Topology-aware Conv1D–LSTM for Streamflow simulating: Integrating Hodge Laplacian Features with Deep Sequential Learning

Reliable hydrological forecasting remains a central challenge in water resources management due to the nonlinear dynamics of rainfall–runoff processes and the complex spatial structure of river networks. While deep learning methods such as long short-term memory (LSTM) and convolutional neural networks (CNNs) have improved predictive capability by extracting sequential and local patterns, most existing models fail to explicitly account for the topological connectivity of catchments. To address this gap, novel hybrid framework that integrates Conv1D layers for local spatiotemporal feature extraction proposed, LSTM layers for long-term memory retention, and algebraic-topological descriptors derived from Hodge Laplacian decomposition to encode higher-order graph-based connectivity of the river network. The model was evaluated using rainfall and discharge records from a five-station basin in southwest Iran, with systematic comparison against conventional Conv1D–LSTM and standalone deep learning architectures. Results indicate that the Conv1D–LSTM–Hodge model achieves consistent improvements in accuracy, yielding RMSE = 0.74, MAE = 0.56, NSE = 0.89, and R² = 0.91, outperforming the baseline Conv1D–LSTM (RMSE = 0.95, NSE = 0.82, R² = 0.85). At lower to moderate flows, the model reproduces the hydrograph with minimal bias, while at high extremes it slightly underestimates peak discharges, consistent with the statistical difficulty of rare-event prediction. Importantly, the inclusion of Hodge features reduces scatter in mid-to-high discharge regimes by encoding gradient- and cycle-based flow structures, thereby enhancing both predictive reliability and structural consistency. Ensemble diagnostics (standard deviation = 0.98, variance = 0.96, range = 7.09, skewness = 0.12, kurtosis = 0.07, entropy = 5.86, CV ≈ 50) confirm robust uncertainty representation without excessive heavy tails, ensuring balanced forecasts. Beyond accuracy, the proposed model advances interpretability by linking algebraic topology with deep learning, bridging physical plausibility and statistical precision. These findings position the Conv1D–LSTM–Hodge framework as a promising data-driven tool for flood forecasting, reservoir operation, and drought preparedness, with broader implications for embedding graph-theoretic insights into hydrological machine learning.