physically constrained proxy framework considering a process-aware gating mechanism for urban flood simulation

Urban pluvial flooding is driven by complex interactions between drainage overflows, rainfall patterns, and multi-scale hydrological memory. Existing data-driven surrogate models often rely on instantaneous forcing, failing to capture the cumulative effects and non-stationary peak evolution of floods. This paper proposes a process-aware and physically-constrained surrogate framework for 2D urban surface inundation emulation. The framework integrates 1D drainage overflows from SWMM as dynamic source-term forcing. The core PG-CNN-LNN model surrogates computationally intensive 2D shallow water equations (2D-SWEs) to predict grid-scale water depth and flow velocity. To transcend traditional instantaneous inputs, we construct a suite of hydrological process indicators-including cumulative overflow, rainfall fluctuation intensity, and time-to-peak scales-to explicitly characterize hydrological memory and event-stage transitions. At the architectural level, the model utilizes Closed-form Continuous-time (CfC) dynamics, transforming Liquid Neural Network (LNN) state evolution into an analytical solution. This resolves numerical instability (stiffness) common in flood emergency simulations. A process-aware gating mechanism enables adaptive spatio-temporal decoupling of multi-source overflows, aligning model representations with physical stages. Furthermore, a negative water depth penalty is embedded in the loss function to ensure physical consistency under extreme conditions. The research results show that the predictive performance of PG-CNN-LNN is significantly superior to the benchmark model: in different geographical environment study areas, its R² values for water depth and flow velocity exceed 0.98 and 0.92 respectively. Compared with the baseline model (LSTM), the average absolute error (MAE) of water depth and flow velocity was reduced by at least 50.0% and 28.6% respectively, which fully validates the excellent accuracy and robustness of this framework. The explainability analysis further indicates that the model's predictions are mainly driven by cumulative rainfall, cumulative overflow, local rainfall variability and historical overflow trajectories; within the liquid neural network, long-term memory dominates (approximately 86 %), consistent with the physical understanding of the slow-changing water accumulation process after the flood peak; the physical constraint reduces the significant negative water depth violation rate from 34.8 % to 0.49 %. This research provides an efficient, robust, and physically traceable technical pathway for real-time urban flood forecasting in complex environments.